Science.gov

Sample records for algebraic approach based

  1. Nontraditional approach to algebra-based general physics

    NASA Astrophysics Data System (ADS)

    Meltzer, David E.

    1997-03-01

    In order to improve the degree of conceptual learning in our algebra-based general physics course, the second semester (of a two-semester sequence) has been taught in a nontraditional format during the past year. The key characteristics of this course were: 1) Intense and continuous use of interactive-engagement methods and cooperative learning; 2) coverage of less than half of the conventional number of topics, 3) heavy emphasis on qualitative questions as opposed to quantitative problems, 4) adjustment of the pacing of the course based on continuous (twice per week) formative assessment. The students enrolled in the course were relatively poorly prepared, with weak mathematical skills. Open-book quizzes stressing qualitative concepts in electricity and magnetism were given twice per week; most were given in "group quiz" format, allowing collaboration. Exams (also open-book) were all done individually. Most of the class time was taken up by quizzes, and by interactive discussion and group work related to quiz questions. New topics were not introduced until a majority of the class demonstrated competence in the topic under discussion. Despite lengthy and intensive focus on qualitative, conceptual questions and simple quantitative problems, only a small minority of the class ultimately demonstrated mastery of the targeted concepts. Frequent testing and re-testing of the students on basic concepts disclosed tenacious persistence of misconceptions.

  2. Partially Flipped Linear Algebra: A Team-Based Approach

    ERIC Educational Resources Information Center

    Carney, Debra; Ormes, Nicholas; Swanson, Rebecca

    2015-01-01

    In this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities.…

  3. Alternative algebraic approaches in quantum chemistry

    SciTech Connect

    Mezey, Paul G.

    2015-01-22

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

  4. A Modified Approach to Team-Based Learning in Linear Algebra Courses

    ERIC Educational Resources Information Center

    Nanes, Kalman M.

    2014-01-01

    This paper documents the author's adaptation of team-based learning (TBL), an active learning pedagogy developed by Larry Michaelsen and others, in the linear algebra classroom. The paper discusses the standard components of TBL and the necessary changes to those components for the needs of the course in question. There is also an empirically…

  5. A modified approach to team-based learning in linear algebra courses

    NASA Astrophysics Data System (ADS)

    Nanes, Kalman M.

    2014-11-01

    This paper documents the author's adaptation of team-based learning (TBL), an active learning pedagogy developed by Larry Michaelsen and others, in the linear algebra classroom. The paper discusses the standard components of TBL and the necessary changes to those components for the needs of the course in question. There is also an empirically controlled analysis of the effects of TBL on the student learning experience in the first year of TBL use.

  6. Extensions of algebraic image operators: An approach to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.

    1990-01-01

    Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed.

  7. The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems: A Didactical Model Based on a Numerical Approach with Junior High Students

    ERIC Educational Resources Information Center

    Rubio, Guillermo; del Valle, Rafael

    2004-01-01

    The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…

  8. A uniform algebraically-based approach to computational physics and efficient programming

    NASA Astrophysics Data System (ADS)

    Raynolds, James; Mullin, Lenore

    2007-03-01

    We present an approach to computational physics in which a common formalism is used both to express the physical problem as well as to describe the underlying details of how computation is realized on arbitrary multiprocessor/memory computer architectures. This formalism is the embodiment of a generalized algebra of multi-dimensional arrays (A Mathematics of Arrays) and an efficient computational implementation is obtained through the composition of of array indices (the psi-calculus) of algorithms defined using matrices, tensors, and arrays in general. The power of this approach arises from the fact that multiple computational steps (e.g. Fourier Transform followed by convolution, etc.) can be algebraically composed and reduced to an simplified expression (i.e. Operational Normal Form), that when directly translated into computer code, can be mathematically proven to be the most efficient implementation with the least number of temporary variables, etc. This approach will be illustrated in the context of a cache-optimized FFT that outperforms or is competitive with established library routines: ESSL, FFTW, IMSL, NAG.

  9. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-10-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  10. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-08-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  11. A Practical Approach to Inquiry-Based Learning in Linear Algebra

    ERIC Educational Resources Information Center

    Chang, J.-M.

    2011-01-01

    Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…

  12. An algebraic approach to the scattering equations

    NASA Astrophysics Data System (ADS)

    Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui

    2015-12-01

    We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

  13. Computer Algebra, Instrumentation and the Anthropological Approach

    ERIC Educational Resources Information Center

    Monaghan, John

    2007-01-01

    This article considers research and scholarship on the use of computer algebra in mathematics education following the instrumentation and the anthropological approaches. It outlines what these approaches are, positions them with regard to other approaches, examines tensions between the two approaches and makes suggestions for how work in this…

  14. Edge covers and independence: Algebraic approach

    NASA Astrophysics Data System (ADS)

    Kalinina, E. A.; Khitrov, G. M.; Pogozhev, S. V.

    2016-06-01

    In this paper, linear algebra methods are applied to solve some problems of graph theory. For ordinary connected graphs, edge coverings and independent sets are considered. Some results concerning minimum edge covers and maximum matchings are proved with the help of linear algebraic approach. The problem of finding a maximum matching of a graph is fundamental both practically and theoretically, and has numerous applications, e.g., in computational chemistry and mathematical chemistry.

  15. Algebraic operator approach to gas kinetic models

    NASA Astrophysics Data System (ADS)

    Il'ichov, L. V.

    1997-02-01

    Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - †Âϕ with the operators Âand† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.

  16. Locally Compact Quantum Groups. A von Neumann Algebra Approach

    NASA Astrophysics Data System (ADS)

    Van Daele, Alfons

    2014-08-01

    In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68-92] locally compact quantum groups are also studied in the von Neumann algebraic context. This approach is independent of the original C^*-algebraic approach in the sense that the earlier results are not used. However, this paper is not really independent because for many proofs, the reader is referred to the original paper where the C^*-version is developed. In this paper, we give a completely self-contained approach. Moreover, at various points, we do things differently. We have a different treatment of the antipode. It is similar to the original treatment in [Ann. Sci. & #201;cole Norm. Sup. (4) 33 (2000), 837-934]. But together with the fact that we work in the von Neumann algebra framework, it allows us to use an idea from [Rev. Roumaine Math. Pures Appl. 21 (1976), 1411-1449] to obtain the uniqueness of the Haar weights in an early stage. We take advantage of this fact when deriving the other main results in the theory. We also give a slightly different approach to duality. Finally, we collect, in a systematic way, several important formulas. In an appendix, we indicate very briefly how the C^*-approach and the von Neumann algebra approach eventually yield the same objects. The passage from the von Neumann algebra setting to the C^*-algebra setting is more or less standard. For the other direction, we use a new method. It is based on the observation that the Haar weights on the C^*-algebra extend to weights on the double dual with central support and that all these supports are the same. Of course, we get the von Neumann algebra by cutting down the double dual with this unique

  17. A Linear Algebraic Approach to Teaching Interpolation

    ERIC Educational Resources Information Center

    Tassa, Tamir

    2007-01-01

    A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

  18. Atomic effect algebras with compression bases

    SciTech Connect

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-15

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  19. Atomic effect algebras with compression bases

    NASA Astrophysics Data System (ADS)

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-01

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  20. Evolution of a Teaching Approach for Beginning Algebra

    ERIC Educational Resources Information Center

    Banerjee, Rakhi; Subramaniam, K.

    2012-01-01

    The article reports aspects of the evolution of a teaching approach over repeated trials for beginning symbolic algebra. The teaching approach emphasized the structural similarity between arithmetic and algebraic expressions and aimed at supporting students in making a transition from arithmetic to beginning algebra. The study was conducted with…

  1. An Inquiry-Based Linear Algebra Class

    ERIC Educational Resources Information Center

    Wang, Haohao; Posey, Lisa

    2011-01-01

    Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…

  2. Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

    PubMed

    Cierniak, Robert; Lorent, Anna

    2016-09-01

    The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. PMID:27289536

  3. An algebraic approach to BCJ numerators

    NASA Astrophysics Data System (ADS)

    Fu, Chih-Hao; Du, Yi-Jian; Feng, Bo

    2013-03-01

    One important discovery in recent years is that the total amplitude of gauge theory can be written as BCJ form where kinematic numerators satisfy Jacobi identity. Although the existence of such kinematic numerators is no doubt, the simple and explicit construction is still an important problem. As a small step, in this note we provide an algebraic approach to construct these kinematic numerators. Under our Feynman-diagram-like construction, the Jacobi identity is manifestly satisfied. The corresponding color ordered amplitudes satisfy off-shell KK-relation and off-shell BCJ relation similar to the color ordered scalar theory. Using our construction, the dual DDM form is also established.

  4. Multi-Server Approach for High-Throughput Molecular Descriptors Calculation based on Multi-Linear Algebraic Maps.

    PubMed

    García-Jacas, César R; Aguilera-Mendoza, Longendri; González-Pérez, Reisel; Marrero-Ponce, Yovani; Acevedo-Martínez, Liesner; Barigye, Stephen J; Avdeenko, Tatiana

    2015-01-01

    The present report introduces a novel module of the QuBiLS-MIDAS software for the distributed computation of the 3D Multi-Linear algebraic molecular indices. The main motivation for developing this module is to deal with the computational complexity experienced during the calculation of the descriptors over large datasets. To accomplish this task, a multi-server computing platform named T-arenal was developed, which is suited for institutions with many workstations interconnected through a local network and without resources particularly destined for computation tasks. This new system was deployed in 337 workstations and it was perfectly integrated with the QuBiLS-MIDAS software. To illustrate the usability of the T-arenal platform, performance tests over a dataset comprised of 15 000 compounds are carried out, yielding a 52 and 60 fold reduction in the sequential processing time for the 2-Linear and 3-Linear indices, respectively. Therefore, it can be stated that the T-arenal based distribution of computation tasks constitutes a suitable strategy for performing high-throughput calculations of 3D Multi-Linear descriptors over thousands of chemical structures for posterior QSAR and/or ADME-Tox studies. PMID:27490863

  5. Principles of Stagewise Separation Process Calculations: A Simple Algebraic Approach Using Solvent Extraction.

    ERIC Educational Resources Information Center

    Crittenden, Barry D.

    1991-01-01

    A simple liquid-liquid equilibrium (LLE) system involving a constant partition coefficient based on solute ratios is used to develop an algebraic understanding of multistage contacting in a first-year separation processes course. This algebraic approach to the LLE system is shown to be operable for the introduction of graphical techniques…

  6. A Technology-Intensive Approach to Algebra.

    ERIC Educational Resources Information Center

    Heid, M. Kathleen; Zbiek, Rose Mary

    1995-01-01

    Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)

  7. Algebraic Thinking: A Problem Solving Approach

    ERIC Educational Resources Information Center

    Windsor, Will

    2010-01-01

    Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…

  8. Simultaneous quantification of protein phosphorylation sites using liquid chromatography-tandem mass spectrometry-based targeted proteomics: a linear algebra approach for isobaric phosphopeptides.

    PubMed

    Xu, Feifei; Yang, Ting; Sheng, Yuan; Zhong, Ting; Yang, Mi; Chen, Yun

    2014-12-01

    As one of the most studied post-translational modifications (PTM), protein phosphorylation plays an essential role in almost all cellular processes. Current methods are able to predict and determine thousands of phosphorylation sites, whereas stoichiometric quantification of these sites is still challenging. Liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS)-based targeted proteomics is emerging as a promising technique for site-specific quantification of protein phosphorylation using proteolytic peptides as surrogates of proteins. However, several issues may limit its application, one of which relates to the phosphopeptides with different phosphorylation sites and the same mass (i.e., isobaric phosphopeptides). While employment of site-specific product ions allows for these isobaric phosphopeptides to be distinguished and quantified, site-specific product ions are often absent or weak in tandem mass spectra. In this study, linear algebra algorithms were employed as an add-on to targeted proteomics to retrieve information on individual phosphopeptides from their common spectra. To achieve this simultaneous quantification, a LC-MS/MS-based targeted proteomics assay was first developed and validated for each phosphopeptide. Given the slope and intercept of calibration curves of phosphopeptides in each transition, linear algebraic equations were developed. Using a series of mock mixtures prepared with varying concentrations of each phosphopeptide, the reliability of the approach to quantify isobaric phosphopeptides containing multiple phosphorylation sites (≥ 2) was discussed. Finally, we applied this approach to determine the phosphorylation stoichiometry of heat shock protein 27 (HSP27) at Ser78 and Ser82 in breast cancer cells and tissue samples. PMID:25403019

  9. Re"modeling" College Algebra: An Active Learning Approach

    ERIC Educational Resources Information Center

    Pinzon, D.; Pinzon, K.; Stackpole, M.

    2016-01-01

    In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

  10. Stability of Linear Equations--Algebraic Approach

    ERIC Educational Resources Information Center

    Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.

    2012-01-01

    This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

  11. An algebraic approach to the Hubbard model

    NASA Astrophysics Data System (ADS)

    de Leeuw, Marius; Regelskis, Vidas

    2016-02-01

    We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su (2 | 2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

  12. Quantum algebraic approach to refined topological vertex

    NASA Astrophysics Data System (ADS)

    Awata, H.; Feigin, B.; Shiraishi, J.

    2012-03-01

    We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W 1+∞ introduced by Miki. Our construction involves trivalent intertwining operators Φ and Φ* associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors ∈ {mathbb{Z}^2} is attached to each intertwining operator, which satisfy the Calabi-Yau and smoothness conditions. It is shown that certain matrix elements of Φ and Φ* give the refined topological vertex C λ μν ( t, q) of Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined topological vertex C λ μ ν ( q, t) of Awata-Kanno. The gluing factors appears correctly when we consider any compositions of Φ and Φ*. The spectral parameters attached to Fock spaces play the role of the Kähler parameters.

  13. Algebraic approach to small-world network models

    NASA Astrophysics Data System (ADS)

    Rudolph-Lilith, Michelle; Muller, Lyle E.

    2014-01-01

    We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.

  14. Quantization of Lie group and algebra of G2 type in the Faddeev-Reshetikhin-Takhtajan approach

    NASA Astrophysics Data System (ADS)

    Sasaki, Norihito

    1995-08-01

    Based on the quantized universal enveloping (QUE) algebras, a quantization of the automorphism group of some nonassociative algebras is given in the formulation employing noncommuting matrix entries. A quantum group of G2 type included in this scheme is studied in detail in the Faddeev-Reshetikhin-Takhtajan (FRT) approach. Also in the formulation employing noncommuting matrix entries, the QUE-algebra of G2 type is reconstructed through the pairing induced by the R-matrix between the quantum group and the QUE-algebra.

  15. Reasoning about nondeterministic and concurrent actions: A process algebra approach

    SciTech Connect

    De Giacomo, G.; Chen, Xiao Jun

    1996-12-31

    In this paper, we study reasoning about actions following a model checking approach in contrast to the usual validity checking one. Specifically, we model a dynamic system as a transition graph which represents all the possible system evolutions in terms of state changes caused by actions. Such a transition graph is defined by means of a suitable process algebra associated with an explicit global store. To reason about system properties we introduce an extension of modal {mu}-calculus. This setting, although directly applicable only when complete information on the system is available, has several interesting features for reasoning about actions. On one hand, it inherits from the vast literature on process algebras tools for dealing with complex systems, treating suitably important aspects like parallelism, communications, interruptions, coordinations among agents. On the other hand, reasoning by model checking is typically much easier than more general logical services such as validity checking.

  16. EPQ Models under Permissible Payment Delay: An Algebraic Approach

    NASA Astrophysics Data System (ADS)

    Huang, Yung-Fu; Hsu, Kuang-Hua

    The purpose of this research is to relax this assumption and establish the retailer`s inventory system as a cost minimization problem to determine the retailer`s optimal inventory cycle time. Then, an algebraic approach is provided and an easy-to-use theorem is derived to efficiently determine the optimal cycle time. From the final numerical examples, result implies that the retailer will order less quantity to take the benefits of the permissible delay in payments more frequently when the larger the differences between the unit selling price per item and the unit purchasing price per item.

  17. An Algebraic Approach to Unital Quantities and their Measurement

    NASA Astrophysics Data System (ADS)

    Domotor, Zoltan; Batitsky, Vadim

    2016-06-01

    The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system's ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity's value into its measuring instrument's pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument's indiscernibility relation, manifested by not being able to distinguish the measured system's topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment.

  18. Structural analysis and design of multivariable control systems: An algebraic approach

    NASA Technical Reports Server (NTRS)

    Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen

    1988-01-01

    The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

  19. Improving model-based diagnosis through algebraic analysis: The Petri net challenge

    SciTech Connect

    Portinale, L.

    1996-12-31

    The present paper describes the empirical evaluation of a linear algebra approach to model-based diagnosis, in case the behavioral model of the device under examination is described through a Petri net model. In particular, we show that algebraic analysis based on P-invariants of the net model, can significantly improve the performance of a model-based diagnostic system, while keeping the integrity of a general framework defined from a formal logical theory. A system called INVADS is described and experimental results, performed on a car fault domain and involving the comparison of different implementations of P-invariant based diagnosis, are then discussed.

  20. Online signal filtering based on the algebraic method and its experimental validation

    NASA Astrophysics Data System (ADS)

    Morales, R.; Segura, E.; Somolinos, J. A.; Núñez, L. R.; Sira-Ramírez, H.

    2016-01-01

    An on-line algebraic filtering scheme, based on the recently introduced algebraic approach to parameter and state estimation, is presented along with successful experimental results. The proposed filtering algorithm is based on the connections between a time derivative estimator and an algebraically based signal filtering option. The main advantages of the proposed approach are: (i) there are no appreciable delays in the filtered signal; (ii) the method does not require any statistical assessment of the noises corrupting the signal; (iii) high attenuation of the noise effects is achieved; (iv) the on-line computations are carried out in real time; and (v) high versatility and ease of implementation. Several experiments related to real depth measurements were conducted to show the effectiveness of the proposed algorithm. Comparisons are performed with different filtering alternatives.

  1. On a quantum algebraic approach to a generalized phase space

    NASA Astrophysics Data System (ADS)

    Bohm, D.; Hiley, B. J.

    1981-04-01

    We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding the solutions of our equations as constants of the motion, rather than as statistical weight factors. We show a close relationship of our work to that of Prigogine and his group. We bring in a new nonnegative probability function, and we propose extensions of the theory to cover thermodynamic processes involving entropy changes, as well as the usual reversible processes.

  2. An algebraic approach to finding the Fermat-Torricelli point

    NASA Astrophysics Data System (ADS)

    Palacios-Vélez, Óscar Luis; Pedraza-Oropeza, Felipe J. A.; Escobar-Villagran, Bernardo Samuel

    2015-11-01

    Using a calculus and an algebraic approach, the Cartesian coordinates of the Fermat-Torricelli point are deduced for triangles with no internal angle greater than 120°. Although in theory, the deduction of these coordinates could be made 'by hand', in practice it is very laborious to obtain them without the aid of mathematical computer software, but with human guidance, since there are mathematical artifices not yet incorporated into the software. It is also shown that these coordinates can be conveniently expressed in terms of the side lengths and the area of the triangle. These coordinates are contrasted with the coordinates of a similar point: one whose sum of the squares of the distances to the vertices of an arbitrary triangle is a minimum.

  3. Process Algebra Approach for Action Recognition in the Maritime Domain

    NASA Technical Reports Server (NTRS)

    Huntsberger, Terry

    2011-01-01

    The maritime environment poses a number of challenges for autonomous operation of surface boats. Among these challenges are the highly dynamic nature of the environment, the onboard sensing and reasoning requirements for obeying the navigational rules of the road, and the need for robust day/night hazard detection and avoidance. Development of full mission level autonomy entails addressing these challenges, coupled with inference of the tactical and strategic intent of possibly adversarial vehicles in the surrounding environment. This paper introduces PACIFIC (Process Algebra Capture of Intent From Information Content), an onboard system based on formal process algebras that is capable of extracting actions/activities from sensory inputs and reasoning within a mission context to ensure proper responses. PACIFIC is part of the Behavior Engine in CARACaS (Cognitive Architecture for Robotic Agent Command and Sensing), a system that is currently running on a number of U.S. Navy unmanned surface and underwater vehicles. Results from a series of experimental studies that demonstrate the effectiveness of the system are also presented.

