#### Sample records for principle mathematical solutions

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

PubMed

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

2008-10-01

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

2. Physical Principles versus Mathematical Rigor.

ERIC Educational Resources Information Center

Patterson, Jim

2000-01-01

While it is most often the case that an understanding of physics can simplify mathematical calculations, occasionally mathematical precision leads directly to a better physical understanding of a situation. Presents an example of a mechanics problem in which careful mathematical derivation can lead directly to a deeper physical understanding of…

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

Gyulov, Tihomir B.; Valkov, Radoslav L.

2011-12-01

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

4. Scaffolding Mathematical Modelling with a Solution Plan

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

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

5. 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.…

6. 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.

7. Intellectual Engagement and Other Principles of Mathematics Instruction

ERIC Educational Resources Information Center

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

2013-01-01

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

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

SciTech Connect

Rivlin, Lev A

2010-12-09

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

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

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah

2014-01-01

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

10. 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…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

Freeman, Gregory D.; Lucius, Lisa B.

2008-01-01

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

13. Solution of mathematical programming formulations of subgame perfect equilibrium problems

SciTech Connect

Macal, C.M.; Hurter, A.P.

1992-02-12

Mathematical programming models have been developed to represent imperfectly competitive (oligopolistic) market structures and the interdependencies of decision-making units in establishing prices and production levels. The solution of these models represents an economic equilibrium. A subgame perfect equilibrium formulation explicitly considers that each agent`s strategies depend on the current state of the system; the state depends solely on previous decisions made by the economic agents. The structure of an industry-wide model that is formulated as a subgame perfect equilibrium problem is a matrix of simultaneous mathematical programming problems, where the rows represent time periods and the columns represent agents. This paper formally defines the subgame perfect equilibrium problem that includes mathematical programs for agent decision problems, and it characterizes the feasible space in a way that is conducive to the solution of the problem. The existence of equilibrium solutions on convex subspaces of the feasible region is proved, and this set is shown to contain the subgame perfect equilibrium solutions. A procedure for computing equilibrium solutions and systematically searching the subspaces is illustrated by a numerical example.

14. Advance directives: principles, problems, and solutions for physicians.

PubMed

Hoffman, B F; Humniski, A

1997-04-01

Given the passage of recent legislation, the appearance of common-law reports in Canada and the United States, and the practical problems of implementation of advance directives in health care, physicians should understand the principles and issues involved. In this article, the advantages, disadvantages, and practical solutions to the problems are explored. Family physicians, geriatricians, neurologists, and psychiatrists are most likely to be consulted about advance directives in health care. PMID:12382657

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

SciTech Connect

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

2009-01-01

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

16. Evaluating Three Elementary Mathematics Programs for Presence of Eight Research-Based Instructional Design Principles

ERIC Educational Resources Information Center

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

2012-01-01

The present review builds on earlier research that evaluated the curricular features of core math programs to improve the performances of students with or at risk for mathematics difficulties. In this review, three elementary math programs, at Grades 2 and 4, were evaluated for the presence of eight instructional principles. Math intervention…

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

ERIC Educational Resources Information Center

Moschkovich, Judit

2013-01-01

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

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

ERIC Educational Resources Information Center

Gabrielson, Curtis A.; Hsi, Sherry

2012-01-01

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

19. A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

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

2002-01-01

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

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

ERIC Educational Resources Information Center

Große, Cornelia S.

2014-01-01

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

1. Mathematical models of polymer solutions motion and their symmetries

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

2015-10-01

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

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

ERIC Educational Resources Information Center

Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

2009-01-01

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

3. 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…

4. Ions in solutions: Determining their polarizabilities from first-principles

Molina, John J.; Lectez, Sébastien; Tazi, Sami; Salanne, Mathieu; Dufrêche, Jean-François; Roques, Jérôme; Simoni, Eric; Madden, Paul A.; Turq, Pierre

2011-01-01

Dipole polarizabilities of a series of ions in aqueous solutions are computed from first-principles. The procedure is based on the study of the linear response of the maximally localized Wannier functions to an applied external field, within density functional theory. For most monoatomic cations (Li ^+, Na ^+, K ^+, Rb ^+, Mg ^{2+}, Ca ^{2+} and Sr ^{2+}) the computed polarizabilities are the same as in the gas phase. For Cs ^+ and a series of anions (F ^-, Cl ^-, Br ^- and I ^-), environmental effects are observed, which reduce the polarizabilities in aqueous solutions with respect to their gas phase values. The polarizabilities of H ^+_(aq), OH ^-_(aq) have also been determined along an ab initio molecular dynamics simulation. We observe that the polarizability of a molecule instantaneously switches upon proton transfer events. Finally, we also computed the polarizability tensor in the case of a strongly anisotropic molecular ion, UO _2^{2+}. The results of these calculations will be useful in building interaction potentials that include polarization effects.

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

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.

6. 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…

7. 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.…

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

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

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

9. Mathematical modeling of methoxyanabasine C11H16N2O polymer solution ultrafiltration

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

2012-06-01

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

10. 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)

11. 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…

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

PubMed Central

Nanninga, Nanne

2001-01-01

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

13. 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…

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

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

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

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

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.

16. Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle

PubMed Central

Ryser, Marc D.; Qu, Yiding; Komarova, Svetlana V.

2012-01-01

Bone is a common site for cancer metastasis. To create space for their growth, cancer cells stimulate bone resorbing osteoclasts. Cytokine RANKL is a key osteoclast activator, while osteoprotegerin (OPG) is a RANKL decoy receptor and an inhibitor of osteoclastogenesis. Consistently, systemic application of OPG decreases metastatic tumor burden in bone. However, OPG produced locally by cancer cells was shown to enhance osteolysis and tumor growth. We propose that OPG produced by cancer cells causes a local reduction in RANKL levels, inducing a steeper RANKL gradient away from the tumor and towards the bone tissue, resulting in faster resorption and tumor expansion. We tested this hypothesis using a mathematical model of nonlinear partial differential equations describing the spatial dynamics of OPG, RANKL, PTHrP, osteoclasts, tumor and bone mass. We demonstrate that at lower expression rates, tumor-derived OPG enhances the chemotactic RANKL gradient and osteolysis, whereas at higher expression rates OPG broadly inhibits RANKL and decreases osteolysis and tumor burden. Moreover, tumor expression of a soluble mediator inducing RANKL in the host tissue, such as PTHrP, is important for correct orientation of the RANKL gradient. A meta-analysis of OPG, RANKL and PTHrP expression in normal prostate, carcinoma and metastatic tissues demonstrated an increase in expression of OPG, but not RANKL, in metastatic prostate cancer, and positive correlation between OPG and PTHrP in metastatic prostate cancer. The proposed mechanism highlights the importance of the spatial distribution of receptors, decoys and ligands, and can be applied to other systems involving regulation of spatially anisotropic processes. PMID:23093918

17. 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.

18. Redox condition in molten salts and solute behavior: A first-principles molecular dynamics study

Nam, Hyo On; Morgan, Dane

2015-10-01

Molten salts technology is of significant interest for nuclear, solar, and other energy systems. In this work, first-principles molecular dynamics (FPMD) was used to model the solute behavior in eutectic LiCl-KCl and FLiBe (Li2BeF4) melts at 773 K and 973 K, respectively. The thermo-kinetic properties for solute systems such as the redox potential, solute diffusion coefficients and structural information surrounding the solute were predicted from FPMD modeling and the calculated properties are generally in agreement with the experiments. In particular, we formulate an approach to model redox energetics vs. chlorine (or fluorine) potential from first-principles approaches. This study develops approaches for, and demonstrates the capabilities of, FPMD to model solute properties in molten salts.

19. 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.

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

ERIC Educational Resources Information Center

Gazit, Avikam; Patkin, Dorit

2012-01-01

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

1. Differential Improvement in Student Understanding of Mathematical Principles following Formative Assessment Intervention

ERIC Educational Resources Information Center

Phelan, Julia; Choi, Kilchan; Vendlinski, Terry; Baker, Eva; Herman, Joan

2011-01-01

The authors describe results from a study of a middle school mathematics formative assessment strategy. They employed a randomized, controlled design to address the following question: Does using our strategy improve student performance on assessments of key mathematical ideas relative to a comparison group? Eighty-five teachers and 4,091 students…

2. Every Word Problem Has a Solution--The Social Rationality of Mathematical Modelling in Schools.

ERIC Educational Resources Information Center

Reusser, Kurt; Stebler, Rita

1997-01-01

Two experiments involving 67 elementary school and 439 high school students show that students present solutions to many unsolvable problems without showing realistic reactions. Results are discussed with respect to the quality of word problems in teaching mathematics, the culture of teaching and learning, and the issue of social rationality in…

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

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.

4. Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule

Luo, Yousong; Eberhard, Andrew

2005-07-01

A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.

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

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.

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

PubMed Central

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

2000-01-01

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

7. CTSPAC: MATHEMATICAL MODEL FOR COUPLED TRANSPORT OF WATER, SOLUTES, AND HEAT IN THE SOIL-PLANT-ATMOSPHERE CONTINUUM. VOLUME 1. MATHEMATICAL THEORY AND TRANSPORT CONCEPTS

EPA Science Inventory

The mathematical structure of the model consists of the coupling of a model for the transport through soils to a model for transport through plants. The coupled model describes uptake of water and solutes by plants from the soil solution. The rate of uptake is a function of the e...

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

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.

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

ERIC Educational Resources Information Center

Pierce, Robyn; Stacey, Kaye

2009-01-01

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

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

ERIC Educational Resources Information Center

Yildirim, Sevda; Ersozlu, Zehra Nur

2013-01-01

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

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

ERIC Educational Resources Information Center

2012-01-01

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

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

Ginzburg, Vitalii L.

1987-01-01

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

13. Principles help to analyse but often give no solution--secondary prevention after a cardiac event.

PubMed

Westin, Lars; Nilstun, Tore

2006-06-01

The aim of this paper is to investigate whether or not ethical conflicts can be identified, analysed and solved using ethical principles. The relation between the physician and the patient with ischemic heart disease (IHD) as life style changes are recommended in a secondary prevention program is used as an example. The principal persons affected (the patient and his or her spouse) and the ethical principles (respect for autonomy, non-maleficence, beneficence and justice) are combined in a two dimensional model. The most important person affected by the recommendations is the patient. His or her autonomy is challenged by the suggested life style changes, the purpose of which is to promote the future wellbeing and health of the patient. The spouse is indirectly involved in and affected by the process. He or she often feels neglected by caregivers. Ethical conflicts can both be identified and analysed using ethical principles, but often no solution is implied. Most (if not all) physicians would strongly encourage life style changes, but surprisingly there is no uncontroversial justification for this conclusion using principles. PMID:17195579

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

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

15. Symmetry analysis and exact solutions for nonlinear equations in mathematical physics

Fushchich, Vil'gel'm. I.; Shtelen', Vladimir M.; Serov, Nikolai I.

The book provides an overview of the current status of theoretical-algebraic methods in relation to linear and nonlinear multidimensional equations in mathematical and theoretical physics that are invariant with respect to the Poincare and Galilean groups and the wider Lie groups. Particular attention is given to the construction, in explicit form, of wide classes of accurate solutions to specific nonlinear partial differential equations, such as nonlinear wave equations for scalar, spinor, and vector fields, Young-Mills equations, and nonlinear quantum electrodynamic equations. A group-theory approach is used to analyze the classical three-body problem.

16. Mathematical model and solution for fingering phenomenon in double phase flow through homogeneous porous media.

PubMed

Mistry, Piyush R; Pradhan, Vikas H; Desai, Khyati R

2013-01-01

The present paper analytically discusses the phenomenon of fingering in double phase flow through homogenous porous media by using variational iteration method. Fingering phenomenon is a physical phenomenon which occurs when a fluid contained in a porous medium is displaced by another of lesser viscosity which frequently occurred in problems of petroleum technology. In the current investigation a mathematical model is presented for the fingering phenomenon under certain simplified assumptions. An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software. PMID:24348161

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

PubMed

Mochizuki, Koji; Takayama, Kozo

2016-07-01

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. PMID:26559666

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

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

2015-07-01

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

19. A Standard Mathematical Treatment of Retardation in Mobile/Immobile Zone Models Violates the Principle of Conservation of Mass

Hansen, S. K.

