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.
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,…
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.…
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…
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…
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.
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…
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.)
Mathematical principles of reinforcement and resistance to change.
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.
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…
Multidrug Resistance: Physiological Principles and Nanomedical Solutions
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
Acceleration of neutrons in a scheme of a tautochronous mathematical pendulum (physical principles)
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)
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,…
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…
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.
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
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…
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…
Photoelectron Spectra of Aqueous Solutions from First Principles
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.
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…
Mathematical, physical and numerical principles essential for models of turbulent mixing
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.
A new mathematical solution for predicting char activation reactions
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.
[3D echocardiography. Mathematical principles and technical realization].
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
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.
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…
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…
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…
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.
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…
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)
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.…
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…
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…
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…
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.
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…
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…
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.
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.
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.
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.
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.
Ab initio identified design principles of solid-solution strengthening in Al.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
A unified electrostatic and cavitation model for first-principles molecular dynamics in solution
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.
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.
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.
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…
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…
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
First principles study of the aggregation of oligo and polythiophene cations in solution
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.
Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification.
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.
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.
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.
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.
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
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…
Facial plastic surgery area acquisition method based on point cloud mathematical model solution.
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.
NASA Astrophysics Data System (ADS)
Baowan, Duangkamon; Thamwattana, Ngamta; Hill, James M.
2007-10-01
A well-known self-assembled hybrid carbon nanostructure is a nanopeapod which may be regarded as the prototype nanocarrier for drug delivery. While the investigation of the packing of C60 molecules inside a carbon nanotube is usually achieved through either experimentation or large scale computation, this paper adopts elementary mechanical principles and classical applied mathematical modeling techniques to formulate explicit analytical criteria and ideal model behavior for such encapsulation. In particular, we employ the Lennard-Jones potential and the continuum approximation to determine three encapsulation mechanisms for a C60 fullerene entering a tube: (i) through the tube open end (head-on), (ii) around the edge of the tube open end, and (iii) through a defect opening on the tube wall. These three encapsulation mechanisms are undertaken for each of the three specific carbon nanotubes (10,10), (16,16), and (20,20). We assume that all configurations are in vacuum and the C60 fullerene is initially at rest. Double integrals are performed to determine the energy of the system and analytical expressions are obtained in terms of hypergeometric functions. Our results suggest that the C60 fullerene is most likely to be encapsulated by head-on through the open tube end and that encapsulation around the tube edge is least likely to occur because of the large van der Waals energy barriers which exist at the tube ends.
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
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
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.
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,…
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.
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.
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.
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.
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.
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.
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…
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…
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.
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.
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.
Alloying Solid Solution Strengthening of Fe-Ga Alloys: A First-Principle Study
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
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.
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.
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…
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…
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…
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.
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.
A first-principles based force-field for Li+ and OH- in ethanolic solution.
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.
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…
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.
Study and numerical solution of a generalized mathematical model of isothermal adsorption
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.
Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling
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
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.
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
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.
First-principle based modeling of urea decomposition kinetics in aqueous solutions
NASA Astrophysics Data System (ADS)
Nicolle, André; Cagnina, Stefania; de Bruin, Theodorus
2016-11-01
This study aims at validating a multi-scale modeling methodology based on an implicit solvent model for urea thermal decomposition pathways in aqueous solutions. The influence of the number of cooperative water molecules on kinetics was highlighted. The obtained kinetic model is able to accurately reproduce urea decomposition in aqueous phase under a variety of experimental conditions from different research groups. The model also highlights the competition between HNCO desorption to gas phase and hydrolysis in aqueous phase, which may influence SCR depollution process operation.
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.
The integration of solution-focused brief therapy principles in nursing: a literature review.
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.
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
Ion Association in AlCl3 Aqueous Solutions from Constrained First-Principles Molecular Dynamics
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.
Solution-based thermodynamic modeling of the Ni-Al-Mo system using first-principles calculations
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.
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.
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(Zn_{1/3}Nb_{2/3})O₃ and Pb(Mg_{1/3}Nb_{2/3})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.
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
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.
Tissue-Engineered Solutions in Plastic and Reconstructive Surgery: Principles and Practice.
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
Tissue-Engineered Solutions in Plastic and Reconstructive Surgery: Principles and Practice
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
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.
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.
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.
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.
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.
Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling
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 Pd_{5}Si-μ, Pd_{9}Si_{2}-α, Pd_{3} Si-β, Pd_{2} 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, Pd_{9} Si_{2}-α, Pd_{3}Si-β, and Pd_{2}Si-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 Pd_{5}Si-μ, Pd_{9}Si_{2}-α, Pd_{3}Si-β, Pd_{2}Si-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.
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.
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.
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.
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
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.
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.
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.
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
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.
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…
The principle of superposition and its application in ground-water hydraulics
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.
A New Principle in Physiscs: the Principle "Finiteness", and Some Consequences
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.
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…
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,…
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…
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.
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.
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.
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.
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.
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.
Mathematical modeling of molecular diffusion through mucus
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
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.
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…
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.
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)
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…
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.
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.
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.
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…
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…
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.
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.
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…
Mathematical modeling in neuroendocrinology.
Bertram, Richard
2015-04-01
Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.
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.
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…
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.
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.
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.
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.
Electronic structures of anatase (TiO2)1-x(TaON)x solid solutions: a first-principles study.
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.
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.
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)
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.
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.
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…
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
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.
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).
Solving Geometry Problems via Mechanical Principles
ERIC Educational Resources Information Center
Man, Yiu Kwong
2004-01-01
The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…
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…
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.)
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…
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…
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.
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…
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.
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…
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…
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…
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…
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…
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…
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…
Compressed modes for variational problems in mathematics and physics.
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.
Compressed modes for variational problems in mathematics and physics
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
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…
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)…
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…
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…
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.
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
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)
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
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…
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,…
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…
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.
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,…
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…
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)
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.
Mathematical modelling for the new millenium: medicine by numbers.
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.
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.
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
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.
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
McClellan, Kathryn T.
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
ERIC Educational Resources Information Center
Martin, Hope
2007-01-01
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…
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.
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.
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.
Enhancing Meaning in Mathematics: Drawing on What Students Know about the Physical World
ERIC Educational Resources Information Center
Marrongelle, Karen A.
2005-01-01
NCTM's Principles and Standards for School Mathematics advises that school mathematics experiences at all levels should include opportunities to learn about mathematics by working on problems arising in contexts outside of mathematics. Students should be given the opportunity to learn mathematics by building on their understandings of how the…
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…
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.…
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…
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)
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.
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…
Mathematical modelling in developmental biology.
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.
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.
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)
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.
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.
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…
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.
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…
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.
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed.
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…
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…
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…
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…
Mathematical methods in systems biology.
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.
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…
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)
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
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
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
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…
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.
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…
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.
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.
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.
Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.
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'.
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'.
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…
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.
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.
Mathematics Worth Teaching, Mathematics Worth Understanding.
ERIC Educational Resources Information Center
Romberg, Thomas A.; Kaput, James J.
This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
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…
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…
Transcranial Electrical Neuromodulation Based on the Reciprocity Principle
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
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…
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…
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…
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…
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
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.
Uses and abuses of mathematics in biology.
May, Robert M
2004-02-06
In the physical sciences, mathematical theory and experimental investigation have always marched together. Mathematics has been less intrusive in the life sciences, possibly because they have until recently been largely descriptive, lacking the invariance principles and fundamental natural constants of physics. Increasingly in recent decades, however, mathematics has become pervasive in biology, taking many different forms: statistics in experimental design; pattern seeking in bioinformatics; models in evolution, ecology, and epidemiology; and much else. I offer an opinionated overview of such uses--and abuses.
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…
Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.
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.
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.
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…
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)
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.
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.