  4. Clifford algebra approach to the coincidence problem for planar lattices.

    PubMed

    Rodríguez, M A; Aragón, J L; Verde-Star, L

    2005-03-01

    The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square, rectangular and rhombic lattices are worked out in detail. One of the aims of this work is to show the potential usefulness of Clifford algebra in crystallography. The power of Clifford algebra for expressing geometric ideas is exploited here and the procedure presented can be generalized to higher dimensions. PMID:15724067

  5. Mat-Rix-Toe: Improving Writing through a Game-Based Project in Linear Algebra

    ERIC Educational Resources Information Center

    Graham-Squire, Adam; Farnell, Elin; Stockton, Julianna Connelly

    2014-01-01

    The Mat-Rix-Toe project utilizes a matrix-based game to deepen students' understanding of linear algebra concepts and strengthen students' ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the…

  6. Algebraic Approach to the Computation of the Defining Polynomial of the Algebraic Riccati Equation

    NASA Astrophysics Data System (ADS)

    Kitamoto, Takuya

    The algebraic Riccati equation, which we denote by ’ARE’ in the rest of the paper, is one of the most important equations of the post modern control theory. It plays important role for solving H 2 and H ∞ optimal control problems.

  7. Software Development Of XML Parser Based On Algebraic Tools

    NASA Astrophysics Data System (ADS)

    Georgiev, Bozhidar; Georgieva, Adriana

    2011-12-01

    In this paper, is presented one software development and implementation of an algebraic method for XML data processing, which accelerates XML parsing process. Therefore, the proposed in this article nontraditional approach for fast XML navigation with algebraic tools contributes to advanced efforts in the making of an easier user-friendly API for XML transformations. Here the proposed software for XML documents processing (parser) is easy to use and can manage files with strictly defined data structure. The purpose of the presented algorithm is to offer a new approach for search and restructuring hierarchical XML data. This approach permits fast XML documents processing, using algebraic model developed in details in previous works of the same authors. So proposed parsing mechanism is easy accessible to the web consumer who is able to control XML file processing, to search different elements (tags) in it, to delete and to add a new XML content as well. The presented various tests show higher rapidity and low consumption of resources in comparison with some existing commercial parsers.

  8. An algebraic approach to computer program design and memory management

    NASA Astrophysics Data System (ADS)

    Raynolds, James; Mullin, Lenore

    2008-03-01

    Beginning with an algebra of multi-dimensional arrays and following a set of reduction rules embodying a calculus of array indices, we translate (in a mechanizable way) from the high-level mathematics of any array-based problem and a machine specification to a mathematically-optimized implementation. Raynolds and Mullin introduced the name Conformal Computing,^to describe this process that will be discussed in the context of data transforms such as the Fast Fourier, Wavelet Transforms and QR decomposition. We discuss the discovery that the access patterns of the Wavelet Transform form a sufficiently regular subset of those for our cache-optimized FFT so that we can be assured of achieving similar efficiency improvements to the Wavelet Transform as those that were found for the FFT. We present recent results in which careful attention to reproducible computational experiments in a dedicated/non-shared environment is demonstrated to be essential in order to optimally measure the response of the system (in this case the computer itself is the object of study) so as to be able to optimally tune the algorithm to the numerous cost functions associated with all of the elements of the memory/disk/network hierarchy. ^ The name Conformal Computing is protected: 2003, The Research Foundation, State University of New York.

  9. Correlates of gender and achievement in introductory algebra based physics

    NASA Astrophysics Data System (ADS)

    Smith, Rachel Clara

    The field of physics is heavily male dominated in America. Thus, half of the population of our country is underrepresented and underserved. The identification of factors that contribute to gender disparity in physics is necessary for educators to address the individual needs of students, and, in particular, the separate and specific needs of female students. In an effort to determine if any correlations could be established or strengthened between sex, gender identity, social network, algebra skill, scientific reasoning ability, and/or student attitude, a study was performed on a group of 82 students in an introductory algebra based physics course. The subjects each filled out a survey at the beginning of the semester of their first semester of algebra based physics. They filled out another survey at the end of that same semester. These surveys included physics content pretests and posttests, as well as questions about the students' habits, attitudes, and social networks. Correlates of posttest score were identified, in order of significance, as pretest score, emphasis on conceptual learning, preference for male friends, number of siblings (negatively correlated), motivation in physics, algebra score, and parents' combined education level. Number of siblings was also found to negatively correlate with, in order of significance, gender identity, preference for male friends, emphasis on conceptual learning, and motivation in physics. Preference for male friends was found to correlate with, in order of significance, emphasis on conceptual learning, gender identity, and algebra score. Also, gender identity was found to correlate with emphasis on conceptual learning, the strongest predictor of posttest score other than pretest score.

  10. Reflections on John Monaghan's "Computer Algebra, Instrumentation, and the Anthropological Approach"

    ERIC Educational Resources Information Center

    Blume, Glen

    2007-01-01

    Reactions to John Monaghan's "Computer Algebra, Instrumentation and the Anthropological Approach" focus on a variety of issues related to the ergonomic approach (instrumentation) and anthropological approach to mathematical activity and practice. These include uses of the term technique; several possibilities for integration of the two approaches;…

  11. Geometric and Algebraic Approaches in the Concept of Complex Numbers

    ERIC Educational Resources Information Center

    Panaoura, A.; Elia, I.; Gagatsis, A.; Giatilis, G.-P.

    2006-01-01

    This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

  12. Robot Control Based On Spatial-Operator Algebra

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Jain, Abhinandan

    1992-01-01

    Method for mathematical modeling and control of robotic manipulators based on spatial-operator algebra providing concise representation and simple, high-level theoretical frame-work for solution of kinematical and dynamical problems involving complicated temporal and spatial relationships. Recursive algorithms derived immediately from abstract spatial-operator expressions by inspection. Transition from abstract formulation through abstract solution to detailed implementation of specific algorithms to compute solution greatly simplified. Complicated dynamical problems like two cooperating robot arms solved more easily.

  13. Infinite-dimensional Lie algebras, classical r-matrices, and Lax operators: Two approaches

    NASA Astrophysics Data System (ADS)

    Skrypnyk, T.

    2013-10-01

    For each finite-dimensional simple Lie algebra {g}, starting from a general {g}⊗ {g}-valued solutions r(u, v) of the generalized classical Yang-Baxter equation, we construct infinite-dimensional Lie algebras widetilde{{g}}-_r of {g}-valued meromorphic functions. We outline two ways of embedding of the Lie algebra widetilde{{g}}-_r into a larger Lie algebra with Kostant-Adler-Symmes decomposition. The first of them is an embedding of widetilde{{g}}-_r into Lie algebra widetilde{{g}}(u^{-1},u)) of formal Laurent power series. The second is an embedding of widetilde{{g}}-_r as a quasigraded Lie subalgebra into a quasigraded Lie algebra widetilde{{g}}_r: widetilde{{g}}_r=widetilde{{g}}-_r+widetilde{{g}}+_r, such that the Kostant-Adler-Symmes decomposition is consistent with a chosen quasigrading. We construct dual spaces widetilde{{g}}^*_r, (widetilde{{g}}^{± }_r)^* and explicit form of the Lax operators L(u), L±(u) as elements of these spaces. We develop a theory of integrable finite-dimensional hamiltonian systems and soliton hierarchies based on Lie algebras widetilde{{g}}_r, widetilde{{g}}^{± }_r. We consider examples of such systems and soliton equations and obtain the most general form of integrable tops, Kirchhoff-type integrable systems, and integrable Landau-Lifshitz-type equations corresponding to the Lie algebra {g}.

  14. Negative base encoding in optical linear algebra processors

    NASA Technical Reports Server (NTRS)

    Perlee, C.; Casasent, D.

    1986-01-01

    In the digital multiplication by analog convolution algorithm, the bits of two encoded numbers are convolved to form the product of the two numbers in mixed binary representation; this output can be easily converted to binary. Attention is presently given to negative base encoding, treating base -2 initially, and then showing that the negative base system can be readily extended to any radix. In general, negative base encoding in optical linear algebra processors represents a more efficient technique than either sign magnitude or 2's complement encoding, when the additions of digitally encoded products are performed in parallel.

  15. Algebraic filter approach for fast approximation of nonlinear tomographic reconstruction methods

    NASA Astrophysics Data System (ADS)

    Plantagie, Linda; Batenburg, Kees Joost

    2015-01-01

    We present a computational approach for fast approximation of nonlinear tomographic reconstruction methods by filtered backprojection (FBP) methods. Algebraic reconstruction algorithms are the methods of choice in a wide range of tomographic applications, yet they require significant computation time, restricting their usefulness. We build upon recent work on the approximation of linear algebraic reconstruction methods and extend the approach to the approximation of nonlinear reconstruction methods which are common in practice. We demonstrate that if a blueprint image is available that is sufficiently similar to the scanned object, our approach can compute reconstructions that approximate iterative nonlinear methods, yet have the same speed as FBP.

  16. JTpack90: A parallel, object-based, Fortran 90 linear algebra package

    SciTech Connect

    Turner, J.A.; Kothe, D.B.; Ferrell, R.C.

    1997-03-01

    The authors have developed an object-based linear algebra package, currently with emphasis on sparse Krylov methods, driven primarily by needs of the Los Alamos National Laboratory parallel unstructured-mesh casting simulation tool Telluride. Support for a number of sparse storage formats, methods, and preconditioners have been implemented, driven primarily by application needs. They describe the object-based Fortran 90 approach, which enhances maintainability, performance, and extensibility, the parallelization approach using a new portable gather/scatter library (PGSLib), current capabilities and future plans, and present preliminary performance results on a variety of platforms.

  17. Lattice algebra approach to multispectral analysis of ancient documents.

    PubMed

    Valdiviezo-N, Juan C; Urcid, Gonzalo

    2013-02-01

    This paper introduces a lattice algebra procedure that can be used for the multispectral analysis of historical documents and artworks. Assuming the presence of linearly mixed spectral pixels captured in a multispectral scene, the proposed method computes the scaled min- and max-lattice associative memories to determine the purest pixels that best represent the spectra of single pigments. The estimation of fractional proportions of pure spectra at each image pixel is used to build pigment abundance maps that can be used for subsequent restoration of damaged parts. Application examples include multispectral images acquired from the Archimedes Palimpsest and a Mexican pre-Hispanic codex. PMID:23385905

  18. Fostering Analogical Transfer: The Multiple Components Approach to Algebra Word Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing

    2012-01-01

    Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated…

  19. Simultaneous algebraic reconstruction technique based on guided image filtering.

    PubMed

    Ji, Dongjiang; Qu, Gangrong; Liu, Baodong

    2016-07-11

    The challenge of computed tomography is to reconstruct high-quality images from few-view projections. Using a prior guidance image, guided image filtering smoothes images while preserving edge features. The prior guidance image can be incorporated into the image reconstruction process to improve image quality. We propose a new simultaneous algebraic reconstruction technique based on guided image filtering. Specifically, the prior guidance image is updated in the image reconstruction process, merging information iteratively. To validate the algorithm practicality and efficiency, experiments were performed with numerical phantom projection data and real projection data. The results demonstrate that the proposed method is effective and efficient for nondestructive testing and rock mechanics. PMID:27410859

  20. Hermite base Bernoulli type polynomials on the umbral algebra

    NASA Astrophysics Data System (ADS)

    Dere, R.; Simsek, Y.

    2015-01-01

    The aim of this paper is to construct new generating functions for Hermite base Bernoulli type polynomials, which generalize not only the Milne-Thomson polynomials but also the two-variable Hermite polynomials. We also modify the Milne-Thomson polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. Moreover, by applying the umbral algebra to these generating functions, we derive new identities for the Bernoulli polynomials of higher order, the Hermite polynomials and numbers of higher order, and the Stirling numbers of the second kind.

  1. A pedagogical presentation of a Csstarf-algebraic approach to quantum tomography

    NASA Astrophysics Data System (ADS)

    Ibort, A.; Man'ko, V. I.; Marmo, G.; Simoni, A.; Ventriglia, F.

    2011-12-01

    It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrödinger-Dirac picture of quantum mechanics on Hilbert spaces. In this picture, states are a primary concept and observables are derived from them. On the other hand, the Heisenberg picture, which has evolved in the Csstarf-algebraic approach to quantum mechanics, starts with the algebra of observables and introduces states as a derived concept. The equivalence between these two pictures amounts, essentially, to the Gelfand-Naimark-Segal construction. In this construction, the abstract Csstarf-algebra is realized as an algebra of operators acting on a constructed Hilbert space. The representation that is defined may be reducible or irreducible, but in either case it allows us to identify a unitary group associated with the Csstarf-algebra by means of its invertible elements. In this picture both states and observables are appropriate functions on the group; it also follows that quantum tomograms are strictly related with appropriate functions (positive-type) on the group. In this paper we present, using very simple examples, a tomographic description emerging from the set of ideas connected with the Csstarf-algebra picture of quantum mechanics. In particular, we introduce the tomographic probability distributions for finite and compact groups, and formulate an autonomous criterion to recognize a given probability distribution as a tomogram of quantum state.

  2. Matrix algebra approach to Gabor-type image representation

    NASA Astrophysics Data System (ADS)

    Zibulski, Meir; Zeevi, Yehoshua Y.

    1993-10-01

    Properties of basis functions which constitute a finite scheme of discrete Gabor representation are investigated. The approach is based on the concept of frames and utilizes the Piecewise Finite Zak Transform (PFZT). The frame operator associated with the Gabor-type frame is examined by representing it as a matrix-values function in the PFZT domain. The frame property of the Gabor representation functions are examined in relation to the properties of the matrix-valued function. The frame bounds are calculated by means of the eignevalues of the matrix-valued function, and the dual frame, which is used in calculation of the expansion coefficients, is expressed by means of the inverse matrix. DFT-based algorithms for computation of the expansion coefficients, and for the reconstruction of signals from these coefficients are generalized for the case of oversampling of the Gabor space. It is illustrated by an example that a better reconstruction is obtained in from the same number of coefficients in the case of oversampling.

  3. The Effects of Representations, Constructivist Approaches, and Engagement on Middle School Students' Algebraic Procedure and Conceptual Understanding

    ERIC Educational Resources Information Center

    Ross, Amanda; Willson, Victor

    2012-01-01

    This study examined the effects of types of representations, constructivist teaching approaches, and student engagement on middle school algebra students' procedural knowledge and conceptual understanding. Data gathered from 16 video lessons and algebra pretest/posttests were used to run three multilevel structural equation models. Symbolic…

  4. Application of Algebra Curriculum-Based Measurements for Decision Making in Middle and High School

    ERIC Educational Resources Information Center

    Johnson, Evelyn S.; Galow, Patricia A.; Allenger, Robert

    2013-01-01

    This article reports the results of a study examining the utility of curriculum-based measurement (CBM) in algebra for predicting performance on a state math assessment and informing instructional placement decisions for students in seventh, eighth, and tenth grades. Students completed six Basic Skills algebra probes across different time…

  5. An Example of Competence-Based Learning: Use of Maxima in Linear Algebra for Engineers

    ERIC Educational Resources Information Center

    Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin

    2011-01-01

    This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

  6. The Effect of Brain Based Instruction on Student Achievement in Algebra I

    ERIC Educational Resources Information Center

    Vass, Melissa G.

    2010-01-01

    This quantitative quasi-experimental study examined the effect of brain-based instruction compared to teacher-centered instruction on student achievement in algebra I. A pre-test and post-test were given to a control group of 30 and experimental group of 42 before and after a unit if study in algebra I, which was taught using the two instructional…

  7. Wigner-Racah Algebra Approach to Caselle-Ponzano Fusion Rules

    NASA Astrophysics Data System (ADS)

    Nomura, Masao

    1991-07-01

    Caselle-Ponzano fusion rules, based on graph theory, are investigated in the framework of Wigner-Racah algebras. While in the graph theory parameters of fusion rules are taken over specific values, the restriction of parameters is removed in the present formalism. Formal extension to q-analogs is also given.

  8. Associative Algebraic Approach to Logarithmic CFT in the Bulk: The Continuum Limit of the {gl(1|1)} Periodic Spin Chain, Howe Duality and the Interchiral Algebra

    NASA Astrophysics Data System (ADS)

    Gainutdinov, A. M.; Read, N.; Saleur, H.

    2016-01-01

    We develop in this paper the principles of an associative algebraic approach to bulk logarithmic conformal field theories (LCFTs). We concentrate on the closed {gl(1|1)} spin-chain and its continuum limit—the {c=-2} symplectic fermions theory—and rely on two technical companion papers, Gainutdinov et al. (Nucl Phys B 871:245-288, 2013) and Gainutdinov et al. (Nucl Phys B 871:289-329, 2013). Our main result is that the algebra of local Hamiltonians, the Jones-Temperley-Lieb algebra JTL N , goes over in the continuum limit to a bigger algebra than {V}, the product of the left and right Virasoro algebras. This algebra, {S}—which we call interchiral, mixes the left and right moving sectors, and is generated, in the symplectic fermions case, by the additional field {S(z,bar{z})≡ S_{αβ} ψ^α(z)bar{ψ}^β(bar{z})}, with a symmetric form {S_{αβ}} and conformal weights (1,1). We discuss in detail how the space of states of the LCFT (technically, a Krein space) decomposes onto representations of this algebra, and how this decomposition is related with properties of the finite spin-chain. We show that there is a complete correspondence between algebraic properties of finite periodic spin chains and the continuum limit. An important technical aspect of our analysis involves the fundamental new observation that the action of JTL N in the {gl(1|1)} spin chain is in fact isomorphic to an enveloping algebra of a certain Lie algebra, itself a non semi-simple version of {sp_{N-2}}. The semi-simple part of JTL N is represented by {U sp_{N-2}}, providing a beautiful example of a classical Howe duality, for which we have a non semi-simple version in the full JTL N image represented in the spin-chain. On the continuum side, simple modules over {S} are identified with "fundamental" representations of {sp_∞}.

  9. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems. PMID:24135792

  10. Superspace formulation in a three-algebra approach to D=3, N=4, 5 superconformal Chern-Simons matter theories

    SciTech Connect

    Chen Famin; Wu Yongshi

    2010-11-15

    We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.

  11. A new Rayleigh quotient minimization algorithm based on algebraic multigrid.

    SciTech Connect

    Lehoucq, Richard B.; Hetmaniuk, Ulrich L.

    2005-01-01

    Mandel and McCormick [2] introduced the RQMG method, which approximately minimizes the Rayleigh quotient over a sequence of grids. In this talk, we will present an algebraic extension. We replace the geometric mesh information with the algebraic information defined by an AMG preconditioner. At each level, we improve the smoother to accelerate the convergence. With a series of numerical experiments, we assess the efficiency of this new algorithm to compute several eigenpairs.

  12. Algebraic Error Based Triangulation and Metric of Lines

    PubMed Central

    Wu, Fuchao; Zhang, Ming; Wang, Guanghui; Hu, Zhanyi

    2015-01-01

    Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image uncertainties. In addition to line triangulation, a better metric is needed to evaluate 3D errors of line triangulation. In this paper, the line triangulation problem is investigated by using the Lagrange multipliers theory. The main contributions include: (i) Based on the Lagrange multipliers theory, a formula to compute the Plücker correction is provided, and from the formula, a new linear algorithm, LINa, is proposed for line triangulation; (ii) two optimal algorithms, OPTa-I and OPTa-II, are proposed by minimizing the algebraic error; and (iii) two metrics on 3D line space, the orthogonal metric and the quasi-Riemannian metric, are introduced for the evaluation of line triangulations. Extensive experiments on synthetic data and real images are carried out to validate and demonstrate the effectiveness of the proposed algorithms. PMID:26218615

  13. Classical versus Computer Algebra Methods in Elementary Geometry

    ERIC Educational Resources Information Center

    Pech, Pavel

    2005-01-01

    Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

  14. An algebraic cluster model based on the harmonic oscillator basis

    NASA Technical Reports Server (NTRS)

    Levai, Geza; Cseh, J.