2009-12-01

A widely used treatment of coupling between mobile and immobile zones in mathematical transport models assumes continuity of aqueous concentration across the zone interface and estimates cross-interface flux using a standard expression, based on Fick's Law. This particular formulation has been used in numerous existing papers, including key analytical solutions for discretely fractured porous media. In cases where matrix sorption retards diffusion in the immobile zone, this is often handled by employing a retardation coefficient other than unity in the model. In this circumstance, it can be shown that the standard formulation ceases to enforce mass balance across the interface between the mobile and immobile zones. The standard treatment generates incorrect results--even if the environment has been characterized perfectly. A novel analysis proves the existence of this mathematical error and shows how to correct it, without introducing any additional physical information. A summary of the analysis, as well as its implications (including the invalidation of parts of a number of published analytic solutions) will be discussed.

20. Phase Diagram of Pb(Zr,Ti)O{sub 3} Solid Solutions from First Principles

SciTech Connect

Kornev, Igor A.; Bellaiche, L.; Janolin, P.-E.; Dkhil, B.; Suard, E.

2006-10-13

A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr{sub 1-x}Ti{sub x})O{sub 3} solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.

1. Phase Diagram of Pb(Zr,Ti)O3 Solid Solutions from First Principles

Kornev, Igor A.; Bellaiche, L.; Janolin, P.-E.; Dkhil, B.; Suard, E.

2006-10-01

A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.

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

ERIC Educational Resources Information Center

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

2014-01-01

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

3. Dynamical Principles of Emotion-Cognition Interaction: Mathematical Images of Mental Disorders

PubMed Central

Rabinovich, Mikhail I.; Muezzinoglu, Mehmet K.; Strigo, Irina; Bystritsky, Alexander

2010-01-01

The key contribution of this work is to introduce a mathematical framework to understand self-organized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized Lotka-Volterra systems. This coupling is based upon competition for common resources. The system can be regarded as a normal or canonical form for any distributed system that shows self-organized dynamics that entail winnerless competition. Crucially, we will show that some of the fundamental instabilities that arise in these coupled systems are remarkably similar to endogenous activity seen in the brain (using EEG and fMRI). Furthermore, by changing a small subset of the system's parameters we can produce bifurcations and metastable sequential dynamics changing, which bear a remarkable similarity to pathological brain states seen in psychiatry. In what follows, we will consider the coupling of two macroscopic modes of brain activity, which, in a purely descriptive fashion, we will label as cognitive and emotional modes. Our aim is to examine the dynamical structures that emerge when coupling these two modes and relate them tentatively to brain activity in normal and non-normal states. PMID:20877723

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

Scherlis, Damián A.; Fattebert, Jean-Luc; Gygi, François; Cococcioni, Matteo; Marzari, Nicola

2006-02-01

The electrostatic continuum solvent model developed by [Fattebert and Gygi J. Comput. Chem. 23, 662 (2002); Int. J. Quantum Chem. 93, 139 (2003)] 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. Our 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. We apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon.

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

SciTech Connect

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

2005-11-14

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

6. Atomistic modeling of amorphous silicon carbide: an approximate first-principles study in constrained solution space.

PubMed

Atta-Fynn, Raymond; Biswas, Parthapratim

2009-07-01

Localized basis ab initio molecular dynamics simulation within the density functional framework has been used to generate realistic configurations of amorphous silicon carbide (a-SiC). Our approach consists of constructing a set of smart initial configurations that conform to essential geometrical and structural aspects of the materials obtained from experimental data, which is subsequently driven via a first-principles force field to obtain the best solution in a reduced solution space. A combination of a priori information (primarily structural and topological) along with the ab initio optimization of the total energy makes it possible to model a large system size (1000 atoms) without compromising the quantum mechanical accuracy of the force field to describe the complex bonding chemistry of Si and C. The structural, electronic and vibrational properties of the models have been studied and compared to existing theoretical models and available data from experiments. We demonstrate that the approach is capable of producing large, realistic configurations of a-SiC from first-principles simulation that display its excellent structural and electronic properties. Our study reveals the presence of predominant short range order in the material originating from heteronuclear Si-C bonds with a coordination defect concentration as small as 5% and a chemical disorder parameter of about 8%. PMID:21828477

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

ERIC Educational Resources Information Center

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

8. The Display and Input of Mathematical Symbols on the Web: Questions and Technical Solutions

ERIC Educational Resources Information Center

Zhi-Feng, Eric; Liu, Ming-Chun Cheng; Liu, Syhan-Ming Yuan; Lo, Win-Tsung

2004-01-01

This study proposed practical ways to display mathematical formula on the Web and input mathematical formulae onto the Web according to the authors' successful experience of implementing mathematical forum which allowed displaying and inputting mathematical notations and equations. Authors believe that this study will pose more questions and…

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

ERIC Educational Resources Information Center

Guberman, Raisa; Leikin, Roza

2013-01-01

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

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

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

2013-12-01

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

11. Phase diagram of PZT solid solutions near the morphotropic phase boundary from first principles

Kornev, I.; Bellaiche, L.; Janolin, P.-E.; Dkhil, B.; Suard, E.

2007-03-01

A first-principles-derived scheme, that incorporates ferroelectric and antiferrodistortive degrees of freedom, is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solutions near its morphotropic phase boundary [1]. The use of this numerical technique (i) resolves controversies about the monoclinic ground-state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points, that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions. [1] Igor A. Kornev, L. Bellaiche, P.-E. Janolin, B. Dkhil, and E. Suard, Phys. Rev. Lett. 97, 157601 (2006) This work is supported by ONR grants N00014-04-1-0413, N00014-01-1-0600 and N00014-01-1-0365, by NSF grant DMR- 0404335, and by DOE grant DE-FG02-05ER46188.

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

SciTech Connect

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

2005-11-14

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

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

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

2012-05-01

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

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

PubMed

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

2016-04-14

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

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

PubMed

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

2010-10-15

The paper provides a new formulation and analytical proposals based on the isohydric solutions concept. It is particularly stated that a mixture formed, according to titrimetric mode, from a weak acid (HX, C(0)mol/L) and a strong acid (HB, Cmol/L) solutions, assumes constant pH, independently on the volumes of the solutions mixed, provided that the relation C(0)=C+C(2)·10(pK(1)) is valid, where pK(1)=-log K(1), K(1) the dissociation constant for HX. The generalized formulation, referred to the isohydric solutions thus obtained, was extended also to more complex acid-base systems. Particularly in the (HX, HB) system, the titration occurs at constant ionic strength (I) value, not resulting from presence of a basal electrolyte. This very advantageous conjunction of the properties provides, among others, a new, very sensitive method for verification of pK(1) value. The new method is particularly useful for weak acids HX characterized by low pK(1) values. The method was tested experimentally on four acid-base systems (HX, HB), in aqueous and mixed-solvent media and compared with the literature data. Some useful (linear and hyperbolic) correlations were stated and applied for validation of pK(1) values. Finally, some practical applications of analytical interest of the isohydricity (pH constancy) principle as one formulated in this paper were enumerated, proving the usefulness of such a property which has its remote roots in the Arrhenius concept. PMID:20875603

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

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

2016-04-01

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

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

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.

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

PubMed

Borghero, Francesco; Demontis, Francesco

2016-09-01

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

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

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

2006-12-01

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

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

PubMed Central

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

2013-01-01

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

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

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.

2. Kinetic Study and Mathematical Model of Hemimorphite Dissolution in Low Sulfuric Acid Solution at High Temperature

Xu, Hongsheng; Wei, Chang; Li, Cunxiong; Deng, Zhigan; Li, Minting; Li, Xingbin

2014-10-01

The dissolution kinetics of hemimorphite with low sulfuric acid solution was investigated at high temperature. The dissolution rate of zinc was obtained as a function of dissolution time under the experimental conditions where the effects of sulfuric acid concentration, temperature, and particle size were studied. The results showed that zinc extraction increased with an increase in temperature and sulfuric acid concentration and with a decrease in particle size. A mathematical model able to describe the process kinetics was developed from the shrinking core model, considering the change of the sulfuric acid concentration during dissolution. It was found that the dissolution process followed a shrinking core model with "ash" layer diffusion as the main rate-controlling step. This finding was supported with a linear relationship between the apparent rate constant and the reciprocal of squared particle radius. The reaction order with respect to sulfuric acid concentration was determined to be 0.7993. The apparent activation energy for the dissolution process was determined to be 44.9 kJ/mol in the temperature range of 373 K to 413 K (100 °C to 140 °C). Based on the shrinking core model, the following equation was established:

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

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

2016-06-01

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

PubMed

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

2014-06-01

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

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

Noo, Frederic

2010-03-01

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

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

SciTech Connect

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

2011-09-01

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

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

Romano, Vittorio; Majorana, Armando; Coco, Marco

2015-12-01

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

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

ERIC Educational Resources Information Center

Matsko, Vince; Thomas, Jerald

2014-01-01

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

9. Mathematics Teaching and Learning Environments Come of Age: Some New Solutions to Some Old Problems.

ERIC Educational Resources Information Center

White, James E.

1989-01-01

Discussion of teaching college level mathematics using computer algebra systems (CAS) focuses on a new microcomputer-based teaching/learning environment called Computer Algebra and Logo (CAL). Highlights include the teachers' role in the development of mathematics teaching and learning environments; methods and goals of implementation; and…

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

ERIC Educational Resources Information Center

Livy, Sharyn; Vale, Colleen

2011-01-01

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

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

Tan, Bikan

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

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

SciTech Connect

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

2015-05-07

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

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

SciTech Connect

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

2012-11-02

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

14. Number Topics in Early Childhood Mathematics Curricula: Historical Background, Dilemmas, and Possible Solutions.

ERIC Educational Resources Information Center

Wright, Bob

1992-01-01

It is argued that Australian elementary mathematics curricula have been influenced by earlier British and United States educational movements and theories and are out of touch with current research emphasizing a constructivist approach. A new model of young children's numerical development is offered, and recommendations for improving mathematical…

15. Undergraduate Students' Preference for Procedural to Conceptual Solutions to Mathematical Problems

ERIC Educational Resources Information Center

Engelbrecht, Johann; Bergsten, Christer; Kagesten, Owe

2009-01-01

This article reports on a collaboration project between South Africa and Sweden, in which we want to investigate whether the emphasis in undergraduate mathematics courses for engineering students should be more conceptual than the current traditional way of teaching. On the basis of a review of the distinction between conceptual and procedural…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

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.

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

PubMed

Marchi, Massimo

2016-07-28

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

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

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

2016-07-01

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

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

NASA Technical Reports Server (NTRS)

Kuhn, Paul

1939-01-01

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

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

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.

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

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.

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

DOE PAGESBeta

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

4. Phase stability of ScN-based solid solutions for thermoelectric applications from first-principles calculations

Kerdsongpanya, Sit; Alling, Björn; Eklund, Per

2013-08-01

We have used first-principles calculations to investigate the trends in mixing thermodynamics of ScN-based solid solutions in the cubic B1 structure. 13 different Sc1-xMxN (M = Y, La, Ti, Zr, Hf, V, Nb, Ta, Gd, Lu, Al, Ga, In) and three different ScN1-xAx (A = P, As, Sb) solid solutions are investigated and their trends for forming disordered or ordered solid solutions or to phase separate are revealed. The results are used to discuss suitable candidate materials for different strategies to reduce the high thermal conductivity in ScN-based systems, a material having otherwise promising thermoelectric properties for medium and high temperature applications. Our results indicate that at a temperature of T = 800 °C, Sc1-xYxN; Sc1-xLaxN; Sc1-xGdxN, Sc1-xGaxN, and Sc1-xInxN; and ScN1-xPx, ScN1-xAsx, and ScN1-xSbx solid solutions have phase separation tendency, and thus, can be used for forming nano-inclusion or superlattices, as they are not intermixing at high temperature. On the other hand, Sc1-xTixN, Sc1-xZrxN, Sc1-xHfxN, and Sc1-xLuxN favor disordered solid solutions at T = 800 °C. Thus, the Sc1-xLuxN system is suggested for a solid solution strategy for phonon scattering as Lu has the same valence as Sc and much larger atomic mass.