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…
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)
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…
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…
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…
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…
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…
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:…
Mathematics analysis of polymerase chain reaction kinetic curves.
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.
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…
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…
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
ERIC Educational Resources Information Center
Moran, Amber Squire
2011-01-01
The purpose of this study was to examine the effectiveness of a mathematics problem solving intervention strategies for 3rd grade students identified as having a Mathematics Disability and students who are English Learners. The intervention targeted specific proposition within word problems as a means to enhance solution accuracy. Three…
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…
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…
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…
Granularity analysis for mathematical proofs.
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.
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…
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
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.
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.
[Mathematical models of hysteresis
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.
ERIC Educational Resources Information Center
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
ERIC Educational Resources Information Center
Lo, Jane-Jane; And Others
Calls for increased student involvement in mathematics classroom learning situations are due primarily to the recognition that a traditional lecture/demonstration format within school mathematics instruction is not effective in fostering and promoting students' problem-solving abilities, mathematical reasoning power, and mathematical communication…
ERIC Educational Resources Information Center
Ricks, Thomas E.
2010-01-01
Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…
Computer Mathematics: An Introduction.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
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
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…
ERIC Educational Resources Information Center
Prichard, Gerald R.
1995-01-01
Reviews the general principles of the reforms addressed by the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards and applies them to community college mathematics. Suggests that challenges to reforming mathematics curricula come primarily from teacher preparation and instruction methodologies and from student-related…
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…
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…
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…
Hobbes on natural philosophy as "True Physics" and mixed mathematics.
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.
Intuitions, principles and consequences
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
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.
Scattered Radiation Emission Imaging: Principles and Applications
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
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.
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.
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)
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.
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…
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.
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.
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.
Discover Mathematical Knowledge through Recreational Mathematics Problems
ERIC Educational Resources Information Center
Sodhi, Amar
2004-01-01
The way in which a mathematical problem was used as a vehicle to introduce the joy of mathematical research to a high school student is demonstrated. The student was interested in learning about other classical problems delighting an eager high school student.
Mathematics Coursework Regulates Growth in Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; Wilkins, Jesse L. M.
2007-01-01
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Mathematics and Sports. Mathematical World. Volume 3.
ERIC Educational Resources Information Center
Sadovskii, L. E.; Sadovskii, A. L.
This volume contains some examples of mathematical applications in sports. Sports discussed include tennis, figure skating, gymnastics, track and field, soccer, skiing, hockey, and swimming. Problems and situations are posed and answers with thorough explanations are provided. Chapters include: (1) Mathematics and Sports; (2) What Is Applied…
Mathematics for Language, Language for Mathematics
ERIC Educational Resources Information Center
Prochazkova, Lenka Tejkalova
2013-01-01
The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…
Mathematical 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.
Adequate mathematical modelling of environmental processes
NASA Astrophysics Data System (ADS)
Chashechkin, Yu. D.
2012-04-01
In environmental observations and laboratory visualization both large scale flow components like currents, jets, vortices, waves and a fine structure are registered (different examples are given). The conventional mathematical modeling both analytical and numerical is directed mostly on description of energetically important flow components. The role of a fine structures is still remains obscured. A variety of existing models makes it difficult to choose the most adequate and to estimate mutual assessment of their degree of correspondence. The goal of the talk is to give scrutiny analysis of kinematics and dynamics of flows. A difference between the concept of "motion" as transformation of vector space into itself with a distance conservation and the concept of "flow" as displacement and rotation of deformable "fluid particles" is underlined. Basic physical quantities of the flow that are density, momentum, energy (entropy) and admixture concentration are selected as physical parameters defined by the fundamental set which includes differential D'Alembert, Navier-Stokes, Fourier's and/or Fick's equations and closing equation of state. All of them are observable and independent. Calculations of continuous Lie groups shown that only the fundamental set is characterized by the ten-parametric Galilelian groups reflecting based principles of mechanics. Presented analysis demonstrates that conventionally used approximations dramatically change the symmetries of the governing equations sets which leads to their incompatibility or even degeneration. The fundamental set is analyzed taking into account condition of compatibility. A high order of the set indicated on complex structure of complete solutions corresponding to physical structure of real flows. Analytical solutions of a number problems including flows induced by diffusion on topography, generation of the periodic internal waves a compact sources in week-dissipative media as well as numerical solutions of the same
Principlism and communitarianism.
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.
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.
Mathematical and statistical analysis
NASA Technical Reports Server (NTRS)
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Developing My Mathematics Identity
ERIC Educational Resources Information Center
Gonzalez, Lidia
2016-01-01
Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.
Mathematical problem solving by analogy.
Novick, L R; Holyoak, K J
1991-05-01
We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.
Driving Toward Guiding Principles
Buckovich, Suzy A.; Rippen, Helga E.; Rozen, Michael J.
1999-01-01
As health care moves from paper to electronic data collection, providing easier access and dissemination of health information, the development of guiding privacy, confidentiality, and security principles is necessary to help balance the protection of patients' privacy interests against appropriate information access. A comparative review and analysis was done, based on a compilation of privacy, confidentiality, and security principles from many sources. Principles derived from ten identified sources were compared with each of the compiled principles to assess support level, uniformity, and inconsistencies. Of 28 compiled principles, 23 were supported by at least 50 percent of the sources. Technology could address at least 12 of the principles. Notable consistencies among the principles could provide a basis for consensus for further legislative and organizational work. It is imperative that all participants in our health care system work actively toward a viable resolution of this information privacy debate. PMID:10094065
ERIC Educational Resources Information Center
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
ERIC Educational Resources Information Center
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
Defining Mathematical Giftedness
ERIC Educational Resources Information Center
Parish, Linda
2014-01-01
This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…
Mathematics. [SITE 2001 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics"…
Mathematics, Programming, and STEM
ERIC Educational Resources Information Center
Yeh, Andy; Chandra, Vinesh
2015-01-01
Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…
ERIC Educational Resources Information Center
Nisbet, Steven
1991-01-01
The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)
ERIC Educational Resources Information Center
Ortiz-Franco, Luis
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
ERIC Educational Resources Information Center
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major…
Mathematical Discovery: Hadamard Resurected
ERIC Educational Resources Information Center
Liljedahl, Peter
2004-01-01
In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
A "Mathematics Background Check"
ERIC Educational Resources Information Center
Hubisz, John
2009-01-01
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
Mathenger Hunt: Mathematics Matters.
ERIC Educational Resources Information Center
Falba, Christy J.; Weiss, Maria J.
1991-01-01
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
Students' Mathematical Noticing
ERIC Educational Resources Information Center
Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan
2013-01-01
Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…
Mathematics and Global Survival.
ERIC Educational Resources Information Center
Schwartz, Richard H.
This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…
ERIC Educational Resources Information Center
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Modern Versus Traditional Mathematics
ERIC Educational Resources Information Center
Roberts, A. M.
1974-01-01
The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)
The purpose of this book is to familiarize the reader with how mathematics can solve important problems in modern military affairs. The authors discuss and explain, without resorting to complex mathematical calculations, the essence of the basic methods which modern mathematics makes available to military problems, design and combat deployment of modern weapons.
ERIC Educational Resources Information Center
Henson, R.; Stumbles, A.
1977-01-01
The relationship between mathematics and chemistry has been changing rapidly in recent years. Some chemistry teachers have experienced difficulties in their teaching with the introduction of modern mathematics in the schools. Some suggestions for reinforcing the concepts and language of modern mathematics are put forth. (Author/MA)
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination.
ERIC Educational Resources Information Center
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
Special relativity from observer's mathematics point of view
NASA Astrophysics Data System (ADS)
Khots, Boris; Khots, Dmitriy
2015-09-01
When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.