    1995-01-01

    We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

  15. Spatio-Temporal Constrained Human Trajectory Generation from the PIR Motion Detector Sensor Network Data: A Geometric Algebra Approach

    PubMed Central

    Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian

    2015-01-01

    Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks. PMID:26729123

  16. Spatio-Temporal Constrained Human Trajectory Generation from the PIR Motion Detector Sensor Network Data: A Geometric Algebra Approach.

    PubMed

    Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian

    2015-01-01

    Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks. PMID:26729123

  17. Procedural Knowledge in the Presence of a Computer Algebra System (CAS): Rating the Drawbacks Using a Multi-Factorial Evaluation Approach

    ERIC Educational Resources Information Center

    Abdullah, Lazim M.

    2007-01-01

    Computer algebra systems (CASs) have been used by thousands of teachers and students for teaching and learning algebra. They have the ability to perform efficiently almost all of the algebraic expansions and simplifications. Nevertheless, the traditional approach of using paper and pencil in acquiring procedural knowledge is still widely…

  18. Algebraic Approach to the Minimum-Cost Multi-Impulse Orbit-Transfer Problem

    NASA Astrophysics Data System (ADS)

    Avendaño, M.; Martín-Molina, V.; Martín-Morales, J.; Ortigas-Galindo, J.

    2016-08-01

    We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general algebraic techniques to solve these equations (resultants, Gr\\"obner bases, etc.) in several situations of practical interest of different degrees of generality. For instance, we provide a proof of the optimality of the Hohmann transfer for the minimum fuel 2-impulse circular to circular orbit transfer problem, and we provide a general formula for the optimal 2-impulse in-plane transfer between two rotated elliptical orbits under a mild symmetry assumption on the two points where the impulses are applied (which we conjecture that can be removed).

  19. Clifford algebra-based spatio-temporal modelling and analysis for complex geo-simulation data

    NASA Astrophysics Data System (ADS)

    Luo, Wen; Yu, Zhaoyuan; Hu, Yong; Yuan, Linwang

    2013-10-01

    The spatio-temporal data simulating Ice-Land-Ocean interaction of Antarctic are used to demonstrate the Clifford algebra-based data model construction, spatio-temporal query and data analysis. The results suggest that Clifford algebra provides a powerful mathematical tool for the whole modelling and analysis chains for complex geo-simulation data. It can also help implement spatio-temporal analysis algorithms more clearly and simply.

  20. A global approach for image orientation using Lie algebraic rotation averaging and convex L∞ minimisation

    NASA Astrophysics Data System (ADS)

    Reich, M.; Heipke, C.

    2014-08-01

    In this paper we present a new global image orientation approach for a set of multiple overlapping images with given homologous point tuples which is based on a two-step procedure. The approach is independent on initial values, robust with respect to outliers and yields the global minimum solution under relatively mild constraints. The first step of the approach consists of the estimation of global rotation parameters by averaging relative rotation estimates for image pairs (these are determined from the homologous points via the essential matrix in a pre-processing step). For the averaging we make use of algebraic group theory in which rotations, as part of the special orthogonal group SO(3), form a Lie group with a Riemannian manifold structure. This allows for a mapping to the local Euclidean tangent space of SO(3), the Lie algebra. In this space the redundancy of relative orientations is used to compute an average of the absolute rotation for each image and furthermore to detect and eliminate outliers. In the second step translation parameters and the object coordinates of the homologous points are estimated within a convex L∞ optimisation, in which the rotation parameters are kept fixed. As an optional third step the results can be used as initial values for a final bundle adjustment that does not suffer from bad initialisation and quickly converges to a globally optimal solution. We investigate our approach for global image orientation based on synthetic data. The results are compared to a robust least squares bundle adjustment. In this way we show that our approach is independent of initial values and more robust against outliers than a conventional bundle adjustment.

  1. Applications of algebraic image operators to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-01-01

    A highly structured and compact algebraic representation of grey-level images is expanded. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, an innovative, efficient edge-detection scheme is devised. A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot-control system.

  2. Teaching of real numbers by using the Archimedes-Cantor approach and computer algebra systems

    NASA Astrophysics Data System (ADS)

    Vorob'ev, Evgenii M.

    2015-11-01

    Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of CAS. In the case of real numbers, the Archimedes-Cantor approach satisfies this requirement. The name of Archimedes brings back the exhaustion method. Cantor's name reminds us of the use of Cauchy rational sequences to represent real numbers. The usage of CAS with the Archimedes-Cantor approach enables the discussion of various representations of real numbers such as graphical, decimal, approximate decimal with precision estimates, and representation as points on a straight line. Exercises with numbers such as e, π, the golden ratio ϕ, and algebraic irrational numbers can help students better understand the real numbers. The Archimedes-Cantor approach also reveals a deep and close relationship between real numbers and continuity, in particular the continuity of functions.

  3. Lax operator algebras and integrable systems

    NASA Astrophysics Data System (ADS)

    Sheinman, O. K.

    2016-02-01

    A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite-dimensional integrable systems with a spectral parameter on a Riemann surface such as the Calogero-Moser and Hitchin systems. In particular, the approach includes (non-twisted) Kac-Moody algebras and integrable systems with a rational spectral parameter. The presentation is based on quite simple ideas about the use of gradings of semisimple Lie algebras and their interaction with the Riemann-Roch theorem. The basic properties of Lax operator algebras and the basic facts about the theory of the integrable systems in question are treated (and proved) from this general point of view. In particular, the existence of commutative hierarchies and their Hamiltonian properties are considered. The paper concludes with an application of Lax operator algebras to prequantization of finite-dimensional integrable systems. Bibliography: 51 titles.

  4. Lie-algebraic approach for pricing moving barrier options with time-dependent parameters

    NASA Astrophysics Data System (ADS)

    Lo, C. F.; Hui, C. H.

    2006-11-01

    In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

  5. Generic Representation of Y( s o(3)) Based on the Lie Algebraic Basis of s o(3)

    NASA Astrophysics Data System (ADS)

    Zhang, Hong-Biao; Wang, Gang-Cheng

    2016-05-01

    We focus on constructing a generic representation of Y( s o(3)) based on the Lie algebraic basis of s o(3) basis, and further developing transition of Yangian operator hat Y. As an application of Y( s o(3)), we calculate all the matrix elements of unit vector operators hat n in angular momentum basis. It is also discovered that the Yangian operator hat Y may work in quantum vector space. In addition, some shift operators hat {O}^{(± )}_{μ } are naturally built on the basis of the representation of Y( s o(3)). As an another application of Y( s o(3)), we can derive the CG cofficients of two coupled angular momenta from the down-shift operator hat {O}^{(-)}_{-1} acting on a s o(3)-coupled tensor basis. This not only explores that Yangian algebras can work in quantum tensor space, but also provides a novel approach to solve CG coefficients for two coupled angular momenta.

  6. Design-Based Research within the Constraints of Practice: AlgebraByExample

    ERIC Educational Resources Information Center

    Booth, Julie L.; Cooper, Laura A.; Donovan, M. Suzanne; Huyghe, Alexandra; Koedinger, Kenneth R.; Paré-Blagoev, E. Juliana

    2015-01-01

    Superintendents from districts in the Minority Student Achievement Network (MSAN) challenged the Strategic Education Research Partnership (SERP) to identify an approach to narrowing the minority student achievement gap in Algebra 1 without isolating minority students for intervention. SERP partnered with 8 MSAN districts and researchers from 3…

  7. Towards Student Instrumentation of Computer-Based Algebra Systems in University Courses

    ERIC Educational Resources Information Center

    Stewart, Sepideh; Thomas, Michael O. J.; Hannah, John

    2005-01-01

    There are many perceived benefits of using technology, such as computer algebra systems, in undergraduate mathematics courses. However, attaining these benefits sometimes proves elusive. Some of the key variables are the teaching approach and the student instrumentation of the technology. This paper considers the instrumentation of computer-based…

  8. The perturbed universe in the deformed algebra approach of loop quantum cosmology

    NASA Astrophysics Data System (ADS)

    Grain, Julien

    2016-06-01

    Loop Quantum Cosmology (LQC) is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical spacetime is inspired by Loop Quantum Gravity (LQG) ideas. In addition, LQC could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modelings in the light of observations. To do so however, modeling both the background evolution and its perturbations is needed. The latter described cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized B-modes exceed the upper bound currently set by observations. The exclusion of this specific version of LQC establishes the falsifiability of the approach, though one shall not conclude here that either LQC or LQG excluded.

  9. Applications Of Algebraic Image Operators To Model-Based Vision

    NASA Astrophysics Data System (ADS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-03-01

    This paper extends our previous research on a highly structured and compact algebraic representation of grey-level images. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, we have devised an innovative, efficient edge detection scheme.We have developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot control system. Model matching is accomplished using both top-down and bottom-up processing: a priori sensor and world model information are used to constrain the search of the image space for features, while extracted image information is used to update the model.

  10. ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy.

    PubMed

    Afsharpour, H; Landry, G; D'Amours, M; Enger, S; Reniers, B; Poon, E; Carrier, J-F; Verhaegen, F; Beaulieu, L

    2012-06-01

    Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy. PMID:22572100

  11. ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy

    NASA Astrophysics Data System (ADS)

    Afsharpour, H.; Landry, G.; D'Amours, M.; Enger, S.; Reniers, B.; Poon, E.; Carrier, J.-F.; Verhaegen, F.; Beaulieu, L.

    2012-06-01

    Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy.

  12. Exploring Algebra Based Problem Solving Methods and Strategies of Spanish-Speaking High School Students

    ERIC Educational Resources Information Center

    Hernandez, Andrea C.

    2013-01-01

    This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking…

  13. A novel Lie algebra of the genetic code over the Galois field of four DNA bases.

    PubMed

    Sánchez, Robersy; Grau, Ricardo; Morgado, Eberto

    2006-07-01

    Starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the main partitions of the genetic code table were obtained as equivalent classes of quotient spaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assignments and physicochemical properties of amino acids. Moreover, a distance defined between codons expresses a physicochemical meaning. It was also noticed that the distance between wild type and mutant codons tends to be small in mutational variants of four genes: human phenylalanine hydroxylase, human beta-globin, HIV-1 protease and HIV-1 reverse transcriptase. These results strongly suggest that deterministic rules in genetic code origin must be involved. PMID:16780898

  14. Optimization techniques for OpenCL-based linear algebra routines

    NASA Astrophysics Data System (ADS)

    Kozacik, Stephen; Fox, Paul; Humphrey, John; Kuller, Aryeh; Kelmelis, Eric; Prather, Dennis W.

    2014-06-01

    The OpenCL standard for general-purpose parallel programming allows a developer to target highly parallel computations towards graphics processing units (GPUs), CPUs, co-processing devices, and field programmable gate arrays (FPGAs). The computationally intense domains of linear algebra and image processing have shown significant speedups when implemented in the OpenCL environment. A major benefit of OpenCL is that a routine written for one device can be run across many different devices and architectures; however, a kernel optimized for one device may not exhibit high performance when executed on a different device. For this reason kernels must typically be hand-optimized for every target device family. Due to the large number of parameters that can affect performance, hand tuning for every possible device is impractical and often produces suboptimal results. For this work, we focused on optimizing the general matrix multiplication routine. General matrix multiplication is used as a building block for many linear algebra routines and often comprises a large portion of the run-time. Prior work has shown this routine to be a good candidate for high-performance implementation in OpenCL. We selected several candidate algorithms from the literature that are suitable for parameterization. We then developed parameterized kernels implementing these algorithms using only portable OpenCL features. Our implementation queries device information supplied by the OpenCL runtime and utilizes this as well as user input to generate a search space that satisfies device and algorithmic constraints. Preliminary results from our work confirm that optimizations are not portable from one device to the next, and show the benefits of automatic tuning. Using a standard set of tuning parameters seen in the literature for the NVIDIA Fermi architecture achieves a performance of 1.6 TFLOPS on an AMD 7970 device, while automatically tuning achieves a peak of 2.7 TFLOPS

  15. Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

    SciTech Connect

    Marquette, Ian; Quesne, Christiane

    2015-06-15

    We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.

  16. Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

    NASA Astrophysics Data System (ADS)

    Marquette, Ian; Quesne, Christiane

    2015-06-01

    We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.

  17. Using a flipped classroom in an algebra-based physics course

    NASA Astrophysics Data System (ADS)

    Smith, Leigh

    2013-03-01

    The algebra-based physics course is taken by Biology students, Pre-Pharmacy, Pre-Medical, and other health related majors such as medical imaging, physical therapy, and so on. Nearly 500 students take the course each Semester. Student learning is adversely impacted by poor math backgrounds as well as extensive work schedules outside of the classroom. We have been researching the use of an intensive flipped-classroom approach where students spend one to two hours each week preparing for class by reading the book, completing a series of conceptual problems, and viewing videos which describe the material. In class, the new response system Learning Catalytics is used which allows much richer problems to be posed in class and includes sketching figures, numerical or symbolic entries, short answers, highlighting text, etc in addition to the standard multiple choice questions. We make direct comparison of student learning for 1200 sudents who have taken the same tests, 25% of which used the flipped classroom approach, and 75% who took a more standard lecture. There is significant evidence of improvements in student learning for students taking the flipped classroom approach over standard lectures. These benefits appear to impact students at all math backgrounds.

  18. Orientation in operator algebras

    PubMed Central

    Alfsen, Erik M.; Shultz, Frederic W.

    1998-01-01

    A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457

  19. Cornell interaction in the two-body semi-relativistic framework: The Lie algebraic approach

    NASA Astrophysics Data System (ADS)

    Panahi, H.; Zarrinkamar, S.; Baradaran, M.

    2016-02-01

    We consider an approximation to the two-body spinless Salpeter equation which is valid for the case of heavy quarks with the Cornell potential. We then replace the square of kinetic term with its nonrelativistic equivalent and obtain an equation which can be alternatively viewed as the generalization of the Schrödinger equation into the relativistic regime. In the calculations, we use the Lie algebraic approach within the framework of quasi-exact solvability. With the help of the representation theory of sl(2) , the ( n+1 -dimensional matrix equation of the problem is constructed in a quite detailed manner and thereby the quasi-exact expressions for the energy eigenvalues and the corresponding wave functions as well as the allowed values of the potential parameters are obtained.

  20. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Connes, Alain

    2007-11-01

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input.

  1. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    SciTech Connect

    Chamseddine, Ali H.; Connes, Alain

    2007-11-09

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input.

  2. Clifford algebra-based structure filtering analysis for geophysical vector fields

    NASA Astrophysics Data System (ADS)

    Yu, Z.; Luo, W.; Yi, L.; Hu, Y.; Yuan, L.

    2013-07-01

    A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002-2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.

  3. Realizations of Galilei algebras

    NASA Astrophysics Data System (ADS)

    Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena

    2016-03-01

    All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.

  4. Gaalop—High Performance Parallel Computing Based on Conformal Geometric Algebra

    NASA Astrophysics Data System (ADS)

    Hildenbrand, Dietmar; Pitt, Joachim; Koch, Andreas

    We present Gaalop (Geometric algebra algorithms optimizer), our tool for high-performance computing based on conformal geometric algebra. The main goal of Gaalop is to realize implementations that are most likely faster than conventional solutions. In order to achieve this goal, our focus is on parallel target platforms like FPGA (field-programmable gate arrays) or the CUDA technology from NVIDIA. We describe the concepts, current status, and future perspectives of Gaalop dealing with optimized software implementations, hardware implementations, and mixed solutions. An inverse kinematics algorithm of a humanoid robot is described as an example.

  5. On the applications of algebraic grid generation methods based on transfinite interpolation

    NASA Technical Reports Server (NTRS)

    Nguyen, Hung Lee

    1989-01-01

    Algebraic grid generation methods based on transfinite interpolation called the two-boundary and four-boundary methods are applied for generating grids with highly complex boundaries. These methods yield grid point distributions that allow for accurate application to regions of sharp gradients in the physical domain or time-dependent problems with small length scale phenomena. Algebraic grids are derived using the two-boundary and four-boundary methods for applications in both two- and three-dimensional domains. Grids are developed for distinctly different geometrical problems and the two-boundary and four-boundary methods are demonstrated to be applicable to a wide class of geometries.

  6. An algebra-based method for inferring gene regulatory networks

    PubMed Central

    2014-01-01

    Background The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used. Results This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also

  7. An Evaluation of Words in Color or Morphologico-Algebraic Approach to Teaching Reading to Functionally Illiterate Adults.

    ERIC Educational Resources Information Center

    Hinds, Lillian R.

    Seventy Cleveland, Ohio, inner city adult illiterates, 33 from an experimental group and 37 from a contrast group, were studied to determine the efficiency and effectiveness of Words in Color or the Morphologico-Algebraic approach to teaching reading. Results indicated that the reading achievement gain of functionally illiterate adults taught by…

  8. Solution of the Dirac equation with some superintegrable potentials by the quadratic algebra approach

    NASA Astrophysics Data System (ADS)

    Aghaei, S.; Chenaghlou, A.

    2014-02-01

    The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

  9. Approach of spherical harmonics to the representation of the deformed su(1,1) algebra

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Ghaneh, T.

    2008-11-01

    The m-shifting generators of su(2) algebra together with a pair of l-shifting ladder symmetry operators have been used in the space of all spherical harmonics Ylm(θ,ϕ) in order to introduce a new set of operators, expressing the transitions between them. It is shown that the space of spherical harmonics whose l +2m or l -2m is given presents negative and positive irreducible representations of a deformed su(1,1) algebra, respectively. These internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum-generating algebras.

  10. Gifted Students' Individual Differences in Distance-Learning Computer-Based Calculus and Linear Algebra.

    ERIC Educational Resources Information Center

    Cope, Eric W.; Suppes, Patrick

    2002-01-01

    Examined student performance in distance computer-based calculus and linear algebra courses offered by Stanford University to pre-college students as part of their Education Program for Gifted youth (EPGY). Puts special emphasis on modeling student performance over time and on capturing long-term trend effects using stochastic and nonlinear…

  11. LETTER TO THE EDITOR: New bases of representation for the unitary parasupersymmetry algebra

    NASA Astrophysics Data System (ADS)

    Fakhri, H.

    2003-01-01

    Representation bases of unitary parasupersymmetry algebra of arbitrary order p is constructed by some one-dimensional models which are shape invariant with respect to the main quantum number n. Consequently, the isospectral Hamiltonians and their exact solutions are obtained as labelled by the main quantum number n.

  12. Mathematics Achievement with Digital Game-Based Learning in High School Algebra 1 Classes

    ERIC Educational Resources Information Center

    Ferguson, Terri Lynn Kurley

    2014-01-01

    This study examined the impact of digital game-based learning (DGBL) on mathematics achievement in a rural high school setting in North Carolina. A causal comparative research design was used in this study to collect data to determine the effectiveness of DGBL in high school Algebra 1 classes. Data were collected from the North Carolina…

  13. Student Incentive Preferences in a Competency-Based Remedial Algebra Course.

    ERIC Educational Resources Information Center

    Albright, Michael J.

    Lack of effort is a major reason for non-success among students in remedial mathematics, and the presence of a reward or an incentive may increase motivation in this learner group. A survey investigated the attitudes of 421 students toward incentive options in a competency-based remedial algebra course at Iowa State University. Students rated the…

  14. Quadratic Algebra Approach to the Dirac Equation with Spin and Pseudospin Symmetry for the 4D Harmonic Oscillator and U(1) Monopole

    NASA Astrophysics Data System (ADS)

    Aghaei, S.; Chenaghlou, A.