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

Sprinťu, Iuliana; Roateşi, Simona

2013-10-01

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

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

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.

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

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

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

2014-05-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

10. Predicting hardness of covalent/ionic solid solution from first-principles theory

Hu, Q. M.; Kádas, K.; Hogmark, S.; Yang, R.; Johansson, B.; Vitos, L.

2007-09-01

We introduce a hardness formula for the multicomponent covalent and ionic solid solutions. This expression is tested on nitride spinel materials A3N4 (A=C,Si,Ge) and applied to titanium nitrogen carbide (TiN1-xCx with 0⩽x ⩽1), off-stoichiometric transition-metal nitride (TiN1-x and VN1-x with x ⩽0.25), and B-doped semiconductors (C1-xBx, Si1-xBx, and Ge1-xBx with x ⩽0.1). In all cases, the theoretical hardness is in good agreement with experiments.

11. Comments on Crocco's solution and the independence principle for compressible turbulent boundary layers

NASA Technical Reports Server (NTRS)

Beckwith, I. E.

1974-01-01

The purpose of the present note is to show that on a flat plate where both the wall temperature and mean wall pressure are constant, neither of the limitations of parallel flow or of unity for the turbulent Prandtl number are required in order for the Crocco solution to apply to the turbulent boundary-layer flow. It is shown herein that this result is subject to restrictions on the magnitude of pressure fluctuations. The same analysis is generalized to show that the compressible turbulent boundary layer on an isothermal swept flat plate is independent of the spanwise flow if the molecular Prandtl number is unity.

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

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

2014-03-01

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

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

PubMed Central

Hedayat, Assem; Elmoselhi, Hamdi; Shoker, Ahmed

2012-01-01

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

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

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.

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

PubMed

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

2016-11-01

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

16. Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

2012-08-01

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

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

SciTech Connect

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

2011-12-15

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

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

DOE PAGESBeta

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

2011-12-15

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

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

PubMed

Ferrannini, Ele; Manca, Maria Laura

2015-04-01

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

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

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.

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

PubMed

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

2008-03-21

A copper (II) ions biosorption by Sargassum sp. biomass was studied in a fixed bed column at 30 degrees C and pH 3.5. The experimental curves were obtained for the following feed concentrations -2.08, 4.16, 6.42 and 12.72mmol/L of the copper ions. The mathematical models developed by Thomas and Bohart-Adams were used for description of ions sorption process in the column. The models principle hypothesis is that the mass transfer controlling stage of the process is the adsorption kinetics between sorbate and adsorbent. The phenomena such as intraparticle diffusion, a mass transfer external resistance and axial dispersion effects were out of considerations. Some of the models parameters were experimentally determined (rho(B), epsilon, u(0), C(0)) and the others were evaluated on the bases of the experimental data (k(a1), k(a2)). The unique fitting parameter in all models was the adsorption kinetic constant. The identification procedure was based on the least square statistical method. Simulation results show that the models describe well a copper ions sorption process in a fixed bed column. The used models can be considered as useful tools for adsorption process design and optimization in fixed bed column by using algae biomass of Sargassum sp. as an adsorbent. PMID:17706867

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

SciTech Connect

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

2015-11-05

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

3. 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.

4. Underground Mathematics

ERIC Educational Resources Information Center

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…

5. Evaluation of alternatives for dysfunctional double lumen central venous catheters using a two-compartmental mathematical model for different solutes.

PubMed

Van Canneyt, Koen; Van Biesen, Wim; Vanholder, Raymond; Segers, Patrick; Verdonck, Pascal; Eloot, Sunny

2013-01-01

Double lumen (DL) central venous catheters (CVC) often suffer from thrombosis, fibrin sheet formation, and/or suction towards the vessel wall, resulting in insufficient blood flow during hemodialysis. Reversing the catheter connection often restores blood flows, but will lead to higher recirculation. Single lumen (SL) CVCs have often fewer flow problems, but they inherently have some degree of recirculation. To assist bedside clinical decision making on optimal catheter application, we investigated mathematically the differences in dialysis adequacy using different modes of access with CVCs. A mathematical model was developed to calculate reduction ratio (RR) and total solute removal (TSR) of urea, methylguanidine (MG), beta-2-microglobulin (β2M), and phosphate (P) during different dialysis scenarios: 4-h dialysis with a well-functioning DL CVC (DL-normal, blood flow QB 350 ml/min), dysfunctional DL CVC (DL-low flow, QB 250), reversed DL CVC (DL-reversed, QB 350, recirculation  R = 10%) and 12 Fr SL CVC (effective QB 273).  With DL-normal as reference, urea RR was decreased by 3.5% (DL-reversed), 13.0% (SL), and 15.6% (DL-low flow), while urea TSR was decreased by 3.3% (DL-reversed), 13.2% (SL), and 13.5% (DL-low flow). The same trend was found for MG and P. However, β2M RR decreased only 1.5% with SL CVC although TSR decrease was 17.2%, while RR decreased 21.1% with DL-low flow although TSR decrease was only 4.9%. In the case of dysfunctional DL CVCs, reversing the catheter connection and restoring the blood flow did not impair TSR, with 10% recirculation. The SL CVC showed suboptimal TSR results that were similar to those of the dysfunctional DL CVC. PMID:23280082

6. Use of Mathematical Models to Generate Alternative Solutions to Water Resources Planning Problems

Chang, Shoou-Yuh; Brill, E. Downey, Jr.; Hopkins, Lewis D.

1982-02-01

An optimization model is generally not a perfect representation of a complex real world planning problem. Optimization models, however, can be used to generate alternatives that are good and different so that analysts and decision makers can examine a wide range of alternatives to gain insight and understanding. Modeling to generate alternatives (MGA) techniques have been designed to serve this purpose. This paper provides a preliminary assessment of the capabilities of the Hop, Skip, Jump (HSJ) method, a random method, and a branch and bound/screening (BBS) method for generating good and different alternative solutions. These three methods are illustrated using an example water resources planning problem represented by a mixed integer programing model. Each method yields sets of alternatives that are different from each other, but for each method the alternatives are different in different ways. Given that all three methods are efficient, it may be most fruitful to use more than one method and thereby to consider alternatives that are not only different, but different in different ways.

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

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.

8. Mathematical analysis of the Saint-Venant-Hirano model and numerical solution by path-conservative methods.

Stecca, Guglielmo; Siviglia, Annunziato; Blom, Astrid

2014-05-01

synchronous approach, by which all the variables are updated simultaneously. The non-conservative problem which stems from the developed matrix-vector formulation is solved using path-conservative methods. We perform numerical applications by comparison with the above linearised solutions and with the data from laboratory experiments. Results show that our solution approach is robust, general and accurate. References - Hirano, M. (1971), River bed degradation with armoring, Trans. Jpn. Soc. Civ. Eng., (3), 194-195. - Hirano, M. (1972), Studies on variation and equilibrium state of a river bed composed of nonuniform material, Trans. Jpn. Soc. Civ. Eng., (4), 128-129. - Stecca, G., A. Siviglia, and A. Blom, Mathematical analysis of the Saint-Venant-Hirano model for mixed-sediment morphodynamics, Submitted to Water Resources Research

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

ERIC Educational Resources Information Center

Reusser, Kurt; And Others

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

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

PubMed Central

Schneider, Hans-Jörg

2015-01-01

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

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

USGS Publications Warehouse

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

1987-01-01

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

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

SciTech Connect

Abraham Sternlieb

2010-06-25

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

13. Mathematical Perspectives

SciTech Connect

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

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

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.

15. Properties of K1-xLixTaO3 Solid Solutions; First-Principles Computations and Comparison with Experiments

Prosandeev, Serguei A.; Cockayne, Eric; Burton, Benjamin; Trepakov, Vladimir; Kapphan, Siegmar; Savinov, Maxim; Jastrabik, Lubomir

2002-11-01

Experiments on K0.957Li0.043TaO3 samples indicate two different relaxation processes (π and π/2). First-principles computations clarify the natures of these relaxations, and yield good agreement with experiment.

16. Mathematical modeling of molecular diffusion through mucus

PubMed Central

Cu, Yen; Saltzman, W. Mark

2008-01-01

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

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

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.

18. A correspondence principle

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.

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

ERIC Educational Resources Information Center

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

2013-01-01

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

20. Mathematics Projects Handbook.

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.

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

2. 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…

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

ERIC Educational Resources Information Center

Knoche, Wilhelm; Rees, Norman H.

1984-01-01

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

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

NASA Technical Reports Server (NTRS)

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.

5. Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in non-linear optics

Webb, Garry; Sørensen, Mads Peter; Brio, Moysey; Zakharian, Aramis R.; Moloney, Jerome V.

2004-04-01

The vector Maxwell equations of non-linear optics coupled to a single Lorentz oscillator and with instantaneous Kerr non-linearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore the properties of Maxwell’s equations in non-linear optics, without resorting to the commonly used non-linear Schrödinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to non-linear sideband wave interactions. This is important in femto-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field E, in terms of the canonical variables, with possible multiple real roots for E. In order to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether’s theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr non-linearity, are shown to reduce to a single ordinary differential equation for the variable y= E2, where E is the electric field intensity. The differential equation has solutions y= y( ξ), where ξ= z- st is the traveling wave variable and s is the velocity of the wave. These solutions exhibit new phenomena not obtainable by the NLS approximation. The characteristics of the solutions depends on the values of the wave velocity s and the energy integration constant ɛ. Both smooth periodic traveling waves and

6. Toddlers' Opportunities to Learn Mathematics

ERIC Educational Resources Information Center

Bjorklund, Camilla

2008-01-01

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

7. 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…

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

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

2016-06-01

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.

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

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.

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

SciTech Connect

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

2009-04-15

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

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

PubMed

McIntosh, Grant J

2013-10-28

A kinetic model of silicate oligomerization in water, up to and including tetramer formation, has been compiled exclusively from rate constants derived from transition state theory based on either quantum chemical data (derived under a hybrid solvation framework) for all bond breaking-forming reactions, or using empirically-based approximated pKa's and diffusion coefficients for rate constants of pH-based and bimolecular steps. The rate constants, based on an exhaustive search of all relevant elementary steps, form the basis of our kinetic model; numerical solution of the resulting rate equations allows the simulation of the reaction system, given a set of initial conditions and with almost no restriction on concentrations, pH, or reaction time, in a matter of only minutes. The model, which we believe contains all possible isomers of both neutral and singly anionic clusters, has been extensively benchmarked and reproduces a number of important experimental observations in the range pH ≈ 4-10. In particular, it provides a good description of the dominant products; product yields and reaction times (also as a function of pH) are in agreement with experiment; the linear relationship between the log of the rate of silica dissolution and pH is well reproduced; the origin of silica scaling naturally arises; and we can also simulate the observed fourth order dependence of the rate of monomer consumption on H4SiO4 concentration. This should be a general approach to exploring solution phase chemistry, and could be a useful complement to more conventional molecular dynamics and Monte Carlo modelling approaches in understanding complex reaction networks in solution. PMID:24026420

12. The mathematical principles and design of the NAIS - a spectrometer for the measurement of cluster ion and nanometer aerosol size distributions

Mirme, S.; Mirme, A.