Control principles of complex systems
NASA Astrophysics Data System (ADS)
Liu, Yang-Yu; Barabási, Albert-László
2016-07-01
A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in dynamical systems and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these questions here recent advances on the controllability and the control of complex networks are reviewed, exploring the intricate interplay between the network topology and dynamical laws. The pertinent mathematical results are matched with empirical findings and applications. Uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.
Ten Problems in Experimental Mathematics
Bailey, David H.; Borwein, Jonathan M.; Kapoor, Vishaal; Weisstein, Eric
2004-09-30
This article was stimulated by the recent SIAM ''100 DigitChallenge'' of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a recent book by two of present authors, where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly arise in ''experimental mathematics''. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally one with proof. Our goal in this article is to provide solutions to these ten problems, and in the process present a concise account of how one combines symbolic and numeric computation, which may be termed ''hybrid computation'', in the process of mathematical discovery.
Inferring Mathematical Equations Using Crowdsourcing
Wasik, Szymon
2015-01-01
Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game—so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players. PMID:26713846
Inferring Mathematical Equations Using Crowdsourcing.
Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw
2015-01-01
Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.
NASA Astrophysics Data System (ADS)
Bolmatov, Dima; Bastrukov, S.; Lai, P.-Y.; Molodtsova, I.
2014-07-01
A fundamental task of statistical physics is to predict the system's statistical properties and compare them with observable data. We formulate the theory of dipolaron solutions and analyze the screening effects for permanent and field-induced dipolarons. The mathematical treatment of the collective behavior and microscopical morphology of dipolaron solutions are discussed. The presented computations show that the electric field shielding of dipolarons in dielectric nanosolutions is quite different from that of counterionic nano-complexes of Debye-Hückel theory of electrolytes. The limiting case of screening length λ=0 in dipolaron solutions corresponds to Coulomb's law for the potential and field of uniformly charged sphere.
The History of Mathematics and Mathematical Education
ERIC Educational Resources Information Center
Grattan-Guinness, I.
1977-01-01
Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)
A mathematical model of a cloud
NASA Astrophysics Data System (ADS)
Wang, A. P.
1980-07-01
The model under consideration is a pencil of radiation incident on a cloud, and the problem is to determine the reflection and transmitted radiation. Based on the method of 'principle of invariance', three mathematical models are constructed. The first is the basic model, which describes the radiation system completely. The second is the flux integral model, in which the integral average intensity is considered. The third is the diffusion model, which gives the most important information about the diffused radiation field.
Principles and the Development of Physical Theory: Case Studies
NASA Astrophysics Data System (ADS)
Hovis, Robert Corby
Three separate articles make up the chapters of this dissertation. They were written with different aims and audiences in mind, but each deals in some way with one or more "principles" that have been invoked in argumentation and explanation in the physical sciences. The principles of concern are propositions which have an "aesthetic" or "foundational" or "philosophical" character and which are (or have been) generally believed to be widely applicable or particularly powerful--for example, the Principle of Plenitude, the Principle of Mathematical Beauty, Occam's Razor, the Cosmological Principle, and the Copernican Principle. Chapter 1 provides an overview of the nature and uses of principles in scientific reasoning and examines in some detail the use of the Principle of Plenitude in the introduction of "tachyons" (faster-than-light particles) into theoretical physics during the 1960s. Chapter 2 is a short biography of P. A. M. Dirac (1902-1984), one of the founders of quantum mechanics, who believed that the Principle of Mathematical Beauty should serve as physicists' guide to truth. Chapter 3 traces the history of the idea of faster-than-light particles in physics since the late 1800s; this idea matured with the rise of the subfield of tachyon physics in the 1960s, and (as mentioned above) physicists appealed to the Principle of Plenitude to argue for the existence of the particles, which are still only hypothetical. According to the thesis developed in these chapters, the epistemological status of principles has evolved over the history of science. While they were once hallowed as a priori truths, in modern science they have increasingly been employed critically, in light of the results of scientific inquiry. That is, science has moved toward making principles testable, subject to rejection or revision, on a par with other scientific propositions.
Instructional Software Design Principles.
ERIC Educational Resources Information Center
Hazen, Margret
1985-01-01
Discusses learner/computer interaction, learner control, sequencing of instructional events, and graphic screen design as effective principles for the design of instructional software, including tutorials. (MBR)
Principles of Multiobjective Optimization.
1984-08-01
theory and mathematical pro- gramming; and ( )implicit utility maximization, the name we use for the popular class o methods introduced by Geoffrion, Dyer ...overlooked approach combining multiattribute decision theory and mathematical . programming, and (iii) implicit utility maximization, the name we use...Explicit Utility Functions The explicit utility function approach is to assess an explicit form of U by techniques of multiattribute decision theory (e.g
Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load
ERIC Educational Resources Information Center
Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.
2017-01-01
Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…
Mathematical modeling of moving boundary problems in thermal energy storage
NASA Technical Reports Server (NTRS)
Solomon, A. D.
1980-01-01
The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.
A Case against Computer Symbolic Manipulation in School Mathematics Today.
ERIC Educational Resources Information Center
Waits, Bert K.; Demana, Franklin
1992-01-01
Presented are two reasons discouraging computer symbol manipulation systems use in school mathematics at present: cost for computer laboratories or expensive pocket computers; and impracticality of exact solution representations. Although development with this technology in mathematics education advances, graphing calculators are recommended to…
Teachers of Mathematics as Problem-Solving Applied Mathematicians
ERIC Educational Resources Information Center
Chick, Helen; Stacey, Kaye
2013-01-01
Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…
Teaching Global Issues Through Mathematics. Development Education Paper No. 20.
ERIC Educational Resources Information Center
Schwartz, Richard H.
The document shows how teachers can use mathematics problems to teach fourth, fifth, and sixth grade students about critical global issues. The problems are arranged according to development topics. For each problem, the solution, reference source, and mathematical skills to be strengthened are given; global issues related to each problem are also…
History of Mathematics and Problem Solving: A Teaching Suggestion
ERIC Educational Resources Information Center
Meavilla, V.; Flores, A.
2007-01-01
This note presents a teaching suggestion, using the history of mathematics, to give students from middle school and high school the possibility of facing problems found in old mathematics books and comparing their solutions with those given in those books. (Contains 3 figures and 1 table.)
Using Problem Solving to Assess Young Children's Mathematics Knowledge
ERIC Educational Resources Information Center
Charlesworth, Rosalind; Leali, Shirley A.
2012-01-01
Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…
NASA Astrophysics Data System (ADS)
Cable, John
2013-07-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.
About a mathematical model of market
NASA Astrophysics Data System (ADS)
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Why Are Mathematics Teachers "Not Sure"?
ERIC Educational Resources Information Center
Fauskanger, Janne; Mosvold, Reidar
2016-01-01
Researchers have widely adopted measures of teachers' mathematical knowledge for teaching (MKT). This paper investigates why teachers select "I'm not sure" as a suggested solution in MKT items. In this study, in-service teachers responded to multiple-choice MKT items, they submitted written responses to open-ended questions, and they…
Mathematical model for predicting human vertebral fracture
NASA Technical Reports Server (NTRS)
Benedict, J. V.
1973-01-01
Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.
Assessment Principles and Tools
Golnik, Karl C.
2014-01-01
The goal of ophthalmology residency training is to produce competent ophthalmologists. Competence can only be determined by appropriately assessing resident performance. There are accepted guiding principles that should be applied to competence assessment methods. These principles are enumerated herein and ophthalmology-specific assessment tools that are available are described. PMID:24791100
Teaching the History of Mathematics: A Trial by Fire.
ERIC Educational Resources Information Center
Miller, Cheryl Chute
2002-01-01
Describes teaching a course on the history of mathematics intended for prospective teachers. Presents a brief overview of the course created, difficulties encountered, and some solutions discovered. (Author/KHR)
NASA Technical Reports Server (NTRS)
Zuk, J.