    2015-01-01

    In this paper, we study the Dirac equation with spin and pseudospin symmetry by the quadratic algebra approach for the 4-dimensional harmonic oscillator. By realization of the quadratic algebras in the deformed oscillator algebra, we obtain the relativistic energy spectrum. Also, by regarding the generalized Kustaanheimo-Stiefel transformation, we obtain the relativistic energy spectrum for the charge-dyon system with the U(1) monopole.

  15. A Comparison of Web-Based and Paper-and-Pencil Homework on Student Performance in College Algebra

    ERIC Educational Resources Information Center

    Hauk, Shandy; Powers, Robert A.; Segalla, Angelo

    2015-01-01

    College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: "WeBWorK," an open-source system for web-based homework, or traditional…

  16. A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry

    ERIC Educational Resources Information Center

    Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew

    2012-01-01

    In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

  17. Developing Concepts and Generalizations to Build Algebraic Thinking: The Reversibility, Flexibility, and Generalization Approach

    ERIC Educational Resources Information Center

    Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Darrough, Rebecca L.; Pfannenstiel, Kathleen Hughes

    2015-01-01

    Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

  18. Transferring a Flipped Class in Algebra-based Physics to New Faculty

    NASA Astrophysics Data System (ADS)

    Smith, Leigh; Sousa, Alexandre

    Transferring existing active classroom educational efforts to new faculty is a challenge that must be met to ensure sustainability of changes. We describe a flipped class approach to teaching algebra-based Physics being transferred to a new faculty member. This flipped class includes extensive video and reading-based preparation materials outside of class, and the use of Learning Catalytics for in-class work is developed and tested by one of the authors. These materials are of course idiosyncratic to the style of the developer. Student results using the new materials are compared with students in more standard classes which suggest significant positive benefit over several years. A faculty member decided to use these materials in his own section of the same course. Our experience shows that it takes some time for the new faculty member to use and adapt the materials in a way which matches his own style, which in the end results in equivalently enhanced results. Lessons learned from this transfer process will be discussed. We acknowledge the financial support of the NSF through DUE 1544001 and 1431350.

  19. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  20. Identifying Potential Areas for Siting Interim Nuclear Waste Facilities Using Map Algebra and Optimization Approaches

    SciTech Connect

    Omitaomu, Olufemi A; Liu, Cheng; Cetiner, Sacit M; Belles, Randy; Mays, Gary T; Tuttle, Mark A

    2013-01-01

    The renewed interest in siting new nuclear power plants in the United States has brought to the center stage, the need to site interim facilities for long-term management of spent nuclear fuel (SNF). In this paper, a two-stage approach for identifying potential areas for siting interim SNF facilities is presented. In the first stage, the land area is discretized into grids of uniform size (e.g., 100m x 100m grids). For the continental United States, this process resulted in a data matrix of about 700 million cells. Each cell of the matrix is then characterized as a binary decision variable to indicate whether an exclusion criterion is satisfied or not. A binary data matrix is created for each of the 25 siting criteria considered in this study. Using map algebra approach, cells that satisfy all criteria are clustered and regarded as potential siting areas. In the second stage, an optimization problem is formulated as a p-median problem on a rail network such that the sum of the shortest distance between nuclear power plants with SNF and the potential storage sites from the first stage is minimized. The implications of obtained results for energy policies are presented and discussed.

  1. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  2. Polyhedral realizations of crystal bases for quantum algebras of classical affine types

    SciTech Connect

    Hoshino, A.

    2013-05-15

    We give the explicit forms of the crystal bases B({infinity}) for the quantum affine algebras of types A{sub 2n-1}{sup (2)}, A{sub 2n}{sup (2)}, B{sub n}{sup (1)}, C{sub n}{sup (1)}, D{sub n}{sup (1)}, and D{sub n+1}{sup (2)} by using the method of polyhedral realizations of crystal bases.

  3. The algebra of Grassmann canonical anticommutation relations and its applications to fermionic systems

    SciTech Connect

    Keyl, Michael; Schlingemann, Dirk-M.

    2010-02-15

    We present an approach to a noncommutativelike phase space which allows to analyze quasifree states on the algebra of canonical anti-commutation relations (CAR) in analogy to quasifree states on the algebra of canonical commutation relations (CCR). The used mathematical tools are based on a new algebraic structure the 'Grassmann algebra of canonical anticommutation relations' (GAR algebra) which is given by the twisted tensor product of a Grassmann and a CAR algebra. As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two quasifree fermionic states which is needed for the study of entanglement distillation within fermionic systems.

  4. Topological membranes, current algebras and H-flux-R-flux duality based on Courant algebroids

    NASA Astrophysics Data System (ADS)

    Bessho, Taiki; Heller, Marc A.; Ikeda, Noriaki; Watamura, Satoshi

    2016-04-01

    We construct a topological sigma model and a current algebra based on a Courant algebroid structure on a Poisson manifold. In order to construct models, we reformulate the Poisson Courant algebroid by supergeometric construction on a QP-manifold. A new duality of Courant algebroids which transforms H-flux and R-flux is proposed, where the transformation is interpreted as a canonical transformation of a graded symplectic manifold.

  5. From Equation to Inequality Using a Function-Based Approach

    ERIC Educational Resources Information Center

    Verikios, Petros; Farmaki, Vassiliki

    2010-01-01

    This article presents features of a qualitative research study concerning the teaching and learning of school algebra using a function-based approach in a grade 8 class, of 23 students, in 26 lessons, in a state school of Athens, in the school year 2003-2004. In this article, we are interested in the inequality concept and our aim is to…

  6. Derivation of rigorous conditions for high cell-type diversity by algebraic approach.

    PubMed

    Yoshida, Hiroshi; Anai, Hirokazu; Horimoto, Katsuhisa

    2007-01-01

    The development of a multicellular organism is a dynamic process. Starting with one or a few cells, the organism develops into different types of cells with distinct functions. We have constructed a simple model by considering the cell number increase and the cell-type order conservation, and have assessed conditions for cell-type diversity. This model is based on a stochastic Lindenmayer system with cell-to-cell interactions for three types of cells. In the present model, we have successfully derived complex but rigorous algebraic relations between the proliferation and transition rates for cell-type diversity by using a symbolic method: quantifier elimination (QE). Surprisingly, three modes for the proliferation and transition rates have emerged for large ratios of the initial cells to the developed cells. The three modes have revealed that the equality between the development rates for the highest cell-type diversity is reduced during the development process of multicellular organisms. Furthermore, we have found that the highest cell-type diversity originates from order conservation. PMID:17293029

  7. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  8. Spatial-Operator Algebra For Flexible-Link Manipulators

    NASA Technical Reports Server (NTRS)

    Jain, Abhinandan; Rodriguez, Guillermo

    1994-01-01

    Method of computing dynamics of multiple-flexible-link robotic manipulators based on spatial-operator algebra, which originally applied to rigid-link manipulators. Aspects of spatial-operator-algebra approach described in several previous articles in NASA Tech Briefs-most recently "Robot Control Based on Spatial-Operator Algebra" (NPO-17918). In extension of spatial-operator algebra to manipulators with flexible links, each link represented by finite-element model: mass of flexible link apportioned among smaller, lumped-mass rigid bodies, coupling of motions expressed in terms of vibrational modes. This leads to operator expression for modal-mass matrix of link.

  9. Teaching of Real Numbers by Using the Archimedes-Cantor Approach and Computer Algebra Systems

    ERIC Educational Resources Information Center

    Vorob'ev, Evgenii M.

    2015-01-01

    Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…

  10. Implementation of Graphing Calculator in Intermediate Algebra with Function Approach in Community College

    ERIC Educational Resources Information Center

    Reznichenko, Nataliya

    2006-01-01

    A major goal of this paper is to document changes that occurred in developmental mathematics classrooms in the community college setting when the graphing calculator (GC) Texas Instruments (TI)-83 was introduced to students. The six-week intervention was conducted during the section of Intermediate Algebra in the Community College Baltimore County…

  11. Taking a College Algebra Course: An Approach that Increased Students' Success Rate

    ERIC Educational Resources Information Center

    Gonzalez-Muniz, Madeline; Klingler, Lee; Moosai, Susan; Raviv, Daniel

    2012-01-01

    Florida Atlantic University implemented a number of changes in the College Algebra course in an attempt to improve student success. We summarize these changes, and how they have affected the course. We also discuss possibilities for future improvements. (Contains 3 figures and 1 footnote.)

  12. Geometric and Algebraic Approaches in the Concept of "Limit" and the Impact of the "Didactic Contract"

    ERIC Educational Resources Information Center

    Elia, Iliada; Gagatsis, Athanasios; Panaoura, Areti; Zachariades, Theodosis; Zoulinaki, Fotini

    2009-01-01

    The present study explores students' abilities in conversions between geometric and algebraic representations, in problem-solving situations involving the concept of "limit" and the interrelation of these abilities with students' constructed understanding of this concept. An attempt is also made to examine the impact of the "didactic contract" on…

  13. From geometry to algebra: the Euclidean way with technology

    NASA Astrophysics Data System (ADS)

    Ferrarello, Daniela; Flavia Mammana, Maria; Pennisi, Mario

    2016-05-01

    In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products.

  14. Symbolic algebra approach to the calculation of intraocular lens power following cataract surgery

    NASA Astrophysics Data System (ADS)

    Hjelmstad, David P.; Sayegh, Samir I.

    2013-03-01

    We present a symbolic approach based on matrix methods that allows for the analysis and computation of intraocular lens power following cataract surgery. We extend the basic matrix approach corresponding to paraxial optics to include astigmatism and other aberrations. The symbolic approach allows for a refined analysis of the potential sources of errors ("refractive surprises"). We demonstrate the computation of lens powers including toric lenses that correct for both defocus (myopia, hyperopia) and astigmatism. A specific implementation in Mathematica allows an elegant and powerful method for the design and analysis of these intraocular lenses.

  15. Towards Metalogical Systematisation of Deontic Action Logics Based on Boolean Algebra

    NASA Astrophysics Data System (ADS)

    Trypuz, Robert; Kulicki, Piotr

    The aim of the present paper is to provide a metalogical systematisation in the area of deontic action logic based on Boolean algebra. Differences among the systems in question lie in two aspects: the level of closedness of a deontic action logic and the possibility of performing no action at all. It is also shown that the existing definitions of obligation in those systems are not acceptable due to their unintuitive interpretation or paradoxical consequences. As a solution we propose an axiomatic characterisation of obligation with an adequate class of models.

  16. Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

    PubMed

    Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

    2016-01-01

    A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively. PMID:27186457

  17. O(6) algebraic approach to three bound identical particles in the hyperspherical adiabatic representation

    NASA Astrophysics Data System (ADS)

    Salom, Igor; Dmitrašinović, V.

    2016-05-01

    We construct the three-body permutation symmetric O (6) hyperspherical harmonics and use them to solve the non-relativistic three-body Schrödinger equation in three spatial dimensions. We label the states with eigenvalues of the U (1) ⊗ SO(3)rot ⊂ U (3) ⊂ O (6) chain of algebras, and we present the K ≤ 4 harmonics and tables of their matrix elements. That leads to closed algebraic form of low-K energy spectra in the adiabatic approximation for factorizable potentials with square-integrable hyper-angular parts. This includes homogeneous pairwise potentials of degree α ≥ - 1. More generally, a simplification is achieved in numerical calculations of non-adiabatic approximations to non-factorizable potentials by using our harmonics.

  18. Spinors in the hyperbolic algebra

    NASA Astrophysics Data System (ADS)

    Ulrych, S.

    2006-01-01

    The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.

  19. Symbolic integration of a class of algebraic functions. [by an algorithmic approach

    NASA Technical Reports Server (NTRS)

    Ng, E. W.

    1974-01-01

    An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.

  20. Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

    NASA Astrophysics Data System (ADS)

    Salazar-Ramírez, M.; Ojeda-Guillén, D.; Mota, R. D.

    2016-09-01

    We study a relativistic quantum particle in cosmic string spacetime in the presence of a magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the su(1 , 1) symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.

  1. Teacher Implementation of Reform-Based Mathematics and Implications for Algebra Readiness: A Qualitative Study of 4th Grade Classrooms

    ERIC Educational Resources Information Center

    Sher, Stephen Korb

    2011-01-01

    This study looked at 4th grade classrooms to see "how" teachers implement NCTM standards-based or reform-based mathematics instruction and then analyzed it for the capacity to improve students' "algebra readiness." The qualitative study was based on classroom observations, teacher and administrator interviews, and teacher surveys. The study took…

  2. The Future of Physics in the Undergraduate Education of Biologists: Beyond the Algebra Based Course

    NASA Astrophysics Data System (ADS)

    de Leone, Charles

    2005-03-01

    The success of quantitative and computational methods of research in the biological sciences has incited calls for change in the undergraduate biological sciences curriculum. This reevaluation of the biology curriculum presents physicists with an opportunity to rethink and rebuild service courses such as the introductory algebra based physics course. Beyond the one-year introductory course, some of the more ambitious curricular reforms include calls for a third semester of physics for students who plan on doing biomedical research. This talk will briefly explore the open question of how we can best serve the evolving needs of our colleagues in biology by considering the calls for change in the biology curriculum such as BIO 2010 and reviewing the current state of the introductory physics course for biologists. In addition, this talk will review the successes and failures of research based courses such as the introductory calculus-based physics course for biologists at Cal State San Marcos.

  3. Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra.

    PubMed

    Fu, Zhongtao; Yang, Wenyu; Yang, Zhen

    2013-08-01

    In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators. PMID:23918347

  4. Operator Product Formulas in the Algebraic Approach of the Refined Topological Vertex

    NASA Astrophysics Data System (ADS)

    Cai, Li-Qiang; Wang, Li-Fang; Wu, Ke; Yang, Jie

    2013-02-01

    The refined topological vertex of Iqbal—Kozçaz—Vafa has been investigated from the viewpoint of the quantum algebra of type W1+∞ by Awata, Feigin, and Shiraishi. They introduced the trivalent intertwining operator Φ which is normal ordered along with some prefactors. We manage to establish formulas from the infinite operator product of the vertex operators and the generalized ones to restore this prefactor, and obtain an explicit formula for the vertex realization of the topological vertex as well as the refined topological vertex.

  5. Vector-algebra approach to extract Denavit-Hartenberg parameters of assembled robot arms

    NASA Technical Reports Server (NTRS)

    Barker, L. K.

    1983-01-01

    The Denavit-Hartenberg parameters characterize the joint axis systems in a robot arm and, naturally, appear in the transformation matrices from one joint axis system to another. These parameters are needed in the control of robot arms and in the passage of sensor information along the arm. This paper presents a vector algebra method to determine these parameters for any assembled robot arm. The idea is to measure the location of the robot hand (or extension) for different joint angles and then use these measurements to calculate the parameters.

  6. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  7. Undergraduate Students' Knowledge of Algebra: Evaluating the Impact of Computer-Based and Traditional Learning Environments

    ERIC Educational Resources Information Center

    Krupa, Erin E.; Webel, Corey; McManus, Jason

    2015-01-01

    We share results from a quasi-experimental study in which we compared achievement between traditional face-to-face and computer-based sections of Intermediate Algebra on a common multiple choice exam as well as performance on open-response tasks. Students in the computer-based group performed better on the final exam and were also more likely to…

  8. Retrieving the saddle-splay elastic constant K24 of nematic liquid crystals from an algebraic approach.

    PubMed

    Fumeron, Sébastien; Moraes, Fernando; Pereira, Erms

    2016-09-01

    The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant K24. However, the usual methods to retrieve the latter involve adjusting of computational parameters through visual comparisons between the experimental light interference pattern or a (2) H-NMR spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant K24. Considering an escaped-radial disclination inside a capillary tube with radius R0 of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle [Formula: see text] . Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius R0, the measurement of [Formula: see text] from the interference experiments involving two different radii allows us to algebraically retrieve K24. Our method allowed us to give the first reported estimation of K24 for the lyotropic chromonic liquid crystal Sunset Yellow FCF: K 24 = 2.1 pN. PMID:27589980

  9. Real-Time Algebraic Derivative Estimations Using a Novel Low-Cost Architecture Based on Reconfigurable Logic

    PubMed Central

    Morales, Rafael; Rincón, Fernando; Gazzano, Julio Dondo; López, Juan Carlos

    2014-01-01

    Time derivative estimation of signals plays a very important role in several fields, such as signal processing and control engineering, just to name a few of them. For that purpose, a non-asymptotic algebraic procedure for the approximate estimation of the system states is used in this work. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of a measurable signal in which two algebraic derivative estimators run simultaneously, but in an overlapping fashion. The algebraic derivative algorithm presented in this paper is computed online and in real-time, offering high robustness properties with regard to corrupting noises, versatility and ease of implementation. Besides, in this work, we introduce a novel architecture to accelerate this algebraic derivative estimator using reconfigurable logic. The core of the algorithm is implemented in an FPGA, improving the speed of the system and achieving real-time performance. Finally, this work proposes a low-cost platform for the integration of hardware in the loop in MATLAB. PMID:24859033

  10. Real-time algebraic derivative estimations using a novel low-cost architecture based on reconfigurable logic.

    PubMed

    Morales, Rafael; Rincón, Fernando; Gazzano, Julio Dondo; López, Juan Carlos

    2014-01-01

    Time derivative estimation of signals plays a very important role in several fields, such as signal processing and control engineering, just to name a few of them. For that purpose, a non-asymptotic algebraic procedure for the approximate estimation of the system states is used in this work. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of a measurable signal in which two algebraic derivative estimators run simultaneously, but in an overlapping fashion. The algebraic derivative algorithm presented in this paper is computed online and in real-time, offering high robustness properties with regard to corrupting noises, versatility and ease of implementation. Besides, in this work, we introduce a novel architecture to accelerate this algebraic derivative estimator using reconfigurable logic. The core of the algorithm is implemented in an FPGA, improving the speed of the system and achieving real-time performance. Finally, this work proposes a low-cost platform for the integration of hardware in the loop in MATLAB. PMID:24859033

  11. TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

    NASA Astrophysics Data System (ADS)

    Huf, P. A.; Carminati, J.

    2015-09-01

    In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.

  12. [Feature extraction for breast cancer data based on geometric algebra theory and feature selection using differential evolution].

    PubMed

    Li, Jing; Hong, Wenxue

    2014-12-01

    The feature extraction and feature selection are the important issues in pattern recognition. Based on the geometric algebra representation of vector, a new feature extraction method using blade coefficient of geometric algebra was proposed in this study. At the same time, an improved differential evolution (DE) feature selection method was proposed to solve the elevated high dimension issue. The simple linear discriminant analysis was used as the classifier. The result of the 10-fold cross-validation (10 CV) classification of public breast cancer biomedical dataset was more than 96% and proved superior to that of the original features and traditional feature extraction method. PMID:25868233

  13. A new mathematical evaluation of smoking problem based of algebraic statistical method.

    PubMed

    Mohammed, Maysaa J; Rakhimov, Isamiddin S; Shitan, Mahendran; Ibrahim, Rabha W; Mohammed, Nadia F

    2016-01-01

    Smoking problem is considered as one of the hot topics for many years. In spite of overpowering facts about the dangers, smoking is still a bad habit widely spread and socially accepted. Many people start smoking during their gymnasium period. The discovery of the dangers of smoking gave a warning sign of danger for individuals. There are different statistical methods used to analyze the dangers of smoking. In this study, we apply an algebraic statistical method to analyze and classify real data using Markov basis for the independent model on the contingency table. Results show that the Markov basis based classification is able to distinguish different date elements. Moreover, we check our proposed method via information theory by utilizing the Shannon formula to illustrate which one of these alternative tables is the best in term of independent. PMID:26858555

  14. The IPAD as a Pedagogical Tool in an Algebra-Based Introductory Physics Class

    NASA Astrophysics Data System (ADS)

    Garriott, Angela; Bush, Leah; Ramos, Roberto

    2012-02-01

    We report our experience in using the IPAD as a pedagogical tool for enhancing physics learning in an introductory algebra-based physics laboratory course for primarily pre-med students. We used several applications including (1) video analysis for experiments in accelerated motion (2) virtual oscilloscope for studying wave motion and circuit response to low frequency driving voltages; (3) applications for visualization of electric fields and magnetic fields. We compare student responses to this platform versus more traditional experiments. Using student surveys and polls. We also evaluate the IPAD as a new and familiar interface versus traditional interfaces like the standard oscilloscope. We report on the advantages and disadvantages of using this mobile, popular platform in delivering experimental physics content and promoting student engagement.