2011-12-01

The paper describes the Nanometer aerosol and Air Ion Spectrometer (NAIS) - a multi-channel aerosol instrument capable of measuring the distribution of ions (charged particles and cluster ions) of both polarities in the electric mobility range from 3.2 to 0.0013 cm2 V-1 s-1 and the distribution of aerosol particles in the size range from 2.0 to 40 nm. We introduce the principles of design, data processing and spectrum deconvolution of the instrument.

13. The mathematical principles and design of the NAIS - a spectrometer for the measurement of cluster ion and nanometer aerosol size distributions

Mirme, S.; Mirme, A.

2013-04-01

The paper describes the Neutral cluster and Air Ion Spectrometer (NAIS) - a multichannel aerosol instrument capable of measuring the distribution of ions (charged particles and cluster ions) of both polarities in the electric mobility range from 3.2 to 0.0013 cm2 V-1 s-1 and the distribution of aerosol particles in the size range from 2.0 to 40 nm. We introduce the principles of design, data processing and spectrum deconvolution of the instrument.

14. Principles of Early Development of Karst Conduits Under Natural and Man-Made Conditions Revealed by Mathematical Analysis of Numerical Models

Dreybrodt, Wolfgang

1996-04-01

Numerical models of the enlargement of primary fissures in limestone by calcite aggressive water show a complex behavior. If the lengths of the fractures are large and hydraulic heads are low, as is the case in nature, dissolution rates at the exit of the channel determine its development by causing a slow increase of water flow, which after a long gestation time by positive feedback accelerates dramatically within a short time span. Mathematical analysis of simplified approximations yields an analytical expression for the breakthrough time, when this happens, in excellent agreement with the results of a numerical model. This expression quantifies the geometrical, hydraulic, and chemical parameters determining such karst processes. If the lengths of the enlarging channels are small, but hydraulic heads are high, as is the case for artificial hydraulic structures such as dams, it is the widening at the entrance of the flow path which determines the enlargement of the conduit. Within the lifetime of the dam this can cause serious water losses. This can also be explained by mathematical analysis of simplified approximations which yield an analytical threshold condition from which the safety of a dam can be judged. Thus in both cases the dynamic processes of karstification are revealed to gain a deeper understanding of the early development of karst systems. As a further important result, one finds that minimum conditions, below which karstification cannot develop, do not exist.

15. The mechanism of the initial step of germanosilicate formation in solution: a first-principles molecular dynamics study.

PubMed

Trinh, Thuat T; Rozanska, Xavier; Delbecq, Françoise; Tuel, Alain; Sautet, Philippe

2016-06-01

The condensation reactions between Ge(OH)4 and Si(OH)4 units in solution are studied to understand the mechanism and stable species during the initial steps of the formation process of Ge containing zeolites under basic conditions. The free energy of formation of (OH)3Ge-O-Ge-(OH)2O(-), (OH)3Si-O-Si-(OH)2O(-), (OH)3Ge-O-Si-(OH)2O(-) and (OH)3Si-O-Ge-(OH)2O(-) dimers is calculated with ab initio molecular dynamics and thermodynamic integration, including an explicit description of the water solvent molecules. Calculations show that the attack of the conjugated base (Ge(OH)3O(-) and Si(OH)3O(-)) proceeds with a smaller barrier at the Ge center. In addition, the formation of the pure germanate dimer is more favorable than that of the germano-silicate structure. These results explain the experimental observation of Ge-Ge and Si-Ge dimer species in solutions, with a few Si-Si ones. PMID:27172391

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

PubMed

Ma, Changru; Pietrucci, Fabio; Andreoni, Wanda

2015-07-14

Aqueous monoethanolamine (MEA) solution is commonly used for post-combustion carbon capture via chemical absorption. Extensive research has been carried out to characterize both uptake and release of carbon dioxide (CO2), with the aim of improving process performance. However, an intensive research is still needed on fundamental aspects of the key chemical reactions, to achieve a comprehensive understanding of the cyclic process at the microscopic level and a quantitative assessment. We present several ab initio simulations of MEA solutions at a concentration of 30 wt %-the current standard in the industry-and study the dynamics of key multistep chemical reactions, using the metadynamics technique. Pathways for the entire cycle are investigated and characterized in terms of related free-energy and enthalpy barriers, and of the accompanying variations in both structural and electronic properties. The results of this study lead us to propose, among competing processes, an unforeseen scenario in which the zwitterion acts as sn intermediate not only of CO2 uptake, in the form of carbamate, but also of its release. Rate-limiting steps are the formation of the zwitterion for the former and MEAH(+) deprotonation for the latter. Water is shown to play a multifaceted role, which is crucial in determining the development and the energetics of each step of the reactions. The level of comprehension here achieved for MEA should help defining a strategy for solvent optimization. PMID:26575756

17. Structural studies of TiC{sub 1−x}O{sub x} solid solution by Rietveld refinement and first-principles calculations

SciTech Connect

Jiang, Bo Hou, Na; Huang, Shanyan; Zhou, Gege; Hou, Jungang; Cao, Zhanmin; Zhu, Hongmin

2013-08-15

The lattice parameters, structural stability and electronic structure of titanium oxycarbides (TiC{sub 1−x}O{sub x}, 0≤x≤1) solid solution were investigated by Rietveld refinement and first-principles calculations. Series of TiC{sub 1−x}O{sub x} were precisely synthesized by sintering process under the vacuum. Rietveld refinement results of XRD patterns show the properties of continuous solid solution in TiC{sub 1−x}O{sub x} over the whole composition range. The lattice parameters vary from 0.4324 nm to 0.4194 nm decreasing with increasing oxygen concentration. Results of first-principles calculations reveal that the disorder C/O structure is stable than the order C/O structure. Further investigations of the vacancy in Ti{sub 1−Va}(C{sub 1−x}O{sub x}){sub 1−Va} solid solution present that the structure of vacancy segregated in TiO-part is more stable than the disorder C/O structure, which can be ascribed to the Ti–Ti bond across O-vacancy and the charge redistributed around Ti-vacancy via the analysis of the electron density difference plots and PDOS. - Graphical abstract: XRD of series of titanium oxycarbides (TiC{sub 1−x}O{sub x}, 0≤x≤1) solid solution prepared by adjusting the proportion of TiO in the starting material. Highlights: • Titanium oxycarbides were obtained by sintering TiO and TiC under carefully controlled conditions. • Rietveld refinement results show continuous solid solution with FCC structure in TiC{sub 1−x}O{sub x}. • The disorder C/O structure is stable than the order C/O structure. • Introduction of vacancy segregated in TiO-part is more stable than disorder C/O structure. • Ti–Ti bond across O-vacancy and the charge redistributed around Ti-vacancy enhance structural stability.

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

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

2016-01-01

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

19. Making Mathematical Connections by Constructing Tetrahedra

ERIC Educational Resources Information Center

Bergner, Jennifer A.; Groth, Randall E.

2005-01-01

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

20. 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.

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

PubMed

Munro, Robin E J; Guo, Yike

2009-01-01

Analytical workflow technology, sometimes also called data pipelining, is the fundamental component that provides the scalable analytical middleware that can be used to enable the rapid building and deployment of an analytical application. Analytical workflows enable researchers, analysts and informaticians to integrate and access data and tools from structured and non-structured data sources so that analytics can bridge different silos of information; compose multiple analytical methods and data transformations without coding; rapidly develop applications and solutions by visually constructing analytical workflows that are easy to revise should the requirements change; access domain-specific extensions for specific projects or areas, for example, text extraction, visualisation, reporting, genetics, cheminformatics, bioinformatics and patient-based analytics; automatically deploy workflows directly into web portals and as web services to be part of a service-oriented architecture (SOA). By performing workflow building, using a middleware layer for data integration, it is a relatively simple exercise to visually design an analytical process for data analysis and then publish this as a service to a web browser. All this is encapsulated into what can be referred to as an 'Embedded Analytics' methodology which will be described here with examples covering different scientifically focused data analysis problems. PMID:19597790

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

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.

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

SciTech Connect

Khots, Boris; Khots, Dmitriy

2014-12-10

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

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

PubMed

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

2015-07-21

Sensitizing wide band gap photo-functional materials under visible-light irradiation is an important task for efficient solar energy conversion. Although nitrogen doping into anatase TiO2 has been extensively studied for this purpose, it is hard to increase the nitrogen content in anatase TiO2 because of the aliovalent nitrogen substituted for oxygen, leading to the formation of secondary phases or defects that hamper the migration of photoexcited charge carriers. In this paper, electronic structures of (TiO2)1-x(TaON)x (0 ≤ x ≤ 1) solid solutions, in which the stoichiometry is satisfied with the co-substitution of Ti for Ta along with O for N, are investigated within the anatase crystal structure using first-principles calculations. Our computational results show that the solid solutions have substantially narrower band gaps than TiO2, without introducing any localized energy states in the forbidden gap. In addition, in comparison with the pristine TiO2, the solid solution has a direct band gap when the content of TaON exceeds 0.25, which is advantageous to light absorption. The valence band maximum (VBM) of the solid solutions, which is mainly composed of N 2p states hybridized with O 2p, Ti 3d or Ta 5d orbitals, is higher in energy than that of pristine anatase TiO2 consisting of non-bonding O 2p states. On the other hand, incorporating TaON into TiO2 causes the formation of d-d bonding states through π interactions and substantially lowers the conduction band minimum (CBM) because of the shortened distance between some metal atoms. As a result, the anatase (TiO2)1-x(TaON)x is expected to become a promising visible-light absorber. In addition, some atomic configurations are found to possess exceptionally narrow band gaps. PMID:26096698

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

PubMed Central

2013-01-01

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

6. Mathematics Underground

ERIC Educational Resources Information Center

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

7. The solvation structure of Mg ions in dichloro complex solutions from first-principles molecular dynamics and simulated X-ray absorption spectra.

PubMed

Wan, Liwen F; Prendergast, David

2014-10-15

The knowledge of Mg solvation structure in the electrolyte is requisite to understand the transport behavior of Mg ions and their dissolution/deposition mechanism at electrolyte/electrode interfaces. In the first established rechargeable Mg-ion battery system [D. Aurbach et al. Nature 2000, 407, 724], the electrolyte is of the dichloro complex (DCC) solution family, Mg(AlCl2BuEt)2/THF, resulting from the reaction of Bu2Mg and EtAlCl2 with a molar ratio of 1:2. There is disagreement in the literature regarding the exact solvation structure of Mg ions in such solutions, i.e., whether Mg(2+) is tetra- or hexacoordinated by a combination of Cl(-) and THF. In this work, theoretical insight into the solvation complexes present is provided based on first-principles molecular dynamics simulations (FPMD). Both Mg monomer and dimer structures are considered in both neutral and positively charged states. We found that, at room temperature, the Mg(2+) ion tends to be tetracoordinated in the THF solution phase instead of hexacoordinated, which is the predominant solid-phase coordination. Simulating the X-ray absorption spectra (XAS) at the Mg K-edge by sampling our FPMD trajectories, our predicted solvation structure can be readily compared with experimental measurements. It is found that when changing from tetra- to hexacoordination, the onset of X-ray absorption should exhibit at least a 1 eV blue shift. We propose that this energy shift can be used to monitor changes in the Mg solvation sphere as it migrates through the electrolyte to electrolyte/electrode interfaces and to elucidate the mechanism of Mg dissolution/deposition. PMID:25243732

ERIC Educational Resources Information Center

Mielke, Paul T., Ed.; And Others

This article presents suggestions to the beginning teacher of college mathematics. It is felt that he should have a knowledge of: (1) the general character of mathematics and its place in our culture, (2) mathematics as a language, (3) mathematics as an art, and (4) mathematics as a science. Suggested principles include: (1) never introduce a new…

9. Mathematics Projects Handbook. Third Edition.

ERIC Educational Resources Information Center

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…

10. Mathematics Projects Handbook. Second Edition.

ERIC Educational Resources Information Center

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…

11. English for Students of Mathematics.

ERIC Educational Resources Information Center

Bensoussan, Marsha; Golan, Jonathan

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

12. An Examination of Gender Differences in Today's Mathematics Classrooms: Exploring Single-Gender Mathematics Classrooms.