1976-01-01
The fundamental principles governing dynamic sealing operation are discussed. Different seals are described in terms of these principles. Despite the large variety of detailed construction, there appear to be some basic principles, or combinations of basic principles, by which all seals function, these are presented and discussed. Theoretical and practical considerations in the application of these principles are discussed. Advantages, disadvantages, limitations, and application examples of various conventional and special seals are presented. Fundamental equations governing liquid and gas flows in thin film seals, which enable leakage calculations to be made, are also presented. Concept of flow functions, application of Reynolds lubrication equation, and nonlubrication equation flow, friction and wear; and seal lubrication regimes are explained.
The Physical Principles of Magnetism
NASA Astrophysics Data System (ADS)
Morrish, Allan H.
2001-01-01
" The Physical Principles of Magnetism . . . is such a classic a comprehensive introduction to all aspects of magnetism . . . The corrected reissue is a welcome addition to this much-needed archival series. Dr. Morrish presents an excellent introduction to the physics and mathematics of magnetism without oversimplification . . . This respected and timeless book clearly elucidates these principles."" Edward Della Torre, The George Washington University, President of the IEEE Magnetics Society The IEEE Press is pleased to reissue this essential book for understanding the basis of modern magnetic materials. Diamagnetism, paramagnetism, ferromagnetism, ferrimagnetism, and antiferromagnetism are covered in an integrated manner unifying subject matter from physics, chemistry, metallurgy, and engineering. Magnetic phenomena are discussed both from an experimental and theoretical point of view. The underlying physical principles are presented first, followed by macroscopic or microscopic theories. Although quantum mechanical theories are given, a phenomenological approach is emphasized. More than half the book is devoted to a discussion of strongly coupled dipole systems, where the molecular field theory is emphasized. THE PHYSICAL PRINCIPLES OF MAGNETISM is a classic must read for anyone working in the magnetics, electromagnetics, computing, and communications fields. About the Author Allan Henry Morrish is a distinguished professor of physics at the University of Manitoba, Canada. He received a B.Sc. degree from the University of Manitoba in 1943, an M.A. from the University of Toronto in 1946, and a Ph.D. from the University of Chicago in 1949, specializing in nuclear physics. From 1953 to 1964, Dr. Morrish was with the Department of Electrical Engineering at the University of Minnesota at Minneapolis, where he held the rank of professor from 1959. During 1974-1975, Dr. Morrish was president of the Canadian Association of Physicists and in 1977 he was awarded their gold
Principles of Technology. Workshop Presenter's Handbook for Pennsylvania Educators.
ERIC Educational Resources Information Center
Wichowski, Chester P.
This workshop presenter's handbook was developed to provide assistance to those who will serve as Principles of Technology trainers of science, industrial arts/technology education, and mathematics teachers throughout Pennsylvania. The handbook provides trainers with presentation materials, transparency masters, suggested activities, and selected…
THEORETICAL BASIS FOR THE PRINCIPLE OF SINGLE CELLED ALGAE CULTIVATION,
The aim of this study is to provide the basis for a mathematical approach to the principle of cultivating chlorella , which will make possible a...biological and design. The mathe matical basis for the amount of chlorella biomass as a function of the duration of its cultivation is presented.
Conceptual Learning in a Principled Design Problem Solving Environment
ERIC Educational Resources Information Center
Prusak, Naomi; Hershkowitz, Rina; Schwarz, Baruch B.
2013-01-01
To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…
Basic principles in the radiation dosimetry of nuclear medicine.
Stabin, Michael; Xu, Xie George
2014-05-01
The basic principles of the use of radiation dosimetry in nuclear medicine are reviewed. The basic structure of the main mathematical equations are given and formal dosimetry systems are discussed. An extensive overview of the history and current status of anthropomorphic models (phantoms) is given. The sources and magnitudes of uncertainties in calculated internal dose estimates are reviewed.
Early childhood mathematics intervention.
Clements, Douglas H; Sarama, Julie
2011-08-19
Preschool and primary grade children have the capacity to learn substantial mathematics, but many children lack opportunities to do so. Too many children not only start behind their more advantaged peers, but also begin a negative trajectory in mathematics. Interventions designed to facilitate their mathematical learning during ages 3 to 5 years have a strong positive effect on these children's lives for many years thereafter.
Progress in recognizing typeset mathematics
NASA Astrophysics Data System (ADS)
Fateman, Richard J.; Tokuyasu, Taku A.
1996-03-01
Printed mathematics has a number of features which distinguish it from conventional text. These include structure in two dimensions (fractions, exponents, limits), frequent font changes, symbols with variable shape (quotient bars), and substantially differing notational conventions from source to source. When compounded with more generic problems such as noise and merged or broken characters, printed mathematics offers a challenging arena for recognition. Our project was initially driven by the goal of scanning and parsing some 5,000 pages of elaborate mathematics (tables of definite integrals). While our prototype system demonstrates success on translating noise-free typeset equations into Lisp expressions appropriate for further processing, a more semantic top-down approach appears necessary for higher levels of performance. Such an approach may benefit the incorporation of these programs into a more general document processing viewpoint. We intend to release to the public our somewhat refined prototypes as utility programs in the hope that they will be of general use in the construction of custom OCR packages. These utilities are quite fast even as originally prototyped in Lisp, where they may be of particular interest to those working on 'intelligent' optical processing. Some routines have been re-written in C++ as well. Additional programs providing formula recognition and parsing also form a part of this system. It is important however to realize that distinct conflicting grammars are needed to cover variations in contemporary and historical typesetting, and thus a single simple solution is not possible.
Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs
ERIC Educational Resources Information Center
Ollerton, Richard L.
2013-01-01
Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers
ERIC Educational Resources Information Center
Cai, Jinfa; Ding, Meixia
2017-01-01
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…
Mathematics for Teaching: A Form of Applied Mathematics
ERIC Educational Resources Information Center
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Exploring Differential Effects of Mathematics Courses on Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; McIntyre, Laureen J.
2005-01-01
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
Mathematical modeling of drug delivery.
Siepmann, J; Siepmann, F
2008-12-08
Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design
Mathematical Metaphors: Problem Reformulation and Analysis Strategies
NASA Technical Reports Server (NTRS)
Thompson, David E.
2005-01-01
This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.
A Protocol for Evaluating Contextual Design Principles
Stamps, Arthur
2014-01-01
This paper explains how scientific data can be incorporated into urban design decisions, such as evaluating contextual design principles. The recommended protocols are based on the Cochrane Reviews that have been widely used in medical research. The major concepts of a Cochrane Review are explained, as well as the underlying mathematics. The underlying math is meta-analysis. Data are reported for three applications and seven contextual design policies. It is suggested that use of the Cochrane protocols will be of great assistance to planners by providing scientific data that can be used to evaluate the efficacies of contextual design policies prior to implementing those policies. PMID:25431448
Adapting mudharabah principle in Islamic option
NASA Astrophysics Data System (ADS)
Suhaimi, Siti Noor Aini binti; Salleh, Hassilah binti
2013-04-01
Most of the options today use the Black-Scholes model as the basis in valuing their price. This conventional model involves the elements that are strictly prohibited in Islam namely riba, gharar and maisir. Hence, this paper introduces a new mathematical model that has been adapted with mudharabah principle to replace the Black-Scholes model. This new model which is more compatible with Islamic values produces a new Islamic option which avoids any form of oppression and injustice to all parties involved.
The Characteristics of Mathematical Creativity
ERIC Educational Resources Information Center
Sriraman, Bharath
2004-01-01
Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…
Remedial Mathematics for Quantum Chemistry
ERIC Educational Resources Information Center
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.
Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process
ERIC Educational Resources Information Center
Bal, Aytgen Pinar; Doganay, Ahmet
2014-01-01
The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…
ERIC Educational Resources Information Center
Tristanti, Lia Budi; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muskar, Makbul
2016-01-01
This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…
Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools
ERIC Educational Resources Information Center
Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava
2014-01-01
Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…
A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics
ERIC Educational Resources Information Center
Liang, Jiajuan; Pan, William S. Y.
2009-01-01
MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…
Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem
ERIC Educational Resources Information Center
Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova
2017-01-01
The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…
Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice
ERIC Educational Resources Information Center
Voss, Richard; Rickards, Tony
2016-01-01
Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…
Computer-Based Mathematics Instructions for Engineering Students
NASA Technical Reports Server (NTRS)
Khan, Mustaq A.; Wall, Curtiss E.
1996-01-01
Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.
Astronomy and Mathematics Education
NASA Astrophysics Data System (ADS)
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
[Collected Papers on Mathematics.
ERIC Educational Resources Information Center
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student…
The Applied Mathematics Laboratory.
ERIC Educational Resources Information Center
Siegel, Martha J.
This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring…
Mathematics. [SITE 2002 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
Developing Mathematically Promising Students.
ERIC Educational Resources Information Center
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
Learning Together: Mathematics
ERIC Educational Resources Information Center
Her Majesty's Inspectorate of Education, 2010
2010-01-01
This guide is intended to stimulate professional reflection, dialogue and debate about mathematics and how to improve it. It draws together themes, features and characteristics of effective improvement in mathematics and descriptions of good practice. It offers a reference point for staff and teachers who are working together to improve…
ERIC Educational Resources Information Center
Carr, Martha, Ed.
The purpose of this book is to bring together research and theory about motivation for mathematics from different perspectives. Chapters are included that present theory and research on the influence of gender, culture, the classroom environment, and curriculum on children's mathematical performance and motivation. Chapters are: (1) "Sociocultural…
Mathematics across the Curriculum.
ERIC Educational Resources Information Center
Kleiman, Glenn M.
1991-01-01
Except for its relationship to science, mathematics is the forgotten cousin in interdisciplinary teaching and learning. In the Journeys in Mathematics project, teachers engage children in imaginative activities that inspire them to identify patterns and relationships, solve problems, and communicate accurately, using Jonathan Swift's…
Experimenting with Mathematical Biology
ERIC Educational Resources Information Center
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
Mathematics in Power Technology.
ERIC Educational Resources Information Center
Trombley, Carl; And Others
This mathematics curriculum is designed to be taught by the technology education teacher during the power technology class over a period of 2 years. It is intended to be elective in nature; upon successful completion of both years, one-half credit in mathematics is to be awarded. A list of the academic competencies contained in the curriculum…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…
NASA Astrophysics Data System (ADS)
Rohrlich, Fritz
2011-12-01
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
Mathematical thinking and origami
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
ERIC Educational Resources Information Center
Morgan, John L.; Ginther, John L.
1994-01-01
Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)
ERIC Educational Resources Information Center
Sharp, John
2012-01-01
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Teaching Mathematical Modelling.
ERIC Educational Resources Information Center
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Mathematics Education in Argentina
ERIC Educational Resources Information Center
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
ERIC Educational Resources Information Center
Heck, Andre; Van Gastel, Leendert
2006-01-01
Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at…
Elementary Mathematics Leaders
ERIC Educational Resources Information Center
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
ERIC Educational Resources Information Center
Fluellen, Jerry
This paper describes a mathematics-centered thematic unit for 5th graders which organizes all the topics in the Houghton Mifflin Mathematics Program by combining critical thinking and whole language frameworks to help students retain, understand, and make active use of knowledge within and across domains. The unit connects inquiry, goals, critical…
Quality Teaching in Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2012-01-01
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Designing Assessment for Mathematics
ERIC Educational Resources Information Center
Depka, Eileen
2007-01-01
Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…
The Impossible in Mathematics.
ERIC Educational Resources Information Center
Adler, Irving
The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…
Integrating Writing and Mathematics
ERIC Educational Resources Information Center
Wilcox, Brad; Monroe, Eula Ewing
2011-01-01
Teachers often find it difficult to integrate writing and mathematics while honoring the integrity of both disciplines. In this article, the authors present two levels of integration that teachers may use as a starting point. The first level, writing without revision, can be worked into mathematics instruction quickly and readily. The second…
Building Mathematics Vocabulary
ERIC Educational Resources Information Center
Kovarik, Madeline
2010-01-01
Although mathematics is visual language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in mathematics, they must recognize, comprehend and apply the requisite vocabulary. Thus, vocabulary instruction is as critical in content areas as it is in language arts. It is especially…
Under Threes' Mathematical Learning
ERIC Educational Resources Information Center
Franzén, Karin
2015-01-01
The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…
Psychology and Mathematics Education.
ERIC Educational Resources Information Center
Fischbein, Efraim
1999-01-01
Analyzes the relationship between cognitive psychology as a broad theoretical framework, and the psychology of mathematics education. Argues that mathematics education should not simply borrow from cognitive psychology; rather, it should provide its own psychological research problems, adapted investigation strategies, and adequate original…
Teaching Mathematics Using Steplets
ERIC Educational Resources Information Center
Bringslid, Odd; Norstein, Anne
2008-01-01
This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…
Philosophy of Teaching Mathematics.
ERIC Educational Resources Information Center
Ediger, Marlow
There are selected philosophies in the teaching of mathematics which can provide guidance to the teacher in developing the curriculum and also a framework for teaching and learning. This paper discusses four such philosophies of teaching mathematics: Idealism, Realism, Experimentalism, and Existentialism. Idealism stresses that students live in an…
Archimedes' Principle in Action
ERIC Educational Resources Information Center
Kires, Marian
2007-01-01
The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers. (Contains 5 figures.)
Chemical Principles Exemplified
ERIC Educational Resources Information Center
Plumb, Robert C.
1972-01-01
Collection of two short descriptions of chemical principles seen in life situations: the autocatalytic reaction seen in the bombardier beetle, and molecular potential energy used for quick roasting of beef. Brief reference is also made to methanol lighters. (PS)
Evolutionary Multiobjective Optimization: Principles, Procedures, and Practices
NASA Astrophysics Data System (ADS)
Deb, Kalyanmoy
2010-10-01
Multi-objective optimization problems deal with multiple conflicting objectives. In principle, they give rise to a set of trade-off Pareto-optimal solutions. Over the past one-and-half decade, evolutionary multi-objective optimization (EMO) has established itself as a mature field of research and application with an extensive literature, commercial softwares, numerous freely downloadable codes, a dedicated biannual conference running successfully five times so far since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. This is because evolutionary algorithms (EAs) work with a population of solutions and in solving multi-objective optimization problems, EAs can be modified to find and capture multiple solutions in a single simulation run. In this article, we make a brief outline of EMO principles, discuss one specific EMO algorithm, and present some current research issues of EMO.
Functional structure of the cryogenic optical sensor and mathematical models of signal
NASA Astrophysics Data System (ADS)
Yatsenko, Vitaliy A.
2003-10-01
Today, remote sensing is one of the fastest growing technologies around. It is a multibillion-dollar industry and remote thematic images are routinely used in an increasing number of fields. The solution of many important practical problems depends on a large-scale usage of the measurement systems and underlying physical principles. These problems include monitoring of the natural resources based on the analysis of the gravity anomalies, studying of global geodynamic processes and evolution of the Earth gravity field, analysis of movement of the Earth poles, etc. In spite of the existence of the considerable achievements in the area of gravity measurements, some important aspects of the problem have not been solved yet due to the absence of appropriate sensitive elements (SE) and sensors with the relevant parameters. The author of the report has proposed a functional structure of the cryogenic-optical sensor based on magnetic bearing phenomenon. A functional structure of the sensitive element consists of a controlled magnetic suspension, a high-precision optical system for registration of levitating body mechanical coordinates, and a signal processing toolbox. This toolbox contents the adaptive compensator, digital filters, inverse mathematical models of the SE, the Kalman filter, the control system, the dynamical analysis system, the mathematical modeling system, the simulation system, the information statistical system, the wavelet analysis system, a neural network, and data base. Mathematical models of the signal and noise are conventionally based on the principles of nonlinear electro-mechanics. Such models explains most basic features of the superconducting sensitive element. We will also discuss a new theoretical framework for adaptive estimation of gravitation perturbations and compare program models to conventional robust estimation models.