  15. Many worlds and modality in the interpretation of quantum mechanics: An algebraic approach

    SciTech Connect

    Domenech, G.; Freytes, H.; Ronde, C. de

    2009-07-15

    Many world interpretations (MWIs) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MIs) which state that quantum mechanics does not provide an account of what 'actually is the case', but rather deals with what 'might be the case', i.e., with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why - even though both interpretations share the same formal structure - MI fall pray of Kochen-Specker-type contradictions while MWI escape them.

  16. A Clifford Algebra Approach to the Classical Problem of a Charge in a Magnetic Monopole Field

    NASA Astrophysics Data System (ADS)

    Vaz, Jayme

    2013-05-01

    The motion of an electric charge in the field of a magnetic monopole is described by means of a Lagrangian model written in terms of the Clifford algebra of the physical space. The equations of motion are written in terms of a radial equation (involving r=| r|, where r( t) is the charge trajectory) and a rotor equation (written in terms of an unitary operator spinor R). The solution corresponding to the charge trajectory in the field of a magnetic monopole is given in parametric form. The model can be generalized in order to describe the motion of a charge in the field of a magnetic monopole and other additional central forces, and as an example, we discuss the classical ones involving linear and inverse square interactions.

  17. Simulation of n-qubit quantum systems: A computer-algebraic approach

    NASA Astrophysics Data System (ADS)

    Radtke, T.; Fritzsche, S.; Surzhykov, A.

    2007-03-01

    During the last decade, the field of quantum computation has attracted a lot of interest and motivated many theoretical and experimental studies of n-qubit quantum systems. But apart from the promise of more efficient quantum algorithms, these investigations also revealed a number of obstacles which still have to be overcome in practice. In this context, the use of simulation programs has proved to be an appropriate method. In order to facilitate the simulation of n-qubit quantum systems, we present the Feynman software program to provide the necessary tools to define and to deal with quantum registers as well as the operators acting on them. Using an interactive design within the framework of the computer algebra system Maple, we hope that the Feynman software program will be useful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future.

  18. Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications.

    PubMed

    Tudor, Tiberiu

    2012-04-01

    In the last decade we have elaborated a mathematical tool for the description of the interaction of polarized light with polarization devices, alternative to the standard matrix (Jones and Mueller) formalisms, namely a vectorial pure operatorial Pauli algebraic one. After a brief, coherent survey of this formalism, we present some applicative results obtained in this frame, referring to the gain and the modification of the state of polarization at the interaction of the polarized light with deterministic devices. Due to an adequate parameterization of the problem, specific to this method, symmetric expressions of the gain and of the generalized Malus' law are obtained. On the other hand, the equation of the ellipsoid in which a Poincaré sphere of a given degree of polarization is mapped by such a device can be established. PMID:22505099

  19. Contraction-based classification of supersymmetric extensions of kinematical lie algebras

    SciTech Connect

    Campoamor-Stursberg, R.; Rausch de Traubenberg, M.

    2010-02-15

    We study supersymmetric extensions of classical kinematical algebras from the point of view of contraction theory. It is shown that contracting the supersymmetric extension of the anti-de Sitter algebra leads to a hierarchy similar in structure to the classical Bacry-Levy-Leblond classification.

  20. Quantum hypercomputation based on the dynamical algebra \\mathfrak{su}(1\\, 1)

    NASA Astrophysics Data System (ADS)

    Sicard, A.; Ospina, J.; Vélez, M.

    2006-10-01

    An adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is presented. The method that was used was to replace the Weyl Heisenberg algebra by other dynamical algebra of low dimension that admits infinite-dimensional irreducible representations with naturally defined generalized coherent states. We have selected the Lie algebra \\mathfrak{su}(1,1) , because this algebra possesses the necessary characteristics to realize the hypercomputation and also because such algebra has been identified as the dynamical algebra associated with many relatively simple quantum systems. In addition to an algebraic adaptation of KHQA over the algebra \\mathfrak{su}(1,1) , we presented an adaptation of KHQA over some concrete physical referents: the infinite square well, the infinite cylindrical well, the perturbed infinite cylindrical well, the Pöschl Teller potentials, the Holstein Primakoff system and the Laguerre oscillator. We conclude that it is possible to have many physical systems within condensed matter and quantum optics in which it is possible to consider an implementation of KHQA.

  1. Transforming Spreadsheet-Based Numerical and Graphical Quadratic Sequences into Pencil-Paper Algebraic Expressions, and Prospective Teachers

    ERIC Educational Resources Information Center

    Gierdien, M. Faaiz

    2011-01-01

    This note demonstrates multiple representations (numerical and graphical) of spreadsheet-based quadratic sequences together with prospective teachers' pencil-paper transformations of these numerical sequences into a corresponding symbolization as algebraic expressions. With the majority of prospective teachers, the experience of school mathematics…

  2. Redesigning College Algebra: Combining Educational Theory and Web-Based Learning to Improve Student Attitudes and Performance

    ERIC Educational Resources Information Center

    Hagerty, Gary; Smith, Stanley; Goodwin, Danielle

    2010-01-01

    In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…

  3. A differential algebraic approach for the modeling of polycrystalline ferromagnetic hysteresis with minor loops and frequency dependence

    NASA Astrophysics Data System (ADS)

    Wang, Dan; Wang, Linxiang; Melnik, Roderick

    2016-07-01

    In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature.

  4. Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer

    NASA Astrophysics Data System (ADS)

    Müller, Dirk K.; Pampel, André; Möller, Harald E.

    2013-05-01

    Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data.

  5. Fuzzy-algebra uncertainty assessment

    SciTech Connect

    Cooper, J.A.; Cooper, D.K.

    1994-12-01

    A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.

  6. A computational algebra approach to the reverse engineering of gene regulatory networks.

    PubMed

    Laubenbacher, Reinhard; Stigler, Brandilyn

    2004-08-21

    This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to meso-scale networks rather than networks on a genome-wide scale. An analysis of the complexity of the algorithm is performed. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster. PMID:15246788

  7. Aquatic Macrophytes Inputs of Middle Chain Length n-alkyl Lipids into Lake Sediments: a Linear Algebra Approach

    NASA Astrophysics Data System (ADS)

    Gao, L.; Huang, Y.

    2009-12-01

    Quantitatively delineating multiple source inputs is a common but often difficult task in geological and environmental researches. Binary mixing model works well for simple two-component mixing problems when the two end members can be accurately defined. However, real world mixing problems usually involve more than two source components, and each component may have many composite profiles. Therefore, binary model is inadequate to provide an accurate estimate of contribution of all the end member sources. In such cases, linear combination model by solving linear algebra equations will have to be developed. In this study, we demonstrate the application of the linear algebra method to accurately calculate the percentage inputs of leaf waxes from different plant groups to lake sediments of Blood Pond and Rocky Pond in Massachusetts. We systematically sampled 28 species, including 6 tree species, 6 grass species, 7 emergent plants, 4 floating and 3 submerged aquatic plants around Blood Pond as well as 6 sediments samples of different depth. The distributions of these plants leaf waxes (n-alkanes and n-alkanoic acids) show distinctively different patterns, but also significant overlaps. To accurately quantify the percentage source inputs, we develop the 4-end member linear combination model. As we have an equation for each of the total 6 n-alkane compounds we use (C23 alkane ~C33 alkane), a 'least square fitting' is applied to solved the overdetermined linear system. Our results show that 91.7% of the total C23 alkane in sediments is derived from floating and submerged plants. We also applied our approach to Rocky Pond in southeastern Massachusetts and found >92 % of mid chain n-alkyl lipids are contributed by floating and submerged plants. Our results provide critical basis for using D/H ratios of mid-chain n-alkyl lipids (such as behenic acid) in lake sediments for reconstructing lake water D/H ratios.

  8. Those Do What? Connecting Eigenvectors and Eigenvalues to the Rest of Linear Algebra: Using Visual Enhancements to Help Students Connect Eigenvectors to the Rest of Linear Algebra

    ERIC Educational Resources Information Center

    Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S.

    2010-01-01

    This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

  9. Earth Algebra.

    ERIC Educational Resources Information Center

    Schaufele, Christopher; Zumoff, Nancy

    Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

  10. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  11. Towards a classification of modular invariant partition functions for theories based on N=4 superconformal algebras

    NASA Astrophysics Data System (ADS)

    Taormina, Anne

    1993-05-01

    The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.

  12. Effect of Teaching of Algebra through Social Constructivist Approach on 7th Graders' Learning Outcomes in Sindh (Pakistan)

    ERIC Educational Resources Information Center

    Ilyas, Bhutto Muhammad; Rawat, Khalid Jamil; Bhatti, Muhammad Tariq; Malik, Najeeb

    2013-01-01

    It is a bitter reality that the curricula and traditional pedagogy prevailing in public schools of Pakistan in general and Sindh in particular do not incorporate the algebraic concepts properly. Both the content and the presentation therein cannot be considered up to the mark, thereby making "Algebra" a tough and dry subject. This…

  13. Methods to Improve Performance of Students with Weaker Math Skills in an Algebra-based Physics Course

    NASA Astrophysics Data System (ADS)

    Smith, Leigh

    2015-03-01

    I will describe methods used at the University of Cincinnati to enhance student success in an algebra-based physics course. The first method is to use ALEKS, an adaptive online mathematics tutorial engine, before the term begins. Approximately three to four weeks before the beginning of the term, the professor in the course emails all of the students in the course informing them of the possibility of improving their math proficiency by using ALEKS. Using only a minimal reward on homework, we have achieved a 70% response rate with students spending an average of 8 hours working on their math skills before classes start. The second method is to use a flipped classroom approach. The class of 135 meets in a tiered classroom twice per week for two hours. Over the previous weekend students spend approximately 2 hours reading the book, taking short multiple choice conceptual quizzes, and viewing videos covering the material. In class, students use Learning Catalytics to work through homework problems in groups, guided by the instructor and one learning assistant. Using these interventions, we have reduced the student DWF rate (the fraction of students receiving a D or lower in the class) from an historical average of 35 to 40% to less than 20%.

  14. Student Preparation, Aptitude, and Performance in a First-Semester Algebra-Based Physics Course

    NASA Astrophysics Data System (ADS)

    Hill, Robert L.; Grosnick, D.; Ober, D.

    2006-12-01

    For several years measures of student performance have been investigated in the first semester of the two-semester algebra-based physics course. Preand post-tests using the Force Concept Inventory (FCI) and course grades were used as measures of student performance and preparation. In addition, information on high school preparation in physics and mathematics, student demographics (college major, classification, SAT math scores, etc.), and grades earned were collected. Results will be presented that indicate high school physics preparation, college major, and SAT math scores strongly correlate with grade earned, FCI pre-instruction scores, and FCI normalized gains. Using the current investigation and institutional data from the work of Coletta and Phillips1, it will be shown that a strong correlation exists between FCI pre-instruction scores and normalized gain. 1. V.P. Coletta and J.A. Phillips, Am. J. Phys 73, 1172 (2005). *Work sponsored by PhysTEC and supported by grants from the National Science Foundation and FIPSE.

  15. A GRASS GIS based Spatio-Temporal Algebra for Raster-, 3D Raster- and Vector Time Series Data

    NASA Astrophysics Data System (ADS)

    Leppelt, Thomas; Gebbert, Sören

    2015-04-01

    Enhancing the well known and widely used map algebra proposed by Dr. Charles Dana Tomlin [1] with the time dimension is an ongoing research topic. The efficient processing of large time series of raster, 3D raster and vector datasets, e. g. raster datasets for temperature or precipitations on continental scale, requires a sophisticated spatio-temporal algebra that is capable of handling datasets with different temporal granularities and spatio-temporal extents. With the temporal enabled GRASS GIS [2] and the GRASS GIS Temporal Framework new spatio-temporal data types are available in GRASS GIS 7, called space time datasets. These space time datasets represent time series of raster, 3D raster and vector map layers. Furthermore the temporal framework provides a wide range of functionalities to support the implementation of a temporal algebra. While spatial capabilities of GRASS GIS are used to perform the spatial processing of the time stamped map layers that are registered in a space time dataset, the temporal processing is provided by the GRASS GIS temporal framework that supports time intervals and time instances. Mixing time instance and time intervals as well as gaps, overlapping or inclusion of intervals and instances is possible. Hence this framework allows an arbitrary layout of the time dimension. We implemented two ways to process space time datasets with arbitrary temporal layout, the temporal topology and the granularity based spatio-temporal algebra. The algebra provides the functionality to define complex spatio-temporal topological operators that process time and space in a single expression. The algebra includes methods to select map layers from space time datasets based on their temporal relations, to temporally shift time stamped map layers, to create temporal buffer and to snap time instances of time stamped map layers to create a valid temporal topology. In addition spatio-temporal operations can be evaluated within conditional statements. These

  16. An Adaptive Algebra Test: A Testlet-Based, Hierarchically-Structured Test with Validity-Based Scoring. Technical Report No. 90-92.

    ERIC Educational Resources Information Center

    Wainer, Howard; And Others

    The initial development of a testlet-based algebra test was previously reported (Wainer and Lewis, 1990). This account provides the details of this excursion into the use of hierarchical testlets and validity-based scoring. A pretest of two 15-item hierarchical testlets was carried out in which examinees' performance on a 4-item subset of each…

  17. The early history of current Algebra

    NASA Astrophysics Data System (ADS)

    Pietschmann, Herbert

    2011-07-01

    The history of Current Algebra is reviewed up to the appearance of the Adler-Weisberger sum rule. Particular emphasis is given to the role of current algebra in the historical struggle in strong interaction physics of elementary particles between field theory and the S-matrix approach based on dispersion relations. The question as to whether some particles are truly fundamental or all hadrons are bound or resonant states of one another played an important role in this struggle and is thus also regarded.

  18. The Algebraic Way

    NASA Astrophysics Data System (ADS)

    Hiley, B. J.

    In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.

  19. Algebraic integrability: a survey.

    PubMed

    Vanhaecke, Pol

    2008-03-28

    We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863

  20. Algebraic Thinking in Adult Education

    ERIC Educational Resources Information Center

    Manly, Myrna; Ginsburg, Lynda

    2010-01-01

    In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…

  1. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  2. Angular momentum and Zeeman effect in the presence of a minimal length based on the Kempf-Mann-Mangano algebra

    NASA Astrophysics Data System (ADS)

    Khosropour, B.

    2016-07-01

    In this work, we consider a D-dimensional ( β, β^' -two-parameters deformed Heisenberg algebra, which was introduced by Kempf et al. The angular-momentum operator in the presence of a minimal length scale based on the Kempf-Mann-Mangano algebra is obtained in the special case of β^' = 2β up to the first order over the deformation parameter β . It is shown that each of the components of the modified angular-momentum operator, commutes with the modified operator {L}2 . We find the magnetostatic field in the presence of a minimal length. The Zeeman effect in the deformed space is studied and also Lande's formula for the energy shift in the presence of a minimal length is obtained. We estimate an upper bound on the isotropic minimal length.

  3. Conditions for the Effectiveness of a Tablet-Based Algebra Program

    ERIC Educational Resources Information Center

    Jaciw, Andrew P.; Toby, Megan; Ma, Boya

    2012-01-01

    Tablets such as the iPad represent the next iteration of technologies that hold promise to facilitate learning, particularly in mathematics. In the case of algebra, tablets have the potential to bring the curriculum to life by easily linking to supporting materials and they allow an interactive experience whereby manipulation of one type of…

  4. Developing a TI-92 Manual Generator Based on Computer Algebra Systems

    ERIC Educational Resources Information Center

    Jun, Youngcook

    2004-01-01

    The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…

  5. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

    NASA Astrophysics Data System (ADS)

    Ibarra-Sierra, V. G.; Sandoval-Santana, J. C.; Cardoso, J. L.; Kunold, A.

    2015-11-01

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai-Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.

  6. An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approach

    NASA Astrophysics Data System (ADS)

    Shyue, Keh-Ming; Xiao, Feng

    2014-07-01

    We describe a novel interface-sharpening approach for efficient numerical resolution of a compressible homogeneous two-phase flow governed by a quasi-conservative five-equation model of Allaire et al. (2001) [1]. The algorithm uses a semi-discrete wave propagation method to find approximate solution of this model numerically. In the algorithm, in regions near the interfaces where two different fluid components are present within a cell, the THINC (Tangent of Hyperbola for INterface Capturing) scheme is used as a basis for the reconstruction of a sub-grid discontinuity of volume fractions at each cell edge, and it is complemented by a homogeneous-equilibrium-consistent technique that is derived to ensure a consistent modeling of the other interpolated physical variables in the model. In regions away from the interfaces where the flow is single phase, standard reconstruction scheme such as MUSCL or WENO can be used for obtaining high-order interpolated states. These reconstructions are then used as the initial data for Riemann problems, and the resulting fluctuations form the basis for the spatial discretization. Time integration of the algorithm is done by employing a strong stability-preserving Runge-Kutta method. Numerical results are shown for sample problems with the Mie-Grüneisen equation of state for characterizing the materials of interests in both one and two space dimensions that demonstrate the feasibility of the proposed method for interface-sharpening of compressible two-phase flow. To demonstrate the competitiveness of our approach, we have also included results obtained using the anti-diffusion interface sharpening method.

  7. Quantum computation using geometric algebra

    NASA Astrophysics Data System (ADS)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  8. Invertible linear transformations and the Lie algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Yufeng; Tam, Honwah; Guo, Fukui

    2008-07-01

    With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.

  9. Infections on Temporal Networks—A Matrix-Based Approach

    PubMed Central

    Koher, Andreas; Lentz, Hartmut H. K.; Hövel, Philipp; Sokolov, Igor M.

    2016-01-01

    We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected. PMID:27035128

  10. Infections on Temporal Networks--A Matrix-Based Approach.

    PubMed

    Koher, Andreas; Lentz, Hartmut H K; Hövel, Philipp; Sokolov, Igor M

    2016-01-01

    We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected. PMID:27035128

  11. Skull base approaches in neurosurgery

    PubMed Central

    2010-01-01

    The skull base surgery is one of the most demanding surgeries. There are different structures that can be injured easily, by operating in the skull base. It is very important for the neurosurgeon to choose the right approach in order to reach the lesion without harming the other intact structures. Due to the pioneering work of Cushing, Hirsch, Yasargil, Krause, Dandy and other dedicated neurosurgeons, it is possible to address the tumor and other lesions in the anterior, the mid-line and the posterior cranial base. With the transsphenoidal, the frontolateral, the pterional and the lateral suboccipital approach nearly every region of the skull base is exposable. In the current state many different skull base approaches are described for various neurosurgical diseases during the last 20 years. The selection of an approach may differ from country to country, e.g., in the United States orbitozygomaticotomy for special lesions of the anterior skull base or petrosectomy for clivus meningiomas, are found more frequently than in Europe. The reason for writing the review was the question: Are there keyhole approaches with which someone can deal with a vast variety of lesions in the neurosurgical field? In my opinion the different surgical approaches mentioned above cover almost 95% of all skull base tumors and lesions. In the following text these approaches will be described. These approaches are: 1) pterional approach 2) frontolateral approach 3) transsphenoidal approach 4) suboccipital lateral approach These approaches can be extended and combined with each other. In the following we want to enhance this philosophy. PMID:20602753

  12. Thinking Visually about Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  13. An Algebraic Approach to the Evolution of Emittances upon Crossing the Linear Coupling Difference Resonance

    SciTech Connect

    Gardner,C.