ERIC Educational Resources Information Center

Dunlap, Celeste Elizabeth

Much research identifies a gender gap in mathematics and some research points to single-gender mathematics classrooms as a solution to the mathematics gender divide. A 7-week study was conducted in which 5th grade students (N=50) were organized into two mathematics classes. The goal was to examine whether single-gender mathematics classes had an…

13. 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…

14. 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…

15. Mathematics, Anyone?

ERIC Educational Resources Information Center

Reys, Robert; Reys, Rustin

2011-01-01

In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…

16. 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.)

17. The Principle of General Tovariance

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

2008-06-01

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

18. 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…

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

ERIC Educational Resources Information Center

Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

2010-01-01

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

20. Moving from Rhetoric to Praxis: Issues Faced by Teachers in Having Students Consider Multiple Solutions for Problems in the Mathematics Classroom

ERIC Educational Resources Information Center

Silver, Edward A.; Ghousseini, Hala; Gosen, Dana; Charalambous, Charalambos; Strawhun, Beatriz T. Font

2005-01-01

Despite general agreement that students should consider more than one way to solve a complex mathematics problem, this practice is rarely observed in U.S. classrooms. In this paper, we examine data that trace the year-long professional development experience of 12 veteran teachers of middle grades mathematics--experienced users of a…

1. On Fences, Forms and Mathematical Modeling

ERIC Educational Resources Information Center

Lege, Jerry

2009-01-01

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

2. 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…

3. 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)…

4. Improving Mathematics Education: Resources for Decision Making.

ERIC Educational Resources Information Center

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

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

5. Bernoulli's Principle

ERIC Educational Resources Information Center

Hewitt, Paul G.

2004-01-01

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

6. Compressed modes for variational problems in mathematics and physics

PubMed Central

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

2013-01-01

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

7. Identification of the noise using mathematical modelling

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.

8. Mathematics and Measurement

PubMed Central

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

2001-01-01

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

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

PubMed

Wagner, Roy

2009-04-01

This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language. PMID:19831223

10. Mathematical foundations of biomechanics.

PubMed

Niederer, Peter F

2010-01-01

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

11. Mathematical Geology.

ERIC Educational Resources Information Center

Jones, Thomas A.

1983-01-01

Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)

12. Mathematic Terminology.

ERIC Educational Resources Information Center

Hanh, Vu Duc, Ed.

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

13. Mathematics disorder

MedlinePlus

14. Mathematical principle of planar Z-plasty.

PubMed

Chu, D Y

2000-01-01

To extend the work of precursors attempting to use Z-plasties with angles that have arbitrary degrees and may or may not be equal in size, a comprehensive study was done to clarify and simplify the correlation among the angles, limbs, and diagonals of the geometrical construction of Z-plasties. In geometry, the truth of a proposition must be proved; it is a question to which the answer must be found. By law and formula, a ternary trigonometric equation was derived from a simplified geometric diagram by a trigonometric approach. A procedure declaration accompanies this formula; neither was previously mentioned in the literature. PMID:10626978

15. Rainforest Mathematics

ERIC Educational Resources Information Center

Kilpatrick, Jeremy

2014-01-01

This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

16. 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…

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

SciTech Connect

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

2010-02-11

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

18. Mathematics and the Learning Cycle: How the Brain Works as It Learns Mathematics

ERIC Educational Resources Information Center

Zambo, Ronald; Zambo, Debby

2007-01-01

The National Council of Teachers of Mathematics (NCTM) poses constructivist ideas in its "Principles and Standards for School Mathematics" (2000). NCTM supports mathematics instruction that takes a developmental perspective; starts and builds on what children know; and leads children to construct relational understanding, problem-solving…

19. Theoretical Mathematics

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.

20. 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…

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

Sternlieb, Abraham

2013-04-01

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

2. Experimental Mathematics and Mathematical Physics

SciTech Connect

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.

3. Principles of optical-data processing techniques

NASA Technical Reports Server (NTRS)

Shulman, A. R.

1968-01-01

Document presents optical-data processing information on a level which will convey the basic principles involved to those having a general technical background. Mathematical discussions are included but are not required for a basic understanding.

4. Mathematics Education.

ERIC Educational Resources Information Center

Langbort, Carol, Ed.; Curtis, Deborah, Ed.

2000-01-01

The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…

5. Technical Mathematics.

ERIC Educational Resources Information Center

Flannery, Carol A.

This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

6. Innovative Mathematics.

ERIC Educational Resources Information Center

Siskiyou County Superintendent of Schools, Yreka, CA.

The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…

7. Mathematics Scrapbook

ERIC Educational Resources Information Center

Prochazka, Helen

2004-01-01

One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…

8. Buridan's Principle

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.

9. Principled Narrative

ERIC Educational Resources Information Center

MacBeath, John; Swaffield, Sue; Frost, David

2009-01-01

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

10. Mathematical Geology.

ERIC Educational Resources Information Center

McCammon, Richard B.

1979-01-01

The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)

11. Mathematics disorder

MedlinePlus

The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.

12. Mathematics Detective.

ERIC Educational Resources Information Center

Johnson, Jerry

1997-01-01

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

13. Mathematical Games

ERIC Educational Resources Information Center

Gardner, Martin

1978-01-01

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

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

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.

15. Mathematics of Experimentally Generated Chemoattractant Gradients.

PubMed

Postma, Marten; van Haastert, Peter J M

2016-01-01

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

16. 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…

17. Problems of Mathematical Finance by Stochastic Control Methods

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.

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

ERIC Educational Resources Information Center

Uebelacker, James W.

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

19. Mathematical vistas

SciTech Connect

Malkevitch, J. ); McCarthy, D. )

1990-01-01

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

20. Quantum Mechanics and the Principle of Least Radix Economy

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.

1. Some unsolved problems in discrete mathematics and mathematical cybernetics

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.

2. First-principles investigation of the elastic, electronic, and thermodynamic properties of a nitrogen-doped (Ti0.75W0.25)C solid solution

Gao, Zhe; Kang, Shinhoo

2013-03-01

(Ti00.75W0.25)C and (Ti0.75W0.25)(C0.75N0.25) are the major components of hard materials used, for example, in cutting tools. The material properties of these components were investigated using first principle methods. The elastic constants and moduli indicated that (Ti0.75W0.25)C was expected to yield good mechanical properties, with the exception of a poor shear modulus, at working temperatures, around 800 °C (1073 K), relevant to cutting tool operation. The shear modulus worsened upon substitution of nitrogen for carbon due to unfavorable shifts in the material electronic and vibrational structures. From a thermodynamic perspective, (Ti0.75W0.25)(CN0.25) was more stable due to a lower free energy of formation at T<2000 K.

3. 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…

4. 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…

5. Towards a simple mathematical theory of citation distributions.

PubMed

Katchanov, Yurij L

2015-01-01

The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles. PMID:26558180

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

ERIC Educational Resources Information Center

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

2014-01-01

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

7. Mathematical Visualization

ERIC Educational Resources Information Center

Rogness, Jonathan

2011-01-01

Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

8. Learning Mathematics.

ERIC Educational Resources Information Center

Lapointe, Archie E.; And Others

In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…

9. Relevant Mathematics.

ERIC Educational Resources Information Center

Catterton, Gene; And Others

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

10. 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.…

11. Optical absorption and band gap reduction in (Fe1-xCrx)2O3 solid solutions: A first-principles study

SciTech Connect

Wang, Yong; Lopata, Kenneth A.; Chambers, Scott A.; Govind, Niranjan; Sushko, Petr V.

2013-12-02

We provide a detailed theoretical analysis of the character of optical transitions and band gap reduction in (Fe1-xCrx)2O3 solid solutions using extensive periodic model and embedded cluster calculations. Optical absorption bands for x = 0.0, 0.5, and 1.0 are assigned on the basis of timedependent density functional theory (TDDFT) calculations. A band-gap reduction of as much as 0.7 eV with respect to that of pure α-Fe2O3 is found. This result can be attributed to predominantly two effects: (i) the higher valence band edge for x ≈ 0.5, as compared to those in pure α-Fe2O3 and α-Cr2O3, and, (ii) the appearance of Cr  Fe d–d transitions in the solid solutions. Broadening of the valence band due to hybridization of the O 2p states with Fe and Cr 3d states also contributes to band gap reduction.

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

PubMed

Sassaroli, E; O'Neill, B E

2014-11-21

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

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

Sassaroli, E.; O'Neill, B. E.

2014-11-01

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

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

PubMed Central

Sassaroli, E; O’Neill, B E

2014-01-01

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

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

PubMed Central

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

2015-01-01

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

16. Applying the four principles.

PubMed

Macklin, R

2003-10-01

Gillon is correct that the four principles provide a sound and useful way of analysing moral dilemmas. As he observes, the approach using these principles does not provide a unique solution to dilemmas. This can be illustrated by alternatives to Gillon's own analysis of the four case scenarios. In the first scenario, a different set of factual assumptions could yield a different conclusion about what is required by the principle of beneficence. In the second scenario, although Gillon's conclusion is correct, what is open to question is his claim that what society regards as the child's best interest determines what really is in the child's best interest. The third scenario shows how it may be reasonable for the principle of beneficence to take precedence over autonomy in certain circumstances, yet like the first scenario, the ethical conclusion relies on a set of empirical assumptions and predictions of what is likely to occur. The fourth scenario illustrates how one can draw different conclusions based on the importance given to the precautionary principle. PMID:14519836

17. Meeting the Curricular Needs of Academically Low-Achieving Students in Middle Grade Mathematics

ERIC Educational Resources Information Center

Woodward, John; Brown, Cyrus

2006-01-01

An important component of the National Council of Teachers of Mathematics Standards is the equity principle: All students should have access to a coherent, challenging mathematics curriculum. Many in the mathematics reform community have maintained that this principle can be achieved through one well-designed curriculum. However, the extant…

18. 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…

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

PubMed Central

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

2015-01-01

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

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

2008-09-01

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

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

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

2016-02-01

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

2. [UO2(NH3)5]Br2·NH3: synthesis, crystal structure, and speciation in liquid ammonia solution by first-principles molecular dynamics simulations.

PubMed

Woidy, Patrick; Bühl, Michael; Kraus, Florian

2015-04-28

Pentaammine dioxido uranium(VI) dibromide ammonia (1/1), [UO2(NH3)5]Br2·NH3, was synthesized in the form of yellow crystals by the reaction of uranyl bromide, UO2Br2, with dry liquid ammonia. The compound crystallizes orthorhombic in space group Cmcm and is isotypic to [UO2(NH3)5]Cl2·NH3 with a = 13.2499(2), b = 10.5536(1), c = 8.9126(1) Å, V = 1246.29(3) Å(3) and Z = 4 at 123 K. The UO2(2+) cation is coordinated by five ammine ligands and the coordination polyhedron can be best described as pentagonal bipyramid. Car-Parrinello molecular dynamics simulations are reported for [UO2(NH3)5](2+) in the gas phase and in liquid NH3 solution (using the BLYP density functional). According to free-energy simulations, solvation by ammonia has only a small effect on the uranyl-NH3 bond strength. PMID:25797497

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

NASA Technical Reports Server (NTRS)

Zak, M. A.

1982-01-01

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

4. Learning to Assess and Assessing to Learn: A Descriptive Study of a District-Wide Mathematics Assessment Implementation

ERIC Educational Resources Information Center

Ringer, Catharina W.

2013-01-01

In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…

5. Principles of Quantum Mechanics

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

6. 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…

7. Mathematizing Darwin.

PubMed

Edwards, A W F

2011-03-01

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

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

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

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

9. Minimum Principles in Motor Control.

PubMed

Engelbrecht, Sascha E.