A correspondence principle for steady-state wave problems
NASA Technical Reports Server (NTRS)
Schmerr, L. W.
1976-01-01
A correspondence principle was developed for treating the steady state propagation of waves from sources moving along a plane surface or interface. This new principle allows one to obtain, in a unified manner, explicit solutions for any source velocity. To illustrate the correspondence principle in a particular case, the problem of a load moving at an arbitrary constant velocity along the surface of an elastic half-space is considered.
Business Mathematics. Mathematics Curriculum Guide (Career Oriented).
ERIC Educational Resources Information Center
Nuschler, Alexandra; And Others
The curriculum guide correlates concepts in business mathematics with career-oriented concepts and activities. The curriculum outline format gives the concepts to be taught, matched with related career-oriented performance objectives, concepts, and suggested instructional activities in facing page layouts. The outline is divided into the major…
Scaffolding students' opportunities to learn mathematics through social interactions
NASA Astrophysics Data System (ADS)
Bell, Clare V.; Pape, Stephen J.
2012-12-01
In this study, we take a sociocultural perspective on teaching and learning to examine how teachers in an urban Algebra 1 classroom constructed opportunities to learn. Drawing on analyses of discourse practices, including videotaped classroom lessons as well as other classroom artifacts and telephone interviews, we describe ways that two teachers and their students interacted to develop mathematical understanding. Through descriptive narrative, we highlight practices that positioned students as competent mathematical thinkers and provided evidence of students' mathematical agency. This study suggests that critical awareness of discourse practices in conjunction with teacher mediation of other affordances for learning within the classroom environment might engage students in mathematical practices such as problem solving, explaining mathematical ideas, arguing for or against specific solutions to problems, and justifying mathematical thinking.
NASA Astrophysics Data System (ADS)
Ngayam-Happy, R.; Becquart, C. S.; Domain, C.
2013-09-01
The formation and medium-term evolution of point defect and solute-rich clusters under neutron irradiation have been modelled in a complex Fe-CuMnNiSiP alloy representative of RPV steels, by means of first principle-based atomistic kinetic Monte Carlo simulations. The results obtained reproduce most features observed in available experimental studies, highlighting the very good agreement between both series. According to simulation, solute-rich clusters form and develop via an induced segregation mechanism on either the vacancy or interstitial clusters, and these point defect clusters are efficiently generated only in cascade debris and not Frenkel pair flux. The results have revealed the existence of two distinct populations of clusters with different characteristic features. Solute-rich clusters in the first group are bound essentially to interstitial clusters and they are enriched in Mn mostly, but also Ni to a lesser extent. Over the low dose regime, their density increases in the alloy as a result of the accumulation of highly stable interstitial clusters. In the second group, the solute-rich clusters are merged with vacancy clusters, and they contain mostly Cu and Si, but also substantial amount of Mn and Ni. The formation of a sub-population of pure solute clusters has been observed, which results from annihilation of the low stable vacancy clusters on sinks. The results indicate finally that the Mn content in clusters is up to 50%, Cu, Si, and Ni sharing the other half in more or less equivalent amounts. This composition has not demonstrated any noticeable modification with increasing dose over irradiation.
ERIC Educational Resources Information Center
Hebert, Michael A.; Powell, Sarah R.
2016-01-01
Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…
Hands-on mathematics: two cases from ancient Chinese mathematics
NASA Astrophysics Data System (ADS)
Wang, Youjun
2009-05-01
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in ancient China is an abundant resource for materials to demonstrate mathematics by hands-on manipulation. In this article I shall present two cases that embody this idea of a hands-on approach in ancient Chinese mathematics, at the same time offering an opportunity to show how to utilize materials from the history of Chinese math in modern mathematical education.
ERIC Educational Resources Information Center
Chiu, Thomas K. F.; Churchill, Daniel
2016-01-01
Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching…
Equilibrium I: Principles. Independent Learning Project for Advanced Chemistry (ILPAC). Unit P2.
ERIC Educational Resources Information Center
Inner London Education Authority (England).
This unit on the principles of equilibrium is one of 10 first year units produced by the Independent Learning Project for Advanced Chemistry (ILPAC). The unit consists of two levels. After a treatment of non-mathematical aspects in level one (the idea of a reversible reaction, characteristics of an equilibrium state, the Le Chatelier's principle),…
Suitable Candidates for Monte Carlo Solutions.
ERIC Educational Resources Information Center
Lewis, Jerome L.
1998-01-01
Discusses Monte Carlo methods, powerful and useful techniques that rely on random numbers to solve deterministic problems whose solutions may be too difficult to obtain using conventional mathematics. Reviews two excellent candidates for the application of Monte Carlo methods. (ASK)
Supporting African American Students' Learning of Mathematics: A Problem of Practice
ERIC Educational Resources Information Center
Jackson, Kara; Wilson, Jonee
2012-01-01
This article reports on a review of the mathematics education research literature 1989-May 2011 specific to K-12 African American students' opportunities to learn mathematics. Although we identify important developments in the literature, we conclude that the existing research base generally remains at the level of broad principles or orientations…
ERIC Educational Resources Information Center
Sood, Sheetal; Jitendra, Asha K.
2007-01-01
This study compared number sense instruction in three first-grade traditional mathematics textbooks and one reform-based textbook ("Everyday Mathematics" [EM]). Textbooks were evaluated with regard to their adherence to principles of effective instruction (e.g., big ideas, conspicuous instruction). The results indicated that traditional textbooks…
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.
An Assessment of the Level of Mathematics in Introductory Meteorology Textbooks.
NASA Astrophysics Data System (ADS)
Ulanski, Stan L.
1992-10-01
A review of introductory meteorology textbooks shows a wide difference in the level of mathematical treatment of atmospheric principles-from virtually none to fairly high. Particular deficiencies include lack of equations integrated into the text, problem-solving examples, and paucity of end-of-chapter questions requiring mathematical reasoning. These issues are raised in order to generate discussion among the meteorological community with regard to the degree of interaction between mathematics and meteorology in introductory courses.
A Principle of Intentionality.
Turner, Charles K
2017-01-01
The mainstream theories and models of the physical sciences, including neuroscience, are all consistent with the principle of causality. Wholly causal explanations make sense of how things go, but are inherently value-neutral, providing no objective basis for true beliefs being better than false beliefs, nor for it being better to intend wisely than foolishly. Dennett (1987) makes a related point in calling the brain a syntactic (procedure-based) engine. He says that you cannot get to a semantic (meaning-based) engine from there. He suggests that folk psychology revolves around an intentional stance that is independent of the causal theories of the brain, and accounts for constructs such as meanings, agency, true belief, and wise desire. Dennett proposes that the intentional stance is so powerful that it can be developed into a valid intentional theory. This article expands Dennett's model into a principle of intentionality that revolves around the construct of objective wisdom. This principle provides a structure that can account for all mental processes, and for the scientific understanding of objective value. It is suggested that science can develop a far more complete worldview with a combination of the principles of causality and intentionality than would be possible with scientific theories that are consistent with the principle of causality alone.
Turner, Charles K.