    2008-09-01

    One of the hallmarks of linear coupling is the resonant exchange of oscillation amplitude between the horizontal and vertical planes when the difference between the unperturbed tunes is close to an integer. The standard derivation of this phenomenon (known as the difference resonance) can be found, for example, in the classic papers of Guignard [1, 2]. One starts with an uncoupled lattice and adds a linear perturbation that couples the two planes. The equations of motion are expressed in hamiltonian form. As the difference between the unperturbed tunes approaches an integer, one finds that the perturbing terms in the hamiltonian can be divided into terms that oscillate slowly and ones that oscillate rapidly. The rapidly oscillating terms are discarded or transformed to higher order with an appropriate canonical transformation. The resulting approximate hamiltonian gives equations of motion that clearly exhibit the exchange of oscillation amplitude between the two planes. If, instead of the hamiltonian, one is given the four-by-four matrix for one turn around a synchrotron, then one has the complete solution for the turn-by-turn (TBT) motion. However, the conditions for the phenomenon of amplitude exchange are not obvious from a casual inspection of the matrix. These conditions and those that give rise to the related sum resonance are identified in this report. The identification is made using the well known formalism of Edwards and Teng [3, 4, 5] and, in particular, the normalized coupling matrix of Sagan and Rubin [6]. The formulae obtained are general in that no particular hamiltonian or coupling elements are assumed. The only assumptions are that the one-turn matrix is symplectic and that it has distinct eigenvalues on the unit circle in the complex plane. Having identified the conditions of the one-turn matrix that give rise to the resonances, we focus on the difference resonance and apply the formulae to the evolution of the horizontal and vertical emittances

  14. Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

    NASA Astrophysics Data System (ADS)

    Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

    Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.

  15. Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.

    ERIC Educational Resources Information Center

    Leitze, Annette Ricks; Kitt, Nancy A.

    2000-01-01

    Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

  16. The Algebra of Lexical Semantics

    NASA Astrophysics Data System (ADS)

    Kornai, András

    The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.

  17. Construction of linear models: A framework based on commutative Jordan algebras

    NASA Astrophysics Data System (ADS)

    Covas, R.; Carvalho, F.

    2016-06-01

    We show how to obtain the necessary structures for statistical analysis of the folllowing orthogonal models Y˜(1 μ +∑i Xiβi ,∑j σj2Mj+σ2I ) . These structures rely on the existence of Jordan algebras, in the sequence of [24], [8], [12], [9], [5] and [10].

  18. Selecting reusable components using algebraic specifications

    NASA Technical Reports Server (NTRS)

    Eichmann, David A.

    1992-01-01

    A significant hurdle confronts the software reuser attempting to select candidate components from a software repository - discriminating between those components without resorting to inspection of the implementation(s). We outline a mixed classification/axiomatic approach to this problem based upon our lattice-based faceted classification technique and Guttag and Horning's algebraic specification techniques. This approach selects candidates by natural language-derived classification, by their interfaces, using signatures, and by their behavior, using axioms. We briefly outline our problem domain and related work. Lattice-based faceted classifications are described; the reader is referred to surveys of the extensive literature for algebraic specification techniques. Behavioral support for reuse queries is presented, followed by the conclusions.

  19. Exploring Algebraic Patterns through Literature.

    ERIC Educational Resources Information Center

    Austin, Richard A.; Thompson, Denisse R.

    1997-01-01

    Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…

  20. Exploring Attitudes and Achievement of Web-Based Homework in Developmental Algebra

    ERIC Educational Resources Information Center

    Leong, Kwan Eu; Alexander, Nathan

    2013-01-01

    The purpose of this study was to understand how students' attitudes were connected to their mathematics learning. This investigation was specific to web-based homework in developmental courses in the community college environment. The mixed-methods approach was used to analyze the relationship between students' attitudes and mathematical…

  1. Implementing dense linear algebra algorithms using multitasking on the CRAY X-MP-4 (or approaching the gigaflop)

    SciTech Connect

    Dongarra, J.J.; Hewitt, T.

    1985-08-01

    This note describes some experiments on simple, dense linear algebra algorithms. These experiments show that the CRAY X-MP is capable of small-grain multitasking arising from standard implementations of LU and Cholesky decomposition. The implementation described here provides the ''fastest'' execution rate for LU decomposition, 718 MFLOPS for a matrix of order 1000.

  2. An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

    SciTech Connect

    Kalay, Berfin; Demiralp, Metin

    2015-12-31

    This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.

  3. New family of Maxwell like algebras

    NASA Astrophysics Data System (ADS)

    Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.

    2016-08-01

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  4. A Balancing Act: Making Sense of Algebra

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  5. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  6. Algebraic and analytic reconstruction methods for dynamic tomography.

    PubMed

    Desbat, L; Rit, S; Clackdoyle, R; Mennessier, C; Promayon, E; Ntalampeki, S

    2007-01-01

    In this work, we discuss algebraic and analytic approaches for dynamic tomography. We present a framework of dynamic tomography for both algebraic and analytic approaches. We finally present numerical experiments. PMID:18002059

  7. Security analysis of boolean algebra based on Zhang-Wang digital signature scheme

    SciTech Connect

    Zheng, Jinbin

    2014-10-06

    In 2005, Zhang and Wang proposed an improvement signature scheme without using one-way hash function and message redundancy. In this paper, we show that this scheme exits potential safety concerns through the analysis of boolean algebra, such as bitwise exclusive-or, and point out that mapping is not one to one between assembly instructions and machine code actually by means of the analysis of the result of the assembly program segment, and which possibly causes safety problems unknown to the software.

  8. Security analysis of boolean algebra based on Zhang-Wang digital signature scheme

    NASA Astrophysics Data System (ADS)

    Zheng, Jinbin

    2014-10-01

    In 2005, Zhang and Wang proposed an improvement signature scheme without using one-way hash function and message redundancy. In this paper, we show that this scheme exits potential safety concerns through the analysis of boolean algebra, such as bitwise exclusive-or, and point out that mapping is not one to one between assembly instructions and machine code actually by means of the analysis of the result of the assembly program segment, and which possibly causes safety problems unknown to the software.

  9. An Interactive Text for Linear Algebra. Final Report.

    ERIC Educational Resources Information Center

    Porter, Gerald J.

    This project supported the creation of a computer-based interactive text for linear algebra using guided discovery in a laboratory-based course which emphasized active learning, collaborative learning, and the use of writing. This pedagogical approach had as its goal improved student understanding and retention of the concepts and methods of…

  10. The Structural Algebra Option: A Discussion Paper.

    ERIC Educational Resources Information Center

    Kirshner, David

    The goal of this paper is to renew interest in the structural option to algebra instruction. Concern for the usual secondary school algebra curriculum related to simplifying expressions, solving equations, and rationalizing numerators and denominators is viewed from three pedagogical approaches: (1) structural approach, (2) empirical approach, and…

  11. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  12. Generalized Flip-Flop Input Equations Based on a Four-Valued Boolean Algebra

    NASA Technical Reports Server (NTRS)

    Tucker, Jerry H.; Tapia, Moiez A.

    1996-01-01

    A procedure is developed for obtaining generalized flip-flop input equations, and a concise method is presented for representing these equations. The procedure is based on solving a four-valued characteristic equation of the flip-flop, and can encompass flip-flops that are too complex to approach intuitively. The technique is presented using Karnaugh maps, but could easily be implemented in software.

  13. Scaling Linear Algebra Kernels using Remote Memory Access

    SciTech Connect

    Krishnan, Manoj Kumar; Lewis, Robert R.; Vishnu, Abhinav

    2010-09-13

    This paper describes the scalability of linear algebra kernels based on remote memory access approach. The current approach differs from the other linear algebra algorithms by the explicit use of shared memory and remote memory access (RMA) communication rather than message passing. It is suitable for clusters and scalable shared memory systems. The experimental results on large scale systems (Linux-Infiniband cluster, Cray XT) demonstrate consistent performance advantages over ScaLAPACK suite, the leading implementation of parallel linear algebra algorithms used today. For example, on a Cray XT4 for a matrix size of 102400, our RMA-based matrix multiplication achieved over 55 teraflops while ScaLAPACK’s pdgemm measured close to 42 teraflops on 10000 processes.

  14. Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry

    NASA Astrophysics Data System (ADS)

    Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.

    2016-09-01

    The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.

  15. Implementation of Math Pre-testing and Tutorials for Improving Student Success in Algebra-based Introductory Physics Course

    NASA Astrophysics Data System (ADS)

    Stokes, Donna

    2012-10-01

    The student success rate in the algebra-based Introductory General Physics I course at the University of Houston (UH) and across the United States is low in comparison to success rates in other service courses. In order to improve student success rates, we have implemented, in addition to interactive teaching techniques, pre-testing as an early intervention process to identify and remediate at-risk students. The pre-testing includes a math and problem-solving skills diagnostic exam and pre-tests administered prior to all regular exams. Students identified as at risk based on their scores on these pre-tests are given incentives to utilize a tutoring intervention consisting of on-line math tutoring to address math deficiencies and tutoring by graduate Physics Teaching Assistants to address student understanding of the physics concepts. Results from 503 students enrolled in three sections of the course showed that 78% of the students identified as at-risk students by the diagnostic exam who completed the math tutorial successfully completed the course, as compared to 45% of at-risk students who did not complete the math tutorial. Results of the pre-testing before each regular exam showed that all students who were identified as at risk based on pre-test scores had positive gains ranging from 9 -- 32% for the three regular exams. However, the large standard deviations of these gains indicate that they are not statistically significant; therefore, pretesting before exams will not be offer in the course. However, utilization of the math tutorials as remediation will continue to be offered to all sections of the algebra-based course at UH with the goal of significantly improving the overall success rates for the introductory physics courses.

  16. SD-CAS: Spin Dynamics by Computer Algebra System.

    PubMed

    Filip, Xenia; Filip, Claudiu

    2010-11-01

    A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples. PMID:20843716

  17. Twisted Quantum Toroidal Algebras

    NASA Astrophysics Data System (ADS)

    Jing, Naihuan; Liu, Rongjia

    2014-09-01

    We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.

  18. QuBiLS-MIDAS: a parallel free-software for molecular descriptors computation based on multilinear algebraic maps.

    PubMed

    García-Jacas, César R; Marrero-Ponce, Yovani; Acevedo-Martínez, Liesner; Barigye, Stephen J; Valdés-Martiní, José R; Contreras-Torres, Ernesto

    2014-07-01

    The present report introduces the QuBiLS-MIDAS software belonging to the ToMoCoMD-CARDD suite for the calculation of three-dimensional molecular descriptors (MDs) based on the two-linear (bilinear), three-linear, and four-linear (multilinear or N-linear) algebraic forms. Thus, it is unique software that computes these tensor-based indices. These descriptors, establish relations for two, three, and four atoms by using several (dis-)similarity metrics or multimetrics, matrix transformations, cutoffs, local calculations and aggregation operators. The theoretical background of these N-linear indices is also presented. The QuBiLS-MIDAS software was developed in the Java programming language and employs the Chemical Development Kit library for the manipulation of the chemical structures and the calculation of the atomic properties. This software is composed by a desktop user-friendly interface and an Abstract Programming Interface library. The former was created to simplify the configuration of the different options of the MDs, whereas the library was designed to allow its easy integration to other software for chemoinformatics applications. This program provides functionalities for data cleaning tasks and for batch processing of the molecular indices. In addition, it offers parallel calculation of the MDs through the use of all available processors in current computers. The studies of complexity of the main algorithms demonstrate that these were efficiently implemented with respect to their trivial implementation. Lastly, the performance tests reveal that this software has a suitable behavior when the amount of processors is increased. Therefore, the QuBiLS-MIDAS software constitutes a useful application for the computation of the molecular indices based on N-linear algebraic maps and it can be used freely to perform chemoinformatics studies. PMID:24889018

  19. Explorations in Algebra: Hands-On Lab Activities.

    ERIC Educational Resources Information Center

    Dougherty, Barbara J.; Matsumoto, Annette N.; Zenigami, Fay

    This book is a compatible instructional component to any algebra textbook and was developed by University of Hawaii under the Dwight D. Eisenhower Mathematics and Science Education Improvement Act. The tasks align with the content and instructional approach used in daily classes that emphasize standards-based teaching and learning. The tasks…

  20. Non-Traditional Methods of Teaching Abstract Algebra

    ERIC Educational Resources Information Center

    Capaldi, Mindy

    2014-01-01

    This article reports on techniques of teaching abstract algebra which were developed to achieve multiple student objectives: reasoning and communication skills, deep content knowledge, student engagement, independence, and pride. The approach developed included a complementary combination of inquiry-based learning, individual (not group) homework…

  1. Spherical harmonics: coherent states constructed by the second lowest and second highest bases of su(1, 1) Lie algebra

    NASA Astrophysics Data System (ADS)

    Dehghani, A.; Fakhri, H.

    2011-02-01

    The second lowest and second highest bases of the discrete positive and negative irreducible representations of su(1, 1) Lie algebra via spherical harmonics are used to construct generalized coherent states. Depending on whether the representation label is an even or odd integer, each of the new coherent states is separated into two different classes. They are constituted by appropriate superpositions of the increasing and decreasing infinite sequences with respect to the m index of the spherical harmonics {Ym2j ± m(θ, phi)}m = mnplusj ± 1±∞ and {Ym2k ± m - 1(θ, phi)}m = mnplusk ± 2±∞, and converge to the known functions. Also the non-oscillating measures to realize the resolution of the identity condition on the unit disk are calculated.

  2. Realization Of Algebraic Processor For XML Documents Processing

    SciTech Connect

    Georgiev, Bozhidar; Georgieva, Adriana

    2010-10-25

    In this paper, are presented some possibilities concerning the implementation of an algebraic method for XML hierarchical data processing which makes faster the XML search mechanism. Here is offered a different point of view for creation of advanced algebraic processor (with all necessary software tools and programming modules respectively). Therefore, this nontraditional approach for fast XML navigation with the presented algebraic processor may help to build an easier user-friendly interface provided XML transformations, which can avoid the difficulties in the complicated language constructions of XSL, XSLT and XPath. This approach allows comparatively simple search of XML hierarchical data by means of the following types of functions: specification functions and so named build-in functions. The choice of programming language Java may appear strange at first, but it isn't when you consider that the applications can run on different kinds of computers. The specific search mechanism based on the linear algebra theory is faster in comparison with MSXML parsers (on the basis of the developed examples with about 30%). Actually, there exists the possibility for creating new software tools based on the linear algebra theory, which cover the whole navigation and search techniques characterizing XSLT/XPath. The proposed method is able to replace more complicated operations in other SOA components.

  3. Realization Of Algebraic Processor For XML Documents Processing

    NASA Astrophysics Data System (ADS)

    Georgiev, Bozhidar; Georgieva, Adriana

    2010-10-01

    In this paper, are presented some possibilities concerning the implementation of an algebraic method for XML hierarchical data processing which makes faster the XML search mechanism. Here is offered a different point of view for creation of advanced algebraic processor (with all necessary software tools and programming modules respectively). Therefore, this nontraditional approach for fast XML navigation with the presented algebraic processor may help to build an easier user-friendly interface provided XML transformations, which can avoid the difficulties in the complicated language constructions of XSL, XSLT and XPath. This approach allows comparatively simple search of XML hierarchical data by means of the following types of functions: specification functions and so named build-in functions. The choice of programming language Java may appear strange at first, but it isn't when you consider that the applications can run on different kinds of computers. The specific search mechanism based on the linear algebra theory is faster in comparison with MSXML parsers (on the basis of the developed examples with about 30%). Actually, there exists the possibility for creating new software tools based on the linear algebra theory, which cover the whole navigation and search techniques characterizing XSLT/XPath. The proposed method is able to replace more complicated operations in other SOA components.

  4. Algebraic vs physical N = 6 3-algebras

    SciTech Connect

    Cantarini, Nicoletta; Kac, Victor G.

    2014-01-15

    In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.

  5. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  6. Lie algebraic approach of a charged particle in presence of a constant magnetic field via the quadratic invariant

    SciTech Connect

    Abdalla, M. Sebawe; Elkasapy, A.I.

    2010-08-15

    In this paper we consider the problem of a charged harmonic oscillator under the influence of a constant magnetic field. The system is assumed to be isotropic and the magnetic field is applied along the z-axis. The canonical transformation is invoked to remove the interaction term and the system is reduced to a model containing the second harmonic generation. Two classes of the real and complex quadratic invariants (constants of motion) are obtained. We have employed the Lie algebraic technique to find the most general solution for the wave function for both real and complex invariants. Some discussions related to the advantage of using the quadratic invariants to solve the Cauchy problem instead of the direct use of the Hamiltonian itself are also given.

  7. GNSS algebraic structures

    NASA Astrophysics Data System (ADS)

    Lannes, A.; Teunissen, P. J. G.

    2011-05-01

    not the case for the satellite-clock biases. The third objective of this paper is to make the link between the CD approach and the GNSS methods based on the notion of double difference. In particular, it is shown that the information provided by a maximum set of independent DDs may not reach that of a complete set of CDs. The corresponding defect is analyzed. One of the main results of the corresponding analysis concerns the DD-CD relationship. In particular, it is shown that the DD ambiguities, once they have been fixed and validated, can be used as input data in the `undifferenced CD equations.' The corresponding algebraic operations are described. The satellite pseudo-clock biases can therefore be also obtained via particular methods in which the notion of double differencing is involved.

  8. Integrable maps from Galois differential algebras, Borel transforms and number sequences

    NASA Astrophysics Data System (ADS)

    Tempesta, Piergiulio

    A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a given differential equation, in particular symmetries and integrability (see Tempesta, 2010 [40]). Our approach is based on the properties of a suitable Galois differential algebra, that we shall call a Rota algebra. A formulation of the procedure in terms of category theory is proposed. In order to render the lattice dynamics confined, a Borel regularization is also adopted. As a byproduct of the theory, a connection between number sequences and integrability is discussed.

  9. Historical Topics in Algebra.

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, Inc., Reston, VA.

    This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…

  10. Semiclassical states on Lie algebras

    SciTech Connect

    Tsobanjan, Artur

    2015-03-15

    The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.

  11. A Structure of BCI-Algebras

    NASA Astrophysics Data System (ADS)

    Chajda, Ivan

    2014-10-01

    Commutative BCI-algebras can be considered as semilattices whose sections are equipped with certain involutions. A similar view can be applied to commutative BCK-algebras. However, for general BCK-algebras a certain construction was settled by the author and J. Kühr (Miskolc Math. Notes 8:11-21, 2007) showing that they can be considered as structures essentially weaker than semilattices but still with certain involutions in sections. The aim of this paper is to involve a similar approach for BCI-algebras.

  12. FAST TRACK COMMUNICATION Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

    NASA Astrophysics Data System (ADS)

    Senovilla, José M. M.

    2010-11-01

    The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved.

  13. Deformations of 3-algebras

    SciTech Connect

    Figueroa-O'Farrill, Jose Miguel

    2009-11-15

    We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.

  14. A Statistical Analysis of Activity-Based and Traditional Introductory Algebra Physics Using the Force and Motion Conceptual Evaluation

    NASA Astrophysics Data System (ADS)

    Trecia Markes, Cecelia

    2006-03-01

    With a three-year FIPSE grant, it has been possible at the University of Nebraska at Kearney (UNK) to develop and implement activity- based introductory physics at the algebra level. It has generally been recognized that students enter physics classes with misconceptions about motion and force. Many of these misconceptions persist after instruction. Pretest and posttest responses on the ``Force and Motion Conceptual Evaluation'' (FMCE) are analyzed to determine the effectiveness of the activity- based method of instruction relative to the traditional (lecture/lab) method of instruction. Data were analyzed to determine the following: student understanding at the beginning of the course, student understanding at the end of the course, how student understanding is related to the type of class taken, student understanding based on gender and type of class. Some of the tests used are the t-test, the chi-squared test, and analysis of variance. The results of these tests will be presented, and their implications will be discussed.