2001-06-01

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

10. 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.

11. Generating Problems from Problems and Solutions from Solutions

ERIC Educational Resources Information Center

Arcavi, Abraham; Resnick, Zippora

2008-01-01

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

12. The Bicentennial of American Mathematics Journals

ERIC Educational Resources Information Center

Zitarelli, David E.

2005-01-01

This is the story of the first American mathematics journal. According to its title page, the journal was "adapted to the present state of learning in America" and "designed to inspire youth with the love of mathematical knowledge, by alluring their attentions to the solutions of pleasant and curious questions".

13. Mathematics and Molecules: Exploring Connections via Programming.

ERIC Educational Resources Information Center

Ploger, Don; Carlock, Margaret

1996-01-01

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

14. 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…

15. 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…

16. Exposomics: mathematics meets biology.

PubMed

Vineis, Paolo

2015-11-01

Although 'exposome' research has started to appear, and the concept is fascinating, we still have little proof-of-principle. This issue of Mutagenesis reports a few examples of exposome research, showing that the approach is providing the first results. In this Commentary, I develop the example of epigenome-wide methylation studies related to smoking as a success story, that fits well with previous research in humans and in vitro on mechanisms of carcinogenesis, and also with conceptual models such as Cairns' model based on asymmetric division of stem cells. The field of exposomics merges different disciplines, notably biology and mathematics, but also the evolutionary theory, and can possibly lead to interesting breakthroughs in the next years. PMID:26371206

17. Slow continuous ultrafiltration with bound solute dialysis.

PubMed

Patzer, John F; Safta, Stefan A; Miller, Richard H

2006-01-01

Bound solute dialysis (BSD), often referred to as "albumin dialysis" (practiced clinically as the molecular adsorbents recirculating system, MARS, or single-pass albumin dialysis, SPAD) or "sorbent dialysis" (practiced clinically as the charcoal-based Biologic-DT), is based upon the thermodynamic principle that the driving force for solute mass transfer across a dialysis membrane is the difference in free solute concentration across the membrane. The clinically relevant practice of slow continuous ultrafiltration (SCUF) for maintenance of patients with liver failure is analyzed in conjunction with BSD. The primary dimensionless operating parameters that describe SCUF-BSD include (1) beta, the dialysate/blood binder concentration ratio; (2) kappa, the dialyzer mass transfer/blood flow rate ratio; (3) alpha, the dialysate/blood flow rate ratio; and, (4) gamma, the ultrafiltration/blood flow rate ratio. Results from mathematical modeling of solute removal during a single pass through a dialyzer and solute removal from a one-compartment model indicate that solute removal is remarkably insensitive to gamma. Solute removal approaches an asymptote (improvement in theoretical clearance over that obtainable with no binder in the dialysate) with increasing beta that is dependent on kappa and independent of alpha. The amount of binder required to approach the asymptote decreases with increasing solute-binder equilibrium constant, i.e., more strongly bound solutes require less binder in the dialysate. The results of experimental observations over a range of blood flow rates, 100 to 180 mL/min, dialysate flow rates, 600 to 2150 mL/h, ultrafiltration rates, 0 to 220 mL/h, and dialysate/blood albumin concentration ratios, beta = 0.01 to 0.04, were independently predicted remarkably well by the one-compartment model (with no adjustable parameters) based on BSD principles. PMID:16436890

18. Mathematical Modeling and the Presidential Election.

ERIC Educational Resources Information Center

Witkowski, Joseph C.

1992-01-01

Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

19. Examining Classroom Interactions & Mathematical Discourses

ERIC Educational Resources Information Center

Grant, Melva R.

2009-01-01

This investigation examined interactions in three classrooms to determine how they influenced Discourses related to mathematics learning and teaching. Mathematics education literature suggests that effective mathematics instruction includes mathematical Discourses. However, effective mathematical Discourses within mathematics classrooms vary…

20. 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…

1. The Shrinking Curriculum: Principles, Problems, and Solutions.

ERIC Educational Resources Information Center

Connelly, F. Michael; Enns, Robin J.

1979-01-01

Basing their remarks on the final report of the Curriculum Task Force of the Commission on Declining Enrollments in Ontario (CODE), the authors present projections of enrollment decline on Ontario's curriculum policy and summarize a number of the task force recommendations to the Ontario government. (Author/MLF)

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

Nikkhah Shirazi, Armin

2014-03-01

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

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

Lopez, Robert

2001-10-01

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

4. Mathematics and Cognition

Kasturirangan, Rajesh

2014-07-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

6. Least Action Principle on an Air Table

ERIC Educational Resources Information Center

Provost, J. P.

1975-01-01

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

7. Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

PubMed

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

2016-01-01

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

8. Transcranial Electrical Neuromodulation Based on the Reciprocity Principle

PubMed Central

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

2016-01-01

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

9. New computer system simplifies programming of mathematical equations

NASA Technical Reports Server (NTRS)

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

1966-01-01

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

10. An Exploration of Mathematical Problem-Solving Processes.

ERIC Educational Resources Information Center

Webb, Norman

The problem-solving strategies used by tenth-grade students in the solution of mathematical problems were investigated. Forty students selected from four high schools were given pretests generating sixteen scores related to mathematics achievement, attitude toward mathematics, and other ability measures. These students were then asked to solve…

11. 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…

12. Mathematical Language and Advanced Mathematics Learning

ERIC Educational Resources Information Center

Ferrari, Pier Luigi

2004-01-01

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

13. 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…

14. Mathematics for Life: Sustainable Mathematics Education

ERIC Educational Resources Information Center

Renert, Moshe

2011-01-01

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

15. 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…

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

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

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

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

ERIC Educational Resources Information Center

Patkin, Dorit; Gazit, Avikam

2011-01-01

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

18. Hamilton's principle in stochastic mechanics

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

19. A mathematical model of a computational problem solving system

Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan

2015-05-01

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

20. Mathematics education for social justice

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

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

ERIC Educational Resources Information Center

Fridriksson, Thor; Stewart, David A.

1988-01-01

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

2. 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…

3. Mathematics and Living Things. Teacher's Commentary. Revised Edition.

ERIC Educational Resources Information Center

Faber, Norman J.; And Others

Mathematics and Living Things (MALT) is designed for grade eight to enrich and supplement the usual courses of instruction. MALT utilizes exercises in biological science to derive data through which mathematical concepts and principles may be introduced and expanded. The Teacher's Commentary includes suggestions for instruction, a list of needed…

4. Teaching Mathematics to Chemistry Students with Symbolic Computation

ERIC Educational Resources Information Center

Ogilvie, J. F.; Monagan, M. B.

2007-01-01

The teaching of mathematics courses to chemistry students that is strongly based on symbolic computation and allows an instructor to explore a topic or principle is reviewed. The mathematical software available, nominally for symbolic computation associated with numerical and graphical capabilities are highly developed and provides an invaluable…

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…

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

ERIC Educational Resources Information Center

Schooler, Susan Rodgers

2004-01-01

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

7. Mathematics 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…

8. Helping Continuation High School Student Become Successful in Mathematics

ERIC Educational Resources Information Center

Villegas, Ramon R.

2011-01-01

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

9. Mathematics 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…

10. Modern Mathematics for Elementary Teachers: A Laboratory Approach

ERIC Educational Resources Information Center

Callahan, John; And Others

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

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

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

2014-02-01

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

12. 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…

13. 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…

14. 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.

15. [Mathematical models of hysteresis

SciTech Connect

Mayergoyz, I.D.

1991-01-01

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

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

ERIC Educational Resources Information Center

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

2011-01-01

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

17. Transforming Primary Mathematics

ERIC Educational Resources Information Center

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…

18. Mathematical Epistemologies at Work.

ERIC Educational Resources Information Center

Noss, Richard

2002-01-01

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

19. It's all just mathematics

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.

20. 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…

1. Functioning Mathematically: 1

ERIC Educational Resources Information Center

Cain, David

2007-01-01

This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…

2. 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…

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

SciTech Connect

Zhu, G.; Lewandowski, A.

2012-11-01

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

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

Thomopoulos, Stelios C.; Braught, Grant

1996-10-01

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

5. Mathematical modelling in MHD technology

SciTech Connect

Scheindlin, A.E.; Medin, S.A. )

1990-01-01

The technological scheme and the general parameters of the commercial scale pilot MHD power plant are described. The characteristics of the flow train components and the electrical equipment are discussed. The basic ideas of the mathematical modelling of the processes and the devices operation in MHD systems are considered. The application of different description levels in computer simulation is analyzed and the examples of typical solutions are presented.

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

Mejjaoli, Hatem; Trimèche, Khalifa

2016-06-01

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

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

PubMed

2016-04-01

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

8. Classical Solution Thermodynamics: A Retrospective View.

ERIC Educational Resources Information Center

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

1985-01-01

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

9. Increasing the accuracy of measurements based on the solution of Pauli's quantum equation

Ermishin, Sergey; Korol, Alexandra

2013-05-01

There is a measurements principle that ensures the increase of accuracy of measurements based on redundant measurements. Main properties of the solution are: a discrete method with a surge of probability within the parent entity and comparison of the graph of the probability distribution for the diffraction grids with the graph of probability density function. Method based on the analog of Pauli equation solution. The method of electronic reference measurements with quantum computing applied to mathematical data processing allows to greatly increase the credibility and accuracy of measurements at low cost, which is confirmed by simulation.

10. 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…

11. 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…

12. 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…

13. 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…

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

ERIC Educational Resources Information Center

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

1979-01-01

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

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

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.

16. 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…

17. Preparatory Mathematics Programs in Departments of Mathematics.

ERIC Educational Resources Information Center

Lindberg, Karl

This paper reports on a survey of remedial mathematics programs offered at the college level. The paper is divided into five sections. Section I describes the sampling procedures used in the study. In Section II, the occurrence of remedial mathematics programs in the various types of institutions and some general characteristics of these programs…

18. Negotiation of Mathematical Meaning and Learning Mathematics.

ERIC Educational Resources Information Center

Voigt, Jorg

1994-01-01

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

19. Mathematical and information maintenance of biometric systems

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.

20. 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.

1. Energy principles in architectural design

SciTech Connect

Dean, E.

1981-01-01

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

2. Physical Principles of Evolution

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

3. Rural Mathematics Educator, 2002.

ERIC Educational Resources Information Center

Rural Mathematics Educator, 2002

2002-01-01

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

4. Mathematics. [SITE 2001 Section].

ERIC Educational Resources Information Center

Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.

This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics" (Kathy R. Autrey and Leigh…

5. Making Mathematics Culturally Relevant.

ERIC Educational Resources Information Center

Moyer, Patricia

2001-01-01

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

6. Creating Words in Mathematics

ERIC Educational Resources Information Center

Galligan, Linda

2016-01-01

A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…

7. Mathematics for Electronics.

ERIC Educational Resources Information Center

Clary, Joseph R.; Nery, Karen P.

This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…

8. Mathematics Teaching Today

ERIC Educational Resources Information Center

Martin, Tami S.; Speer, William R.