2017-01-01
The mainstream theories and models of the physical sciences, including neuroscience, are all consistent with the principle of causality. Wholly causal explanations make sense of how things go, but are inherently value-neutral, providing no objective basis for true beliefs being better than false beliefs, nor for it being better to intend wisely than foolishly. Dennett (1987) makes a related point in calling the brain a syntactic (procedure-based) engine. He says that you cannot get to a semantic (meaning-based) engine from there. He suggests that folk psychology revolves around an intentional stance that is independent of the causal theories of the brain, and accounts for constructs such as meanings, agency, true belief, and wise desire. Dennett proposes that the intentional stance is so powerful that it can be developed into a valid intentional theory. This article expands Dennett’s model into a principle of intentionality that revolves around the construct of objective wisdom. This principle provides a structure that can account for all mental processes, and for the scientific understanding of objective value. It is suggested that science can develop a far more complete worldview with a combination of the principles of causality and intentionality than would be possible with scientific theories that are consistent with the principle of causality alone. PMID:28223954
Principles of multisensory behavior.
Otto, Thomas U; Dassy, Brice; Mamassian, Pascal
2013-04-24
The combined use of multisensory signals is often beneficial. Based on neuronal recordings in the superior colliculus of cats, three basic rules were formulated to describe the effectiveness of multisensory signals: the enhancement of neuronal responses to multisensory compared with unisensory signals is largest when signals occur at the same location ("spatial rule"), when signals are presented at the same time ("temporal rule"), and when signals are rather weak ("principle of inverse effectiveness"). These rules are also considered with respect to multisensory benefits as observed with behavioral measures, but do they capture these benefits best? To uncover the principles that rule benefits in multisensory behavior, we here investigated the classical redundant signal effect (RSE; i.e., the speedup of response times in multisensory compared with unisensory conditions) in humans. Based on theoretical considerations using probability summation, we derived two alternative principles to explain the effect. First, the "principle of congruent effectiveness" states that the benefit in multisensory behavior (here the speedup of response times) is largest when behavioral performance in corresponding unisensory conditions is similar. Second, the "variability rule" states that the benefit is largest when performance in corresponding unisensory conditions is unreliable. We then tested these predictions in two experiments, in which we manipulated the relative onset and the physical strength of distinct audiovisual signals. Our results, which are based on a systematic analysis of response time distributions, show that the RSE follows these principles very well, thereby providing compelling evidence in favor of probability summation as the underlying combination rule.
Mathematization in introductory physics
NASA Astrophysics Data System (ADS)
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice
ERIC Educational Resources Information Center
Anderson-Pence, Katie L.
2015-01-01
This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…
Rethinking Mathematics: Teaching Social Justice by the Numbers
ERIC Educational Resources Information Center
Gutstein, Eric, Ed.; Peterson, Bob, Ed.
2005-01-01
This unique collection of more than 30 articles shows teachers how to weave social-justice principles throughout the math curriculum, and how to integrate social-justice math into other curricular areas as well. "Rethinking Mathematics" presents teaching ideas, lesson plans and reflections by practicing classroom teachers and distinguished…
Mathematics. Iowa Developed Energy Activity Sampler, 6-12. Revised.
ERIC Educational Resources Information Center
Iowa State Dept. of Education, Des Moines.
The revised Iowa Developed Energy Activity Sampler (IDEAS) was compiled using the original IDEAS program and the Energy Conservation Activity Packets (ECAPS). This document is one of the series of revised IDEAS booklets, and provides activities for teaching mathematics. The activities are intended to present energy principles in an interesting…
Mathematics Enrichment: Grade 4. Curriculum Bulletin Number 236.
ERIC Educational Resources Information Center
Johnston, Patsy
Enrichment activities for fourth-grade mathematics are presented. Some of the activities reinforce principles taught in the regular program; others introduce new concepts to challenge students. The activities are divided into the following categories: number pictures; multiplying or dividing by 10, 100, or 1000; tic-tac-toe word problems; map…
Designing Professional Learning Tasks for Mathematics Learning Trajectories
ERIC Educational Resources Information Center
Wilson, P. Holt; Sztajn, Paola; Edgington, Cyndi
2013-01-01
In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers' learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning…
Control Engineering, System Theory and Mathematics: The Teacher's Challenge
ERIC Educational Resources Information Center
Zenger, K.
2007-01-01
The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are…
The Importance of Appropriate Problems in the Teaching of Mathematics
ERIC Educational Resources Information Center
Georgescu-Buzau, E.; And Others
1970-01-01
Discussion is focused on standard teaching procedures that contain the elements of modern mathematics. Of the various methods which have been tested, it is concluded that the solving of problems remains the most effective basic activity. A sample collection of problems is presented to indicate relationships and the principles they illustrate. (RP)
The Principle of Energetic Consistency: Application to the Shallow-Water Equations
NASA Technical Reports Server (NTRS)
Cohn, Stephen E.
2009-01-01
If the complete state of the earth's atmosphere (e.g., pressure, temperature, winds and humidity, everywhere throughout the atmosphere) were known at any particular initial time, then solving the equations that govern the dynamical behavior of the atmosphere would give the complete state at all subsequent times. Part of the difficulty of weather prediction is that the governing equations can only be solved approximately, which is what weather prediction models do. But weather forecasts would still be far from perfect even if the equations could be solved exactly, because the atmospheric state is not and cannot be known completely at any initial forecast time. Rather, the initial state for a weather forecast can only be estimated from incomplete observations taken near the initial time, through a process known as data assimilation. Weather prediction models carry out their computations on a grid of points covering the earth's atmosphere. The formulation of these models is guided by a mathematical convergence theory which guarantees that, given the exact initial state, the model solution approaches the exact solution of the governing equations as the computational grid is made more fine. For the data assimilation process, however, there does not yet exist a convergence theory. This book chapter represents an effort to begin establishing a convergence theory for data assimilation methods. The main result, which is called the principle of energetic consistency, provides a necessary condition that a convergent method must satisfy. Current methods violate this principle, as shown in earlier work of the author, and therefore are not convergent. The principle is illustrated by showing how to apply it as a simple test of convergence for proposed methods.
Mathematical and Statistical Opportunities in Cyber Security
Meza, Juan; Campbell, Scott; Bailey, David
2009-03-23
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We start by posing the question 'What fundamental problems exist within cyber security research that can be helped by advanced mathematics and statistics'? Our first and most important assumption is that access to real-world data is necessary to understand large and complex systems like the Internet. Our second assumption is that many proposed cyber security solutions could critically damage both the openness and the productivity of scientific research. After examining a range of cyber security problems, we come to the conclusion that the field of cyber security poses a rich set of new and exciting research opportunities for the mathematical and statistical sciences.
Magic star puzzle for educational mathematics
NASA Astrophysics Data System (ADS)
Gan, Yee Siang; Fong, Wan Heng; Sarmin, Nor Haniza
2013-04-01
One of the interesting fields in recreational mathematics is the magic number arrangement. There are different kinds of arrays in the arrangement for a group of numbers. In particular, one of the arrays in magic number arrangement is called magic star. In fact, magic star involves combinatorics that contributes to geometrical analysis and number theory. Hence, magic star is suitable to be introduced as educational mathematics to cultivate interest in different area of mathematics. To obtain the solutions of normal magic stars of order six, the possible sets of numbers for every line in a magic star have been considered. Previously, the calculation for obtaining the solutions has been done manually which is time-consuming. Therefore, a programming code to generate all the fundamental solutions for normal magic star of order six without including the properties of rotation and reflection has been done. In this puzzle, a magic star puzzle is created by using Matlab software, which enables a user to verify the entries for the cells of magic star of order six. Moreover, it is also user-friendly as it provides interactive commands on the inputs given by the user, which enables the user to detect the incorrect inputs. In addition, user can also choose to view all the fundamental solutions as generated by the programming code.