  15. Using the Internet To Investigate Algebra.

    ERIC Educational Resources Information Center

    Sherwood, Walter

    The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…

  16. Algebraic Formulas for Areas between Curves.

    ERIC Educational Resources Information Center

    Gabai, Hyman

    1982-01-01

    Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)

  17. Quantum cluster algebras and quantum nilpotent algebras

    PubMed Central

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  18. Quantized Nambu-Poisson manifolds and n-Lie algebras

    SciTech Connect

    DeBellis, Joshua; Saemann, Christian; Szabo, Richard J.

    2010-12-15

    We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of R{sup n} by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.

  19. Quantized Nambu-Poisson manifolds and n-Lie algebras

    NASA Astrophysics Data System (ADS)

    DeBellis, Joshua; Sämann, Christian; Szabo, Richard J.

    2010-12-01

    We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of {{R}}^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.

  20. Algebraic approach to the structure of the low-lying states in A ≈100 Ru isotopes

    NASA Astrophysics Data System (ADS)

    Kisyov, S.; Bucurescu, D.; Jolie, J.; Lalkovski, S.

    2016-04-01

    The structure of the low-lying states in the odd- and even-mass A ≈100 Ru isotopes is studied in the framework of two algebraic models. The even-mass Ru nuclei are first described within the interacting boson model 1 (IBM-1). The output of these calculations was then used to calculate the odd-A isotopes within the interacting boson-fermion model 1 (IBFM-1), where a coupling of the odd neutron to the even-even core is considered. The level energies and transition probabilities calculated in the present work are tested against the experimental data. One-nucleon transfer spectroscopic factors as well as electromagnetic moments were also calculated for the odd-A Ru and compared to the experimental values. The transitional character of the isotopes is studied. Most of the low-lying positive-parity states in the odd-A Ru nuclei below 2 MeV are interpreted on the basis of ν d5 /2 and ν g7 /2 configurations. The role of the ν s1 /2 orbital in the nuclear structure of the odd-mass Ru nuclei at low energies is also studied. The negative-parity states are interpreted as ν h11 /2 excitations coupled to the core. The evolution of the IBM-1 and IBFM-1 parameters is discussed.

  1. Lymphocyte subset analysis by Boolean algebra: a phenotypic approach using a cocktail of 5 antibodies and 3 color immunofluorescence.

    PubMed

    Hunter, S D; Peters, L E; Wotherspoon, J S; Crowe, S M

    1994-03-01

    Commercial reagent kits for the evaluation of leukocyte subsets involve the staining of a panel of up to six tubes using combinations of pre-mixed fluorescein isothiocyanate (FITC) and R-phycoerythrin (PE) conjugated monoclonal antibodies. We describe a rapid method whereby total CD3+ T-cells, CD4+ T-cells (CD3+ CD4+), CD8+ T-cells (CD3+ CD8+), putative gamma delta-receptor-T-cells (CD3+ CD4- CD8-), and T-cells that are CD3+ CD4+ CD8+ as well as B-lymphocytes and NK-cells can be enumerated after staining in a single tube. Whole blood specimens are labelled with a mixture of antibodies: FITC-conjugated antibodies to CD4 and CD19, PE-conjugated antibodies to CD8 and CD16, and either peridinin chlorophyll protein (PerCP) or allophycocyanin (APC) labelling for antibodies to CD3. After recording 20,000 events the data were analysed on the Consort 32 computer system and LYSYS-II (Becton Dickinson, San Jose, CA) and all of the lymphocyte subset values were determined by Boolean algebra using a technique we refer to as Boolean gate analysis (BGA). Our study has shown that BGA is statistically equivalent to SimulSET lymphocyte subset analysis. Furthermore, the procedure reduces the number of tubes required to two with consequential saving in reagents, consumables, and time. PMID:7514523

  2. C∗-completions and the DFR-algebra

    NASA Astrophysics Data System (ADS)

    Forger, Michael; Paulino, Daniel V.

    2016-02-01

    The aim of this paper is to present the construction of a general family of C∗-algebras which includes, as a special case, the "quantum spacetime algebra" introduced by Doplicher, Fredenhagen, and Roberts. It is based on an extension of the notion of C∗-completion from algebras to bundles of algebras, compatible with the usual C∗-completion of the appropriate algebras of sections, combined with a novel definition for the algebra of the canonical commutation relations using Rieffel's theory of strict deformation quantization. Taking the C∗-algebra of continuous sections vanishing at infinity, we arrive at a functor associating a C∗-algebra to any Poisson vector bundle and recover the original DFR-algebra as a particular example.

  3. Scalable Parallel Algebraic Multigrid Solvers

    SciTech Connect

    Bank, R; Lu, S; Tong, C; Vassilevski, P

    2005-03-23

    The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

  4. Providing Feedback on Computer-Based Algebra Homework in Middle-School Classrooms

    ERIC Educational Resources Information Center

    Fyfe, Emily R.

    2016-01-01

    Homework is transforming at a rapid rate with continuous advances in educational technology. Computer-based homework, in particular, is gaining popularity across a range of schools, with little empirical evidence on how to optimize student learning. The current aim was to test the effects of different types of feedback on computer-based homework.…

  5. Beyond Dirac - a Unified Algebra

    NASA Astrophysics Data System (ADS)

    Lundberg, Wayne R.

    2001-10-01

    A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.

  6. Role of division algebra in seven-dimensional gauge theory

    NASA Astrophysics Data System (ADS)

    Kalauni, Pushpa; Barata, J. C. A.

    2015-03-01

    The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.

  7. Classification of central extensions of Lax operator algebras

    SciTech Connect

    Schlichenmaier, Martin

    2008-11-18

    Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever's theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost-graded central extensions. It turns out that in case that the finite-dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost-graded central extension up to equivalence and rescaling of the central element.

  8. Materiality in a Practice-Based Approach

    ERIC Educational Resources Information Center

    Svabo, Connie

    2009-01-01

    Purpose: The paper aims to provide an overview of the vocabulary for materiality which is used by practice-based approaches to organizational knowing. Design/methodology/approach: The overview is theoretically generated and is based on the anthology Knowing in Organizations: A Practice-based Approach edited by Nicolini, Gherardi and Yanow. The…

  9. Analysis of algebraic reconstruction technique for accurate imaging of gas temperature and concentration based on tunable diode laser absorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Hui-Hui, Xia; Rui-Feng, Kan; Jian-Guo, Liu; Zhen-Yu, Xu; Ya-Bai, He

    2016-06-01

    An improved algebraic reconstruction technique (ART) combined with tunable diode laser absorption spectroscopy(TDLAS) is presented in this paper for determining two-dimensional (2D) distribution of H2O concentration and temperature in a simulated combustion flame. This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy. It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid, and after that point, the number of projection rays has little influence on reconstruction accuracy. It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method. In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed, and the capability of this new method is evaluated by using appropriate assessment parameters. By using this new approach, not only the concentration reconstruction accuracy is greatly improved, but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation. Finally, a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method. Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles. This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices. Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61205151), the National Key Scientific Instrument and Equipment Development Project of China (Grant

  10. Compatible Relaxation and Coarsening in Algebraic Multigrid

    SciTech Connect

    Brannick, J J; Falgout, R D

    2009-09-22

    We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.

  11. Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution

    NASA Astrophysics Data System (ADS)

    Hu, Yinlong; Chen, Michael Z. Q.; Shu, Zhan; Huang, Lixi

    2015-06-01

    This paper is concerned with the problem of analysis and optimisation of the inerter-based isolators based on a "uni-axial" single-degree-of-freedom isolation system. In the first part, in order to gain an in-depth understanding of inerter from the prospective of vibration, the frequency responses of both parallel-connected and series-connected inerters are analysed. In the second part, three other inerter-based isolators are introduced and the tuning procedures in both the H∞ optimisation and the H2 optimisation are proposed in an analytical manner. The achieved H2 and H∞ performance of the inerter-based isolators is superior to that achieved by the traditional dynamic vibration absorber (DVA) when the same inertance-to-mass (or mass) ratio is considered. Moreover, the inerter-based isolators have two unique properties, which are more attractive than the traditional DVA: first, the inertance-to-mass ratio of the inerter-based isolators can easily be larger than the mass ratio of the traditional DVA without increasing the physical mass of the whole system; second, there is no need to mount an additional mass on the object to be isolated.

  12. Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

    NASA Astrophysics Data System (ADS)

    Baykara, N. A.

    2015-12-01

    Recent studies on quantum evolutionary problems in Demiralp's group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

  13. Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

    SciTech Connect

    Baykara, N. A.

    2015-12-31

    Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

  14. Structured adaptive grid generation using algebraic methods

    NASA Technical Reports Server (NTRS)

    Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.

    1993-01-01

    The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration

  15. Learning Algebra in a Computer Algebra Environment

    ERIC Educational Resources Information Center

    Drijvers, Paul

    2004-01-01

    This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…

  16. A Study of Student Learning Outcomes and Effectiveness of the Computer Based Algebra I Credit Recovery Course Offered at Louisiana Traditional Schools and the Algebra I Credit Recovery Course Offered in a Virtual Environment at Louisiana Virtual School

    ERIC Educational Resources Information Center

    Mack, Roy James

    2011-01-01

    The central purpose of this research was to assess student learning outcomes in the Algebra I credit recovery course offered at traditional schools in Louisiana and the Algebra I credit recovery course offered online by the Louisiana Virtual School (LVS). It was also conducted to assess the associations of gender, grade level, and socio-economic…

  17. Adaptive Algebraic Smoothers

    SciTech Connect

    Philip, Bobby; Chartier, Dr Timothy

    2012-01-01

    methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.

  18. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  19. Developing Thinking in Algebra

    ERIC Educational Resources Information Center

    Mason, John; Graham, Alan; Johnson-Wilder, Sue

    2005-01-01

    This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

  20. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  1. Applied Algebra Curriculum Modules.

    ERIC Educational Resources Information Center

    Texas State Technical Coll., Marshall.

    This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…

  2. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  3. Ternary Virasoro - Witt algebra.

    SciTech Connect

    Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.

  4. Teaching Algebra to Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Impecoven-Lind, Linda S.; Foegen, Anne

    2010-01-01

    Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

  5. Algebra: How Is It for You?

    ERIC Educational Resources Information Center

    Rickard, Caroline

    2008-01-01

    Shortly after starting work for the University of Chichester in the School of Teacher Education, the author was planning a session relating to algebra and found herself inspired by an article in MT182: "Algebraic Infants" by Andrews and Sayers (2003). Based on the making of families of "Multilink" animals, Andrews and Sayers (2003) claim that…

  6. Encrypted imaging based on algebraic implementation of double random phase encoding.

    PubMed

    Nakano, Kazuya; Takeda, Masafumi; Suzuki, Hiroyuki; Yamaguchi, Masahiro

    2014-05-10

    The security of important information captured by sensors and cameras is currently a growing concern as information theft via techniques such as side-channel attacks become increasingly more prevalent. Double random phase encoding (DRPE) is an optical encryption method based on optical Fourier transform that is currently being used to implement secure coherent optical systems. In this paper, we propose a new DRPE implementation for incoherent optical systems based on integral photography that can be applied to "encrypted imaging (EI)" to optically encrypt an image before it is captured by an image sensor. Because the proposed incoherent DRPE is constituted from conventional DRPE by rewriting the optical encryption via discretization and Euler's formula, its security level is the same as that of conventional DRPE. The results of an experiment in which we encrypted a plaintext image optically and then decrypted it numerically demonstrate that our proposed incoherent optical security system is feasible. PMID:24922013

  7. The differential algebra based multiple level fast multipole algorithm for 3D space charge field calculation and photoemission simulation

    SciTech Connect

    None, None

    2015-09-28

    Coulomb interaction between charged particles inside a bunch is one of the most importance collective effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast Electron Microscope (UEM) development currently underway at Michigan State University. In addition, space charge effects are the key limiting factor in the development of ultrafast atomic resolution electron imaging and diffraction technologies and are also correlated with an irreversible growth in rms beam emittance due to fluctuating components of the nonlinear electron dynamics. In the short pulse regime used in the UEM, space charge effects also lead to virtual cathode formation in which the negative charge of the electrons emitted at earlier times, combined with the attractive surface field, hinders further emission of particles and causes a degradation of the pulse properties. Space charge and virtual cathode effects and their remediation are core issues for the development of the next generation of high-brightness UEMs. Since the analytical models are only applicable for special cases, numerical simulations, in addition to experiments, are usually necessary to accurately understand the space charge effect. In this paper we will introduce a grid-free differential algebra based multiple level fast multipole algorithm, which calculates the 3D space charge field for n charged particles in arbitrary distribution with an efficiency of O(n), and the implementation of the algorithm to a simulation code for space charge dominated photoemission processes.

  8. The differential algebra based multiple level fast multipole algorithm for 3D space charge field calculation and photoemission simulation

    DOE PAGESBeta

    None, None

    2015-09-28

    Coulomb interaction between charged particles inside a bunch is one of the most importance collective effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast Electron Microscope (UEM) development currently underway at Michigan State University. In addition, space charge effects are the key limiting factor in the development of ultrafast atomic resolution electron imaging and diffraction technologies and are also correlated with an irreversible growth in rms beam emittance due to fluctuating components of the nonlinear electron dynamics.more » In the short pulse regime used in the UEM, space charge effects also lead to virtual cathode formation in which the negative charge of the electrons emitted at earlier times, combined with the attractive surface field, hinders further emission of particles and causes a degradation of the pulse properties. Space charge and virtual cathode effects and their remediation are core issues for the development of the next generation of high-brightness UEMs. Since the analytical models are only applicable for special cases, numerical simulations, in addition to experiments, are usually necessary to accurately understand the space charge effect. In this paper we will introduce a grid-free differential algebra based multiple level fast multipole algorithm, which calculates the 3D space charge field for n charged particles in arbitrary distribution with an efficiency of O(n), and the implementation of the algorithm to a simulation code for space charge dominated photoemission processes.« less

  9. Effects of Multimedia-Based Instructional Technology on African American Ninth Grade Students' Mastery of Algebra Concepts

    ERIC Educational Resources Information Center

    Malik, Ishan Z.

    2011-01-01

    Urban African American students lack an abstract understanding of algebra and are below their academic level in comparison to other ethnic groups, and this is a pervasive problem (McKinney, Chappell, Berry, & Hickman, 2009). The purpose of this quantitative study using a quasi-experimental design was to determine whether the use of…

  10. Using PROC GLIMMIX to Analyze the Animal Watch, a Web-Based Tutoring System for Algebra Readiness

    ERIC Educational Resources Information Center

    Barbu, Otilia C.

    2012-01-01

    In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch…

  11. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  12. Algebra Aerobics

    ERIC Educational Resources Information Center

    Barnes, Julie; Jaqua, Kathy

    2011-01-01

    A kinesthetic approach to developing ideas of function transformations can get students physically and intellectually involved. This article presents low- or no-cost activities which use kinesthetics to support high school students' mathematical understanding of transformations of function graphs. The important point of these activities is to help…

  13. Effectiveness of Cognitive Tutor Algebra I at Scale

    ERIC Educational Resources Information Center

    Pane, John F.; Griffin, Beth Ann; McCaffrey, Daniel F.; Karam, Rita

    2014-01-01

    This article examines the effectiveness of a technology-based algebra curriculum in a wide variety of middle schools and high schools in seven states. Participating schools were matched into similar pairs and randomly assigned to either continue with the current algebra curriculum for 2 years or to adopt Cognitive Tutor Algebra I (CTAI), which…

  14. Moving frames and prolongation algebras

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.

    1982-01-01

    Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

  15. I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2009

    2009-01-01

    The I CAN Learn[R] Education System is an interactive, self-paced, mastery-based software system that includes the I CAN Learn[R] Fundamentals of Math (5th-6th grade math) curriculum, the I CAN Learn[R] Pre-Algebra curriculum, and the I CAN Learn[R] Algebra curriculum. College algebra credit is also available to students in participating schools…

  16. Computational triadic algebras of signs

    SciTech Connect

    Zadrozny, W.

    1996-12-31

    We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.

  17. Facilitating case reuse during problem solving in algebra-based physics

    NASA Astrophysics Data System (ADS)

    Mateycik, Frances Ann

    This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual clinical interviews were conducted and quantitative examination data were collected to assess students' conceptual understanding, knowledge organization, and problem solving performance on a variety of problem tasks. The study began with a short one-time treatment of two independent, research-based strategies chosen to facilitate case reuse. Exploration of students' perceptions and use of the strategies lead investigators to select one of the two strategies to be implemented over a full semester of focus group interviews. The strategy chosen was structure mapping. Structure maps are defined as visual representations of quantities and their associations. They were created by experts to model the appropriate mental organization of knowledge elements for a given physical concept. Students were asked to use these maps as they were comfortable while problem solving. Data obtained from this phase of our study (Phase I) offered no evidence of improved problem solving schema. The 11 contact hour study was barely sufficient time for students to become comfortable using the maps. A set of simpler strategies were selected for their more explicit facilitation of analogical reasoning, and were used together during two more semester long focus group treatments (Phase II and Phase III of this study). These strategies included the use of a step-by-step process aimed at reducing cognitive load associated with mathematical procedure, direct reflection of principles involved in a given set of problems, and the direct comparison of problem pairs designed to be void of surface similarities (similar objects or object orientations) and sharing

  18. Strategies for Teaching Algebra to Students with Learning Disabilities: Making Research to Practice Connections

    ERIC Educational Resources Information Center

    Strickland, Tricia K.; Maccini, Paula

    2010-01-01

    To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic…

  19. On q-deformed infinite-dimensional n-algebra

    NASA Astrophysics Data System (ADS)

    Ding, Lu; Jia, Xiao-Yu; Wu, Ke; Yan, Zhao-Wen; Zhao, Wei-Zhong

    2016-03-01

    The q-deformation of the infinite-dimensional n-algebras is investigated. Based on the structure of the q-deformed Virasoro-Witt algebra, we derive a nontrivial q-deformed Virasoro-Witt n-algebra which is nothing but a sh-n-Lie algebra. Furthermore in terms of the pseud-differential operators, we construct the (co)sine n-algebra and the q-deformed S Diff (T2)n-algebra. We find that they are the sh-n-Lie algebras for the n even case. In terms of the magnetic translation operators, an explicit physical realization of the (co)sine n-algebra is given.

  20. An Introduction to Algebraic Multigrid

    SciTech Connect

    Falgout, R D

    2006-04-25

    Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments

  1. Birman-Wenzl-Murakami algebra, topological parameter and Berry phase

    NASA Astrophysics Data System (ADS)

    Zhou, Chengcheng; Xue, Kang; Gou, Lidan; Sun, Chunfang; Wang, Gangcheng; Hu, Taotao

    2012-12-01

    In this paper, a 3 × 3-matrix representation of Birman-Wenzl-Murakami (BWM) algebra has been presented. Based on which, unitary matrices A( θ, φ 1, φ 2) and B( θ, φ 1, φ 2) are generated via Yang-Baxterization approach. A Hamiltonian is constructed from the unitary B( θ, φ) matrix. Then we study Berry phase of the Yang-Baxter system, and obtain the relationship between topological parameter and Berry phase.

  2. Phase Boundaries in Algebraic Conformal QFT

    NASA Astrophysics Data System (ADS)

    Bischoff, Marcel; Kawahigashi, Yasuyuki; Longo, Roberto; Rehren, Karl-Henning

    2016-02-01

    We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These can be formulated in a common framework originating in Algebraic QFT, with the principle of Einstein Causality playing a prominent role. We classify the phase boundary conditions by the centre of a certain universal construction, which produces a reducible representation in which all possible boundary conditions are realized. For a large class of models, the classification reproduces results obtained in a different approach by Fuchs et al. before.

  3. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…

  4. [Orbitozygomatic approaches to the skull base].

    PubMed

    Cherekaev, V A; Gol'bin, D A; Belov, A I; Radchenkov, N S; Lasunin, N V; Vinokurov, A G

    2015-01-01

    The paper is written in the lecture format and dedicated to one of the main basal approaches, the orbitozygomatic approach, that has been widely used by neurosurgeons for several decades. The authors describe the historical background of the approach development and the surgical technique features and also analyze the published data about application of the orbitozygomatic approach in surgery for skull base tumors and cerebral aneurysms. PMID:26529627

  5. Filtering Algebraic Multigrid and Adaptive Strategies

    SciTech Connect

    Nagel, A; Falgout, R D; Wittum, G

    2006-01-31

    Solving linear systems arising from systems of partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. The method is used in an adaptive, self-correcting framework and tested numerically.