2009-01-01

This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

9. Mathematics and mysticism.

PubMed

Abraham, Ralph

2015-12-01

Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination. PMID:26278644

10. Making Mathematics Phenomenal

ERIC Educational Resources Information Center

Pratt, Dave

2012-01-01

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

11. Applying Mathematical Processes (AMP)

ERIC Educational Resources Information Center

Kathotia, Vinay

2011-01-01

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

12. Mathematical Epistemologies at Work.

ERIC Educational Resources Information Center

Noss, Richard

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

13. Revisiting Mathematics Manipulative Materials

ERIC Educational Resources Information Center

Swan, Paul; Marshall, Linda

2010-01-01

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

14. Mathematics in Masons' Workplace

ERIC Educational Resources Information Center

Moreira, Darlinda; Pardal, Eugénia

2012-01-01

This paper presents masons' professional practices, which are related to mathematics. It aims to contribute to the area of adult mathematics education and to enlarge knowledge about how mathematics is used at the workplace. Methodologically it was followed an ethnographic approach. The key informants of the study were four masons aged between 40…

15. Latinos and Mathematics.

ERIC Educational Resources Information Center

Ortiz-Franco, Luis

An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…

16. 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)

17. 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…

18. Who Can Know Mathematics?

ERIC Educational Resources Information Center

Walshaw, Margaret

2014-01-01

This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…

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

ERIC Educational Resources Information Center

Darlington, Ellie

2014-01-01

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

20. 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 resource…

1. 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…

2. Mathematics and Music.

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)

3. The Creative Mathematics Teacher.

ERIC Educational Resources Information Center

Ediger, Marlow

The creative mathematics teacher who has love and enthusiasm for mathematics as a curriculum area should be in great demand in all schools. This paper discusses the characteristics of creative mathematics teachers, including those who guide students to engage in divergent thinking; have learners do much creative writing; and integrate creative…

4. 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…

5. Topics in Mathematics.

ERIC Educational Resources Information Center

Posey, Johnsie Jo, Ed.; And Others

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

6. Mathematics and Sports

ERIC Educational Resources Information Center

Gallian, Joseph A., Ed.

2010-01-01

"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…

7. Mathematical Friends and Relations

ERIC Educational Resources Information Center

Tomalin, Jo

2012-01-01

The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…

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

ERIC Educational Resources Information Center

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

2013-01-01

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

9. Didactic toy for teaching the Fourier principle

Medina-Villanueva, Miguel; Medina-Tamez, Victor; Medina-Tamez, Javier; Garcia-Mederez, Adrian

2002-11-01

The mathematical tool of Fourier analysis is used in many areas like vibrations, communications, optics, electronics, etc. The understanding of this subject sometimes causes frustration in students. The main purpose of this presentation is to propose a didactic toy that calculates the harmonic magnitudes through the discrete values of analog periodic signals. This device shows the rotative vectors in a physical way that makes the principle of Fourier understandable.

10. 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.

11. Entropy Solutions to a Genuinely Nonlinear Ultraparabolic Kolmogorov-Type Equation

Sazhenkov, S. A.

2007-04-01

We consider a non-isotropic convection-diffusion-reaction equation of a very general form, in which the diffusion matrix is nonnegative and may change its rank depending on temporal and spatial variables, and convection and reaction terms may be discontinuous. This equation arises in astrophysics and plasma physics, in fluid dynamics, mathematical biology and financial mathematics. We assume that the equation a priori admits the maximum principle and is genuinely nonlinear, and we prove that there exists at least one entropy solution and that the genuinely nonlinear structure of the equation rules out fine oscillatory regimes in entropy solutions. The proofs rely on the method of kinetic equation and on theory of H-measures.

12. Ten Problems in Experimental Mathematics

SciTech Connect

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

2004-09-30

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

13. 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)

14. 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.

15. Inferring Mathematical Equations Using Crowdsourcing

PubMed Central

Wasik, Szymon

2015-01-01

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

16. Inferring Mathematical Equations Using Crowdsourcing.

PubMed

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

2015-01-01

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

17. Principles of Modern Soccer.

ERIC Educational Resources Information Center

Beim, George

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

18. 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…

19. Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles

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.

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

ERIC Educational Resources Information Center

Richardson, Kathy

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

1. MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

PubMed Central

ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN

2013-01-01

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

2. [Principle of genetic equilibrium for two gene loci].

PubMed

Pan, Shen-Yuan; Qu, Ai; Hui, Peng; Li, Ai-Ling

2004-03-01

Because linkage equilibrium is introduced by directly quoting the conclusions or imprecise mathematical reasoning in most of textbooks, many students are puzzled with the problem of linkage equilibrium when they learn population genetics. Based on the radical conditions of genetic equilibrium, the principle of linkage equilibrium condition and process, for two gene loci is introduced by precise mathematical reasoning. The article may provide reference to teachers and students in the teaching and learning of population genetics. PMID:15639991

3. Turbulence and the Stabilization Principle

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

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

4. Driving Toward Guiding Principles

PubMed Central

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

5. Mathematical Ties That Bind.

ERIC Educational Resources Information Center

House, Peggy A.

1994-01-01

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

6. Philosophy and mathematics: interactions.

PubMed

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. PMID:25029825

7. 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…

8. 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.

9. 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…

10. Values That Occasion and Guide Mathematics in the Family

ERIC Educational Resources Information Center

Pea, Roy; Martin, Lee

2010-01-01

In this chapter, the authors illustrate on mathematical problem-solving activities within families how the functions and structures of their mathematics at home are dependent on values, and how interacting values during problem situations came to shape what counted as solutions. These values examples from family math illustrate the complex…

11. 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.)

12. 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…

13. The International Mathematical Olympiad Training Session.

ERIC Educational Resources Information Center

Rousseau, Cecil; Patruno, Gregg

1985-01-01

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

14. 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.

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

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.

16. 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…

17. 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…

18. 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…

19. 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…

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

ERIC Educational Resources Information Center

Wang, Youjun

2009-01-01

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

1. Physical vs. Mathematical Models in Rock Mechanics

Morozov, I. B.; Deng, W.

2013-12-01

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

2. The Third U.S.A. Mathematical Olympiad

ERIC Educational Resources Information Center

Greitzer, Samuel L.

1975-01-01

The 1974 Third United States of America Mathematical Olympiad for secondary school students is described. Included are five test problems with solutions, a brief statistical analysis of test scores, and a list of the eight finalists. (CR)

3. 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…

4. 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…

5. The Relativity of Mathematics.

ERIC Educational Resources Information Center

Kleiner, Israel; Avital, Shmuel

1984-01-01

The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

6. 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…

7. Mathematics on the Threshold

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…

8. Mathematics in History.

ERIC Educational Resources Information Center

Hallenberg, Harvey

1995-01-01

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

9. 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…

10. Modularizing Remedial Mathematics

ERIC Educational Resources Information Center

Wong, Aaron

2013-01-01

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

11. 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…

12. 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)…

13. Is This Mathematical?

ERIC Educational Resources Information Center

Dodd, Jennifer

2010-01-01

In this article, the author reports on the findings of her research on what her Year 10 students consider to be "mathematical." The class contains thirteen students who will all sit the higher tier IGCSE next year. The author found out that the students considered things she told them to have a higher mathematical status than work they did…

14. Mathematics: The Universal Language?

ERIC Educational Resources Information Center

Hoffert, Sharon B.

2009-01-01

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

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…

16. Skill Games for Mathematics.

ERIC Educational Resources Information Center

Corle, Clyde G.

This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…

17. Mathematical Graphic Organizers

ERIC Educational Resources Information Center

Zollman, Alan

2009-01-01

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

18. Learning Mathematics while Black

ERIC Educational Resources Information Center

Martin, Danny Bernard

2012-01-01

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

19. Counting on Mathematics.

ERIC Educational Resources Information Center

Goldsmith, Lynn T.

2000-01-01

Parents can help ensure that their children are well-equipped with the necessary mathematical skills and understanding for the future by: having high expectations for their children's learning; helping their children see mathematical connections and applications in the world; being curious about their children's thinking; and being enthusiastic…

20. See a Different Mathematics

ERIC Educational Resources Information Center

Stallings, L. Lynn

2007-01-01

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

1. [Collected Papers on Mathematics.

ERIC Educational Resources Information Center

Connell, Michael L., Ed.

This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student Learning and…

2. Astronomy and Mathematics Education

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.

3. Mathematics and Gender.

ERIC Educational Resources Information Center

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

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

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…

ERIC Educational Resources Information Center

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

2010-01-01

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

6. Mathematics and Art

ERIC Educational Resources Information Center

Sharp, John

2012-01-01

This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…

7. Genders, Mathematics, and Feminisms.

ERIC Educational Resources Information Center

Damarin, Suzanne

Historical studies reveal that mathematics has been claimed as a private domain by men, while studies of the popular press document that women and girls are considered incompetent in that field. The study of gender and mathematics as viewed through feminism can create a new reading which exposes hidden assumptions, unwarranted conclusions, and…

8. Why physics needs mathematics

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.

9. Developing Mathematical Proficiency

ERIC Educational Resources Information Center

Groves, Susie

2012-01-01

It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as "relational" rather than "instrumental" understanding. More recently, Kilpatrick, Swafford and Findell (2001)…

10. Mathematics, Vol. 1.

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…

11. Issues in Teaching Mathematics

ERIC Educational Resources Information Center

Ediger, Marlow

2013-01-01

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

12. 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…

13. Dyslexia, Dyspraxia and Mathematics.

ERIC Educational Resources Information Center

Yeo, Dorian

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

14. Mathematical thinking and origami

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.

15. 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…

16. The Language of Mathematics.

ERIC Educational Resources Information Center

Oldfield, Christine

1996-01-01

Describes aspects of learning the language of mathematics including vocabulary and grammar, the origins of the vocabulary, the pronunciation problem, and translation of English phrases and sentences into mathematical language accompanied by conceptual understanding of the process being described. Gives suggestions for teachers in class and…

17. 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…

18. Student Nurses and Mathematics.

ERIC Educational Resources Information Center

Hutton, B. Meriel

For the safety of the public, it is essential that nurses are competent at least in the mathematics that enables them to calculate medications accurately. From a survey by G. Hek (1994), it is apparent that mathematics is not universally included in the nursing curricula, nor asked for as a pre-requisite to entry. Changes in the profile of the…

19. 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.

20. Encouraging Good Mathematical Writing

ERIC Educational Resources Information Center

O'Shea, J.

2006-01-01

This paper is a report on an attempt to teach students in their first and second year of university how to write mathematics. The problems faced by these students are outlined and the system devised to emphasize the importance of communicating mathematics is explained.

1. What Is Discrete Mathematics?

ERIC Educational Resources Information Center

Sharp, Karen Tobey

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

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

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.

3. 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.

4. Mathematical models of diabetes progression.

PubMed

De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels

2008-12-01

Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. PMID:18780774

5. Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons ``piloted'' (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

Vigier, Jean-Pierre

1991-02-01

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

6. Assessing Students Beliefs about Mathematics.

ERIC Educational Resources Information Center

Spangler, Denise A.

1992-01-01

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

7. Creating a Differentiated Mathematics Classroom

ERIC Educational Resources Information Center

Strong, Richard; Thomas, Ed; Perini, Matthew; Silver, Harvey

2004-01-01

Student differences in learning mathematics are categorized under four different mathematical learning styles. The names of books providing examples on how mathematics teachers can differentiate their classroom instructions are mentioned.

8. Guiding Principles for Evaluators.

ERIC Educational Resources Information Center

Shadish, William R., Ed.; And Others

1995-01-01

The 12 articles (including an index) of this theme issue are devoted to documenting and critiquing the American Evaluation Association's "Guiding Principles for Evaluators," a code of ethics and standards. The development of these principles is traced, and their strengths and weaknesses are analyzed at general and specific levels. (SLD)

9. Assessment Principles and Tools

PubMed Central

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

10. Principled Grammar Teaching

ERIC Educational Resources Information Center

Batstone, Rob; Ellis, Rod

2009-01-01

A key aspect of the acquisition of grammar for second language learners involves learning how to make appropriate connections between grammatical forms and the meanings which they typically signal. We argue that learning form/function mappings involves three interrelated principles. The first is the Given-to-New Principle, where existing world…

11. Hamilton's Principle for Beginners

ERIC Educational Resources Information Center

Brun, J. L.