ERIC Educational Resources Information Center
Reynolds, Thomas D.; And Others
This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…
Koller, C. M.; Koutná, N.; Ramm, J.; Kolozsvári, S.; Paulitsch, J.; Mayrhofer, P. H.; Holec, D.
2016-02-15
Density Functional Theory applying the generalised gradient approximation is used to study the phase stability of (Al{sub x}Cr{sub 1−x}){sub 2}O{sub 3} solid solutions in the context of physical vapour deposition (PVD). Our results show that the energy of formation for the hexagonal α phase is lower than for the metastable cubic γ and B1-like phases–independent of the Al content x. Even though this suggests higher stability of the α phase, its synthesis by physical vapour deposition is difficult for temperatures below 800 °C. Aluminium oxide and Al-rich oxides typically exhibit a multi-phased, cubic-dominated structure. Using a model system of (Al{sub 0.69}Cr{sub 0.31}){sub 2}O{sub 3} which experimentally yields larger fractions of the desired hexagonal α phase, we show that point defects strongly influence the energetic relationships. Since defects and in particular point defects, are unavoidably present in PVD coatings, they are important factors and can strongly influence the stability regions. We explicitly show that defects with low formation energies (e.g. metal Frenkel pairs) are strongly preferred in the cubic phases, hence a reasonable factor contributing to the observed thermodynamically anomalous phase composition.
Mathematical manipulative models: in defense of "beanbag biology".
Jungck, John R; Gaff, Holly; Weisstein, Anton E
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
Mathematical Manipulative Models: In Defense of “Beanbag Biology”
Gaff, Holly; Weisstein, Anton E.
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952
Mathematics, anxiety, and the brain.
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
2017-02-03
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Spaceborne receivers: Basic principles
NASA Technical Reports Server (NTRS)
Stacey, J. M.
1984-01-01
The underlying principles of operation of microwave receivers for space observations of planetary surfaces were examined. The design philosophy of the receiver as it is applied to operate functionally as an efficient receiving system, the principle of operation of the key components of the receiver, and the important differences among receiver types are explained. The operating performance and the sensitivity expectations for both the modulated and total power receiver configurations are outlined. The expressions are derived from first principles and are developed through the important intermediate stages to form practicle and easily applied equations. The transfer of thermodynamic energy from point to point within the receiver is illustrated. The language of microwave receivers is applied statistics.
Basic Principles of Chromatography
NASA Astrophysics Data System (ADS)
Ismail, Baraem; Nielsen, S. Suzanne
Chromatography has a great impact on all areas of analysis and, therefore, on the progress of science in general. Chromatography differs from other methods of separation in that a wide variety of materials, equipment, and techniques can be used. [Readers are referred to references (1-19) for general and specific information on chromatography.]. This chapter will focus on the principles of chromatography, mainly liquid chromatography (LC). Detailed principles and applications of gas chromatography (GC) will be discussed in Chap. 29. In view of its widespread use and applications, high-performance liquid chromatography (HPLC) will be discussed in a separate chapter (Chap. 28). The general principles of extraction are first described as a basis for understanding chromatography.
ERIC Educational Resources Information Center
Yang, Euphony F. Y.; Chang, Ben; Cheng, Hercy N. H.; Chan, Tak-Wai
2016-01-01
This study examined how to foster pupils' mathematical communication abilities by using tablet PCs. Students were encouraged to generate math creations (including mathematical representation, solution, and solution explanation of word problems) as their teaching materials and reciprocally tutor classmates to increase opportunities for mathematical…
How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling
ERIC Educational Resources Information Center
Johnston, Peter R.
2013-01-01
The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…
Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.
ERIC Educational Resources Information Center
Cosler, Norma, Ed.
This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…
Using Mathematics in Science: Working with Your Mathematics Department
ERIC Educational Resources Information Center
Lyon, Steve
2014-01-01
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
Promoting Critical Mathematics Literacy in Secondary Mathematics Teacher Education
ERIC Educational Resources Information Center
Fish, Michael Charles
2012-01-01
This study examines how critical mathematical literacy teachers conceptualize their practices and how those practices were demonstrated in the classroom. Practices were considered from an ontology of mathematics education, specific to critical mathematical literacy, in which classroom interactions question what it means to do mathematics as an…
Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication
ERIC Educational Resources Information Center
Kaya, Defne; Aydin, Hasan
2016-01-01
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
ERIC Educational Resources Information Center
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
ERIC Educational Resources Information Center
Cable, John
2014-01-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…
[Ethical principles in electronvulsivotherapy].
Richa, S; De Carvalho, W
2016-12-01
ECT or electroconvulsive therapy (ECT) is a therapeutic technique invented in 1935 but which was really developed after World War II and then spreading widely until the mid 1960s. The source of this technique, and some forms of stigma including films, have participated widely to make it suspect from a moral point of view. The ethical principles that support the establishment of a treatment by ECT are those relating to any action in psychiatry and are based on the one hand on the founding principles of bioethics: autonomy, beneficence, non-malfeasance, and justice, and on the other hand on the information on the technical and consent to this type of care.
NASA Technical Reports Server (NTRS)
Hankins, D. B.; Wake, W. H.
1981-01-01
The potential remote sensing user community is enormous, and the teaching and training tasks are even larger; however, some underlying principles may be synthesized and applied at all levels from elementary school children to sophisticated and knowledgeable adults. The basic rules applying to each of the six major elements of any training course and the underlying principle involved in each rule are summarized. The six identified major elements are: (1) field sites for problems and practice; (2) lectures and inside study; (3) learning materials and resources (the kit); (4) the field experience; (5) laboratory sessions; and (6) testing and evaluation.
Benjamin Banneker's Mathematical Puzzles.
ERIC Educational Resources Information Center
Mahoney, John F.
2003-01-01
Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)
Fostering Mathematical Curiosity.
ERIC Educational Resources Information Center
Knuth, Eric J.
2002-01-01
Demonstrates what it might mean to engage students in problem posing and how teachers might begin to create classroom environments that encourage, develop, and foster mathematical curiosity. (Author/NB)
Mathematics: Contributions by Women.
ERIC Educational Resources Information Center
Dewar, Jacqueline M.
1991-01-01
Describes a core course in a women's-studies program at Loyola Marymount University. Provides information, resources, and an annotated bibliography useful for making students more aware of women's contributions to mathematics. Contains 38 references. (ASK)
Black African Traditional Mathematics
ERIC Educational Resources Information Center
Zaslavsky, Claudia
1970-01-01
Discusses the traditional number systems and the origin of the number names used by several African peoples living south of the Sahara. Also included are limitations in African mathematical development, and possible topics for research. (RP)
Mathematics Case Methods Project.
ERIC Educational Resources Information Center
Barnett, Carne S.
1998-01-01
Presents an overview and analysis of the Mathematics Case Methods Project, which uses cases in order to examine and reflect upon teaching. Focuses on a special kind of teacher knowledge, coined pedagogical-content knowledge. (ASK)
Ferrari, Pier Luigi
2003-01-01
Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658
ERIC Educational Resources Information Center
Goos, Merrilyn
2000-01-01
Presents an activity using the familiar fairy tale "Cinderella" to provide the context for stimulating mathematical thinking about a real life problem. Makes use of graphing calculator technology to investigate the relationship between shoe sizes and shoe lengths. (ASK)
Landauer, C.; Bellman, K.L.
1996-12-31
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.
NASA Astrophysics Data System (ADS)
Ligomenides, Panos A.
2009-05-01
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
A mathematical formulation of the Scole control problem, part 1
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1985-01-01
A mathematical formulation of the SCOLE control problem in terms of a continuous model described by partial differential equations with delta functions on the boundary is presented along with three techniques of solution. The abstract wave equation approach leads immediately to a linear feedback law that can ensure (strong) stability. The boundary control approach yields an explicit solution, albeit in a simple case.