2007-01-01

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

12. The genetic difference principle.

PubMed

Farrelly, Colin

2004-01-01

In the newly emerging debates about genetics and justice three distinct principles have begun to emerge concerning what the distributive aim of genetic interventions should be. These principles are: genetic equality, a genetic decent minimum, and the genetic difference principle. In this paper, I examine the rationale of each of these principles and argue that genetic equality and a genetic decent minimum are ill-equipped to tackle what I call the currency problem and the problem of weight. The genetic difference principle is the most promising of the three principles and I develop this principle so that it takes seriously the concerns of just health care and distributive justice in general. Given the strains on public funds for other important social programmes, the costs of pursuing genetic interventions and the nature of genetic interventions, I conclude that a more lax interpretation of the genetic difference principle is appropriate. This interpretation stipulates that genetic inequalities should be arranged so that they are to the greatest reasonable benefit of the least advantaged. Such a proposal is consistent with prioritarianism and provides some practical guidance for non-ideal societies--that is, societies that do not have the endless amount of resources needed to satisfy every requirement of justice. PMID:15186680

ERIC Educational Resources Information Center

Burns, Gerald P.

The primary but not exclusive concern in this monograph is the principles and qualities of dynamic leaders of people rather than of ideas or cultural and artistic pursuits. Theories of leadership in the past, present, and future are discussed, as are the principles, rewards, exercise, and philosophy of leadership. A bibliography is included. (MSE)

14. Government Information Policy Principles.

ERIC Educational Resources Information Center

Hernon, Peter

1991-01-01

Analyzes the utility of policy principles advanced by professional associations for public access to government information. The National Commission on Libraries and Information Science (NCLIS), the Information Industry Association (IIA), and the Office of Technology Assessment (OTA) urge the adoption of principles for the dissemination of public…

15. 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.

16. Mathematics as verbal behavior.

PubMed

Marr, M Jackson

2015-04-01

"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. PMID:25595115

17. Dynamic sealing principles

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.

18. Principlism and communitarianism.

PubMed

Callahan, D

2003-10-01

The decline in the interest in ethical theory is first outlined, as a background to the author's discussion of principlism. The author's own stance, that of a communitarian philosopher, is then described, before the subject of principlism itself is addressed. Two problems stand in the way of the author's embracing principlism: its individualistic bias and its capacity to block substantive ethical inquiry. The more serious problem the author finds to be its blocking function. Discussing the four scenarios the author finds that the utility of principlism is shown in the two scenarios about Jehovah's Witnesses but that when it comes to selling kidneys for transplantation and germline enhancement, principlism is of little help. PMID:14519838

19. The Physical Principles of Magnetism

Morrish, Allan H.

2001-01-01

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

20. A 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…

1. 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…

2. 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…

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

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

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

4. Measuring the Effectiveness of a Mathematics Support Service: An Email Survey

ERIC Educational Resources Information Center

Gillard, Jonathan; Robathan, Kirsty; Wilson, Robert

2011-01-01

Over the last decade the "mathematics problem" (students lacking basic mathematical skills on entry into higher education), and proposed solutions of this problem have been widely debated. One method to help combat this issue has been the introduction of mathematics support centres across higher education institutions. This article describes the…

5. An Interview with the 1985 USA Team to the International Mathematical Olympiad.

ERIC Educational Resources Information Center

Page, Warren

1985-01-01

This interview with the six members of the 1985 American team to the International Mathematical Olympiad (IMO) focuses on such areas as their evolving mathematical knowledge, mathematical pursuits, accomplishments, and interests. Also included are biographical sketches of the team members and the 1985 IMO problems (with solutions). (JN)

6. Understanding Profile from the Philosophy, Principles, and Characteristics of RME

ERIC Educational Resources Information Center

Julie, Hongki; Suwarsono, St.; Juniati, Dwi

2014-01-01

The aim of this study is to create understanding profiles of elementary school teachers who have been and have not been following the workshop PMRI, before and after they learned the learning resource about philosophy, principles, and characteristics of realistic mathematics approach. This type of research used in this study is a combination of…

7. 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…

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

ERIC Educational Resources Information Center

Pingle, Mark

2003-01-01

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

9. Five Easy Principles to Make Math Moments Count

ERIC Educational Resources Information Center

Cutler, Carrie S.

2011-01-01

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

10. Scaffolding students' opportunities to learn mathematics through social interactions

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.

11. 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…

12. Mathematization in introductory physics

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

13. The Greatest Mathematical Discovery?

SciTech Connect

Bailey, David H.; Borwein, Jonathan M.

2010-05-12

What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.

14. Abstraction in mathematics.

PubMed

Ferrari, Pier Luigi

2003-07-29

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

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)

16. Standards in Mathematics Teaching.

ERIC Educational Resources Information Center

Brookes, Bill

1978-01-01

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

17. 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)

18. 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)

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

ERIC Educational Resources Information Center

Austin, Joe Dan, Ed.

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

20. 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…

1. 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…

2. 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…

3. Handwritten mathematical symbols dataset

PubMed Central

Chajri, Yassine; Bouikhalene, Belaid

2016-01-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975

4. The reality of Mathematics

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.

5. Handwritten mathematical symbols dataset.

PubMed

Chajri, Yassine; Bouikhalene, Belaid

2016-06-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975

6. Mathematical foundations of neurocomputing

SciTech Connect

Amari, S. . Faculty of Engineering)

1990-09-01

Neurocomputing makes use of parallel dynamical interactions of modifiable neuron-like elements. It is important to show, by mathematical treatments, the capabilities and limitations of information processing by various architectures of neural networks. This paper, gives mathematical foundations to neurocomputing. It considers the capabilities of transformations by layered networks, statistical neurodynamics, the dynamical characteristics of associative memory, a general theory of neural learning, and self-organization of neural networks.

7. Mathematics and linguistics

SciTech Connect

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.

8. Mathematical and Statistical Opportunities in Cyber Security

SciTech Connect

Meza, Juan; Campbell, Scott; Bailey, David

2009-03-23

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

9. A Constructivist Computational Tool to Assist in Learning Primary School Mathematical Equations

ERIC Educational Resources Information Center

Figueira-Sampaio, Aleandra da Silva; dos Santos, Eliane Elias Ferreira; Carrijo, Gilberto Arantes

2009-01-01

In constructivist principles, learning is a process in which individuals construct knowledge. Research in Mathematics Education looks for ways to make mathematics education less dry and more attractive. When solving polynomial equations of the first degree, it is very common for teachers to work with the mistaken idea of "changing the sign" when…

10. Algebraic Equations: Can Middle-School Students Meaningfully Translate from Words to Mathematical Symbols?

ERIC Educational Resources Information Center

Capraro, Mary Margaret; Joffrion, Heather

2006-01-01

Using symbolic algebra to represent and solve linear equations is one of the expectations within the "Algebra" content standard for the 6-8-grade band in the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (2000). Students' understanding of these concepts, even before a formal algebra course,…

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

PubMed Central

2015-01-01

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

12. 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…

13. A mathematical model for the deformation of the eyeball by an elastic band.

PubMed

Keeling, Stephen L; Propst, Georg; Stadler, Georg; Wackernagel, Werner

2009-06-01

In a certain kind of eye surgery, the human eyeball is deformed sustainably by the application of an elastic band. This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given. PMID:19351791

14. A Protocol for Evaluating Contextual Design Principles

PubMed Central

Stamps, Arthur

2014-01-01

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

15. Adapting mudharabah principle in Islamic option

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.

16. Common Grounds for Modelling Mathematics in Educational Software

ERIC Educational Resources Information Center

Neuper, Walther

2010-01-01

Two kinds of software, CAS and DGS, are starting to work towards mutual integration. This paper envisages common grounds for such integration based on principles of computer theorem proving (CTP). Presently, the CTP community seems to lack awareness as to which of their products' features might serve mathematics education from high-school to…

17. Teachers' Beliefs that Matter in Secondary Mathematics Classrooms

ERIC Educational Resources Information Center

Beswick, Kim

2007-01-01

This paper reports the findings of a study that sought to identify particular centrally held beliefs of secondary mathematics teachers that underpinned the establishment of classroom environments that were consistent with the principles of constructivism. The nine crucial beliefs identified were held by one or other of two teachers and emerged…

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

SciTech Connect

Khots, Dmitriy; Khots, Boris

2010-05-04

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

ERIC Educational Resources Information Center

Colgan, Mark D.

2006-01-01

This article explores the mathematics involved in the NCAA basketball tournament including data analysis, basic probability, expected value, and the multiplication principle. A fun activity is presented that applies these concepts and involves students shooting Ping-Pong balls to discover a best strategy. (Contains 3 tables and 3 figures.)

20. 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…

1. 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…

2. 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…

3. Using a Card Trick to Teach Discrete Mathematics

ERIC Educational Resources Information Center

Simonson, Shai; Holm, Tara S.

2003-01-01

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

4. Missouri's Framework for Curriculum Development in Mathematics K-12.

ERIC Educational Resources Information Center

Coutts, Linda; And Others

Missouri's Frameworks for Curriculum Development in Mathematics acknowledges that teachers will bring the vision, ideals, and principles of the Show-Me Standards into their classrooms in exciting and innovative ways. The role of the frameworks is to provide districts with a "frame" for building curricula using the standards as a foundation. The…

5. Magic star puzzle for educational mathematics

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.

6. Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

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

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

ERIC Educational Resources Information Center

Reynolds, Thomas D.; And Others

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

8. Archimedes' Principle in Action

ERIC Educational Resources Information Center

Kires, Marian

2007-01-01

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

9. Chemical Principles Exemplified

ERIC Educational Resources Information Center

Plumb, Robert C.

1972-01-01

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

10. Global ethics and principlism.

PubMed

Gordon, John-Stewart

2011-09-01

This article examines the special relation between common morality and particular moralities in the four-principles approach and its use for global ethics. It is argued that the special dialectical relation between common morality and particular moralities is the key to bridging the gap between ethical universalism and relativism. The four-principles approach is a good model for a global bioethics by virtue of its ability to mediate successfully between universal demands and cultural diversity. The principle of autonomy (i.e., the idea of individual informed consent), however, does need to be revised so as to make it compatible with alternatives such as family- or community-informed consent. The upshot is that the contribution of the four-principles approach to global ethics lies in the so-called dialectical process and its power to deal with cross-cultural issues against the background of universal demands by joining them together. PMID:22073817

11. Physical and mathematical cochlear models

Lim, Kian-Meng

2000-10-01

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

12. Principles of Tendon Transfer.

PubMed

Wilbur, Danielle; Hammert, Warren C

2016-08-01

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

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

ERIC Educational Resources Information Center

Cable, John

2014-01-01

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

14. A Course in Multicultural Mathematics

ERIC Educational Resources Information Center

Hall, Rachel W.

2007-01-01

The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…

15. Discrete Mathematics and Curriculum Reform.

ERIC Educational Resources Information Center

Kenney, Margaret J.

1996-01-01

Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)

16. Assessing Innovative Proposals in Mathematics.

ERIC Educational Resources Information Center

Ediger, Marlow

Mathematics is at the apex in priorities pertaining to state-mandated testing of students. With 49 out of 50 states having mandated the testing of students, all of these have mathematics in the testing format. This paper discusses the modern school mathematics movement, recent approaches in improving the teaching of mathematics, and specific…

17. Book Mathematics--Part 1

ERIC Educational Resources Information Center

Gough, John

2008-01-01

It is potentially arresting when a mathematical implication is offered in a non-mathematical book. This author contends that students are encouraged to develop mathematical thinking when they read mathematical challenges in books. Aspects of books such as time-lines, historical relationships, maps, journeys, cause-and-affect, deductive inference,…

18. Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

19. Mathematics Is a Spectator Sport

ERIC Educational Resources Information Center

Foster, Colin; Williams, Helen

2007-01-01

This article presents a conversation between two editors of "Mathematics Teaching Incorporating Micromath." Topics discussed include the 2004 Association of Teachers of Mathematics conference, titled "Mathematics is Not a Spectator Sport," and the thought of engaging in mathematics and what that might mean. One of the editors stresses the need to…

20. Semantic Processing of Mathematical Gestures

ERIC Educational Resources Information Center

Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

2009-01-01

Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…