  6. Algebraic method for finding equivalence groups

    NASA Astrophysics Data System (ADS)

    Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O.

    2015-06-01

    The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the corresponding equivalence algebra. Two versions of the method are presented, where the first involves the automorphism group of this algebra and the second is based on a list of its megaideals. We illustrate the megaideal-based version of the method with the computation of the complete equivalence group of a class of nonlinear wave equations with applications in nonlinear elasticity.

  7. Contractions of affine Kac-Moody algebras

    NASA Astrophysics Data System (ADS)

    Daboul, J.; Daboul, C.; de Montigny, M.

    2008-08-01

    I review our recent work on contractions of affine Kac-Moody algebras (KMA) and present new results. We study generalized contractions of KMA with respect to their twisted and untwisted KM subalgebras. As a concrete example, we discuss contraction of D(1)4 and D(3)4, based on Z3-grading. We also describe examples of 'level-dependent' contractions, which are based on Z-gradings of KMA. Our work generalizes the Inönü-Wigner contraction of P. Majumdar in several directions. We also give an algorithm for constructing Kac-Moody-like algebras hat g for any Lie algebra g.

  8. SU-E-J-02: 4D Digital Tomosynthesis Based On Algebraic Image Reconstruction and Total-Variation Minimization for the Improvement of Image Quality

    SciTech Connect

    Kim, D; Kang, S; Kim, T; Suh, T; Kim, S

    2014-06-01

    Purpose: In this paper, we implemented the four-dimensional (4D) digital tomosynthesis (DTS) imaging based on algebraic image reconstruction technique and total-variation minimization method in order to compensate the undersampled projection data and improve the image quality. Methods: The projection data were acquired as supposed the cone-beam computed tomography system in linear accelerator by the Monte Carlo simulation and the in-house 4D digital phantom generation program. We performed 4D DTS based upon simultaneous algebraic reconstruction technique (SART) among the iterative image reconstruction technique and total-variation minimization method (TVMM). To verify the effectiveness of this reconstruction algorithm, we performed systematic simulation studies to investigate the imaging performance. Results: The 4D DTS algorithm based upon the SART and TVMM seems to give better results than that based upon the existing method, or filtered-backprojection. Conclusion: The advanced image reconstruction algorithm for the 4D DTS would be useful to validate each intra-fraction motion during radiation therapy. In addition, it will be possible to give advantage to real-time imaging for the adaptive radiation therapy. This research was supported by Leading Foreign Research Institute Recruitment Program (Grant No.2009-00420) and Basic Atomic Energy Research Institute (BAERI); (Grant No. 2009-0078390) through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP)

  9. Slower Algebra Students Meet Faster Tools: Solving Algebra Word Problems with Graphing Software

    ERIC Educational Resources Information Center

    Yerushalmy, Michal

    2006-01-01

    The article discusses the ways that less successful mathematics students used graphing software with capabilities similar to a basic graphing calculator to solve algebra problems in context. The study is based on interviewing students who learned algebra for 3 years in an environment where software tools were always present. We found differences…

  10. Exponential growth of codimensions of identities of algebras with unity

    NASA Astrophysics Data System (ADS)

    Zaicev, M. V.; Repovš, D.

    2015-10-01

    The asymptotic behaviour is studied of exponentially bounded sequences of codimensions of identities of algebras with unity. A series of algebras is constructed for which the base of the exponential increases by exactly 1 when an outer unity is adjoined to the original algebra. It is shown that the PI-exponents of unital algebras can take any value greater than 2, and the exponents of finite-dimensional unital algebras form a dense subset in the domain \\lbrack 2,∞). Bibliography: 34 titles.

  11. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  12. Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

    ERIC Educational Resources Information Center

    Cook, John Paul

    2015-01-01

    This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

  13. Toward robust scalable algebraic multigrid solvers.

    SciTech Connect

    Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

    2010-10-01

    This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.

  14. Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras

    NASA Astrophysics Data System (ADS)

    Kimura, Yusuke

    2015-07-01

    It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.

  15. Semigroups And Computer Algebra In Discrete Structures

    NASA Astrophysics Data System (ADS)

    Bijev, G.

    2010-10-01

    Some concepts in semigroup theory are interpreted in discrete structures such as finite lattices, binary relations, and finite semilattices. An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. By analogy with the linear spaces in the linear algebra semilattice homomorphisms, isomorphisms, projections on Boolean vector spaces are defined and some properties of them are investigated in detail. Maps, corresponding to them in the linear algebra, are connected with matrices and their pseudouinverse. Important properties of these maps, which are essential for solving linear systems, remain the same in the Boolean vector spaces. Stochastic experiments using the maps defined and computer algebra methods have been made for solving linear equations Ax = b. The Hamming distance between b and the projection p(b) = Ax of b is equal or close to the least possible one, if the system has no solutions.

  16. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  17. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…

  18. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  19. Catching Up on Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

  20. Application of geometric algebra for the description of polymer conformations.

    PubMed

    Chys, Pieter

    2008-03-14

    In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length (l), valence angle (theta), and rotation angle (phi) of each of the preceding bonds in the chain. Hence, the set of geometrical parameters {l(i),theta(i),phi(i)} yields all the position coordinates p(i) of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built. PMID:18345877

  1. Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra

    NASA Astrophysics Data System (ADS)

    Moayedi, S. K.; Setare, M. R.; Khosropour, B.

    2013-11-01

    In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β‧)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (\\triangle Xi)\\min = \\hbar √ {Dβ +β '}, \\forall i\\in \\{1, 2, ..., D\\}. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β‧ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

  2. Semigroups and computer algebra in algebraic structures

    NASA Astrophysics Data System (ADS)

    Bijev, G.

    2012-11-01

    Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.

  3. Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*

    DOE PAGESBeta

    Bank, R.; Falgout, R. D.; Jones, T.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J. W.

    2015-10-29

    In modern large-scale supercomputing applications, algebraic multigrid (AMG) is a leading choice for solving matrix equations. However, the high cost of communication relative to that of computation is a concern for the scalability of traditional implementations of AMG on emerging architectures. This paper introduces two new algebraic multilevel algorithms, algebraic multigrid domain decomposition (AMG-DD) and algebraic multigrid range decomposition (AMG-RD), that replace traditional AMG V-cycles with a fully overlapping domain decomposition approach. While the methods introduced here are similar in spirit to the geometric methods developed by Brandt and Diskin [Multigrid solvers on decomposed domains, in Domain Decomposition Methods inmore » Science and Engineering, Contemp. Math. 157, AMS, Providence, RI, 1994, pp. 135--155], Mitchell [Electron. Trans. Numer. Anal., 6 (1997), pp. 224--233], and Bank and Holst [SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443], they differ primarily in that they are purely algebraic: AMG-RD and AMG-DD trade communication for computation by forming global composite “grids” based only on the matrix, not the geometry. (As is the usual AMG convention, “grids” here should be taken only in the algebraic sense, regardless of whether or not it corresponds to any geometry.) Another important distinguishing feature of AMG-RD and AMG-DD is their novel residual communication process that enables effective parallel computation on composite grids, avoiding the all-to-all communication costs of the geometric methods. The main purpose of this paper is to study the potential of these two algebraic methods as possible alternatives to existing AMG approaches for future parallel machines. As a result, this paper develops some theoretical properties of these methods and reports on serial numerical tests of their convergence properties over a spectrum of problem parameters.« less

  4. Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*

    SciTech Connect

    Bank, R.; Falgout, R. D.; Jones, T.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J. W.

    2015-10-29

    In modern large-scale supercomputing applications, algebraic multigrid (AMG) is a leading choice for solving matrix equations. However, the high cost of communication relative to that of computation is a concern for the scalability of traditional implementations of AMG on emerging architectures. This paper introduces two new algebraic multilevel algorithms, algebraic multigrid domain decomposition (AMG-DD) and algebraic multigrid range decomposition (AMG-RD), that replace traditional AMG V-cycles with a fully overlapping domain decomposition approach. While the methods introduced here are similar in spirit to the geometric methods developed by Brandt and Diskin [Multigrid solvers on decomposed domains, in Domain Decomposition Methods in Science and Engineering, Contemp. Math. 157, AMS, Providence, RI, 1994, pp. 135--155], Mitchell [Electron. Trans. Numer. Anal., 6 (1997), pp. 224--233], and Bank and Holst [SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443], they differ primarily in that they are purely algebraic: AMG-RD and AMG-DD trade communication for computation by forming global composite “grids” based only on the matrix, not the geometry. (As is the usual AMG convention, “grids” here should be taken only in the algebraic sense, regardless of whether or not it corresponds to any geometry.) Another important distinguishing feature of AMG-RD and AMG-DD is their novel residual communication process that enables effective parallel computation on composite grids, avoiding the all-to-all communication costs of the geometric methods. The main purpose of this paper is to study the potential of these two algebraic methods as possible alternatives to existing AMG approaches for future parallel machines. As a result, this paper develops some theoretical properties of these methods and reports on serial numerical tests of their convergence properties over a spectrum of problem parameters.

  5. Vague Congruences and Quotient Lattice Implication Algebras

    PubMed Central

    Qin, Xiaoyan; Xu, Yang

    2014-01-01

    The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given. PMID:25133207

  6. One-Equation Algebraic Model Of Turbulence

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Barth, T. J.

    1993-01-01

    One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

  7. Three-algebra for supermembrane and two-algebra for superstring

    NASA Astrophysics Data System (ADS)

    Lee, Kanghoon; Park, Jeong-Hyuck

    2009-04-01

    While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that Script M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.

  8. Lie algebra extensions of current algebras on S3

    NASA Astrophysics Data System (ADS)

    Kori, Tosiaki; Imai, Yuto

    2015-06-01

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

  9. Leibniz algebras associated with representations of filiform Lie algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.

    2015-12-01

    In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.

  10. Coreflections in Algebraic Quantum Logic

    NASA Astrophysics Data System (ADS)

    Jacobs, Bart; Mandemaker, Jorik

    2012-07-01

    Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.

  11. Computer algebra and transport theory.

    SciTech Connect

    Warsa, J. S.

    2004-01-01

    Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.

  12. q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

    SciTech Connect

    Georgieva, A. I.; Sviratcheva, K. D.; Ivanov, M. I.; Draayer, J. P.

    2011-06-15

    With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su{sub q}(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u{sub q}(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0{sup +} states in the deformed and nondeformed cases.

  13. Developing Algebraic Thinking.

    ERIC Educational Resources Information Center

    Alejandre, Suzanne

    2002-01-01

    Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)

  14. Algebraic Semantics for Narrative

    ERIC Educational Resources Information Center

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  15. A subgrid based approach for morphodynamic modelling

    NASA Astrophysics Data System (ADS)

    Volp, N. D.; van Prooijen, B. C.; Pietrzak, J. D.; Stelling, G. S.

    2016-07-01

    To improve the accuracy and the efficiency of morphodynamic simulations, we present a subgrid based approach for a morphodynamic model. This approach is well suited for areas characterized by sub-critical flow, like in estuaries, coastal areas and in low land rivers. This new method uses a different grid resolution to compute the hydrodynamics and the morphodynamics. The hydrodynamic computations are carried out with a subgrid based, two-dimensional, depth-averaged model. This model uses a coarse computational grid in combination with a subgrid. The subgrid contains high resolution bathymetry and roughness information to compute volumes, friction and advection. The morphodynamic computations are carried out entirely on a high resolution grid, the bed grid. It is key to find a link between the information defined on the different grids in order to guaranty the feedback between the hydrodynamics and the morphodynamics. This link is made by using a new physics-based interpolation method. The method interpolates water levels and velocities from the coarse grid to the high resolution bed grid. The morphodynamic solution improves significantly when using the subgrid based method compared to a full coarse grid approach. The Exner equation is discretised with an upwind method based on the direction of the bed celerity. This ensures a stable solution for the Exner equation. By means of three examples, it is shown that the subgrid based approach offers a significant improvement at a minimal computational cost.

  16. Aprepro - Algebraic Preprocessor

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  17. Geometric Algebra for Physicists

    NASA Astrophysics Data System (ADS)

    Doran, Chris; Lasenby, Anthony

    2007-11-01

    Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

  18. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  19. Maximum/Minimum Problems Solved Using an Algebraic Way

    ERIC Educational Resources Information Center

    Modica, Erasmo

    2010-01-01

    This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…

  20. Comparing the Effectiveness of Collaborative Instructional Practices in Algebra

    ERIC Educational Resources Information Center

    Triaga, Russell D.

    2014-01-01

    The use of multiple forms of collaborative instruction to teach integrated algebra makes it difficult for teachers to determine which collaborative form is best suited for the curriculum. An inconsistent approach to integrated algebra instruction at the study school needed to be addressed for the benefit of teacher effectiveness and student…

  1. Emphasizing Language and Visualization in Teaching Linear Algebra

    ERIC Educational Resources Information Center

    Hannah, John; Stewart, Sepideh; Thomas, Mike

    2013-01-01

    Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his…

  2. Learning Beginning Algebra with Spreadsheets in a Computer Intensive Environment

    ERIC Educational Resources Information Center

    Tabach, Michal; Hershkowitz, Rina; Arcavi, Abraham

    2008-01-01

    This study is part of a large research and development project aimed at observing, describing and analyzing the learning processes of two seventh grade classes during a yearlong beginning algebra course in a computer intensive environment (CIE). The environment includes carefully designed algebra learning materials with a functional approach, and…

  3. Phase transition studies of the odd-mass 123‑135Xe isotopes based on SU(1,1) algebra in IBFM

    NASA Astrophysics Data System (ADS)

    Jafarizadeh, M. A.; Fouladi, N.; Ghapanvari, M.; Fathi, H.

    2016-07-01

    In this paper, we have investigated the positive-parity states in the odd-mass transitional 123‑135Xe isotopes within the framework of the interacting boson-fermion model. Two solvable extended transitional Hamiltonians which are based on SU(1,1) algebra are employed to provide an investigation of quantum phase transition (QPT) between the spherical and deformed gamma — unstable shapes along the chain of Xe isotopes. The low-states energy spectra and B(E2) values for these nuclei have been calculated and compared with the experimental data. The predicted excitation energies and B(E2) transition rates of the odd isotopes are found to agree well with the experimental data. We have also analyzed the critical behavior of even-odd Xe isotopes via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces and special isotopes which are the best candidates for the critical point are identified.

  4. DG Poisson algebra and its universal enveloping algebra

    NASA Astrophysics Data System (ADS)

    Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin

    2016-05-01

    In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

  5. Hearing Math: Algebra Supported eText for Students With Visual Impairments.

    PubMed

    Bouck, Emily C; Weng, Pei-Lin

    2014-01-01

    Supported eText for students with visual impairments in mathematics has a promising, emerging literature base, although little of the existing research focuses on implementation within a classroom setting. This qualitative study sought to understand the use of supported eText to deliver algebra to students with visual impairments enrolled in algebra mathematics courses. The study also sought to explore supported eText in contrast to students' traditional means of accessing an algebra text. The main results suggest supported eText holds potential in terms of delivering mathematics content; however, more research and more reflection on the field is needed regarding this approach as a sole means of presenting text. Implications for teacher professional development and implementation practices are discussed. PMID:26131793

  6. A process algebra model of QED

    NASA Astrophysics Data System (ADS)

    Sulis, William

    2016-03-01

    The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.

  7. Algebraic independence properties related to certain infinite products

    NASA Astrophysics Data System (ADS)

    Tanaka, Taka-aki

    2011-09-01

    In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.

  8. Physics-based approach to haptic display

    NASA Technical Reports Server (NTRS)

    Brown, J. Michael; Colgate, J. Edward

    1994-01-01

    This paper addresses the implementation of complex multiple degree of freedom virtual environments for haptic display. We suggest that a physics based approach to rigid body simulation is appropriate for hand tool simulation, but that currently available simulation techniques are not sufficient to guarantee successful implementation. We discuss the desirable features of a virtual environment simulation, specifically highlighting the importance of stability guarantees.

  9. Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2014-01-01

    Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

  10. Putting Algebra Progress Monitoring into Practice: Insights from the Field

    ERIC Educational Resources Information Center

    Foegen, Anne; Morrison, Candee

    2010-01-01

    Algebra progress monitoring is a research-based practice that extends a long history of research in curriculum-based measurement (CBM). This article describes the theoretical foundations and research evidence for algebra progress monitoring, along with critical features of the practice. A detailed description of one practitioner's implementation…

  11. Advanced Approach of Multiagent Based Buoy Communication

    PubMed Central

    Gricius, Gediminas; Drungilas, Darius; Andziulis, Arunas; Dzemydiene, Dale; Voznak, Miroslav; Kurmis, Mindaugas; Jakovlev, Sergej

    2015-01-01

    Usually, a hydrometeorological information system is faced with great data flows, but the data levels are often excessive, depending on the observed region of the water. The paper presents advanced buoy communication technologies based on multiagent interaction and data exchange between several monitoring system nodes. The proposed management of buoy communication is based on a clustering algorithm, which enables the performance of the hydrometeorological information system to be enhanced. The experiment is based on the design and analysis of the inexpensive but reliable Baltic Sea autonomous monitoring network (buoys), which would be able to continuously monitor and collect temperature, waviness, and other required data. The proposed approach of multiagent based buoy communication enables all the data from the costal-based station to be monitored with limited transition speed by setting different tasks for the agent-based buoy system according to the clustering information. PMID:26345197

  12. Advanced Approach of Multiagent Based Buoy Communication.

    PubMed

    Gricius, Gediminas; Drungilas, Darius; Andziulis, Arunas; Dzemydiene, Dale; Voznak, Miroslav; Kurmis, Mindaugas; Jakovlev, Sergej

    2015-01-01

    Usually, a hydrometeorological information system is faced with great data flows, but the data levels are often excessive, depending on the observed region of the water. The paper presents advanced buoy communication technologies based on multiagent interaction and data exchange between several monitoring system nodes. The proposed management of buoy communication is based on a clustering algorithm, which enables the performance of the hydrometeorological information system to be enhanced. The experiment is based on the design and analysis of the inexpensive but reliable Baltic Sea autonomous monitoring network (buoys), which would be able to continuously monitor and collect temperature, waviness, and other required data. The proposed approach of multiagent based buoy communication enables all the data from the costal-based station to be monitored with limited transition speed by setting different tasks for the agent-based buoy system according to the clustering information. PMID:26345197

  13. Global Rotation Estimation Using Weighted Iterative Lie Algebraic Averaging

    NASA Astrophysics Data System (ADS)

    Reich, M.; Heipke, C.

    2015-08-01

    In this paper we present an approach for a weighted rotation averaging to estimate absolute rotations from relative rotations between two images for a set of multiple overlapping images. The solution does not depend on initial values for the unknown parameters and is robust against outliers. Our approach is one part of a solution for a global image orientation. Often relative rotations are not free from outliers, thus we use the redundancy in available pairwise relative rotations and present a novel graph-based algorithm to detect and eliminate inconsistent rotations. The remaining relative rotations are input to a weighted least squares adjustment performed in the Lie algebra of the rotation manifold SO(3) to obtain absolute orientation parameters for each image. Weights are determined using the prior information we derived from the estimation of the relative rotations. Because we use the Lie algebra of SO(3) for averaging no subsequent adaptation of the results has to be performed but the lossless projection to the manifold. We evaluate our approach on synthetic and real data. Our approach often is able to detect and eliminate all outliers from the relative rotations even if very high outlier rates are present. We show that we improve the quality of the estimated absolute rotations by introducing individual weights for the relative rotations based on various indicators. In comparison with the state-of-the-art in recent publications to global image orientation we achieve best results in the examined datasets.

  14. An Evaluation of Saxon's Algebra Test.

    ERIC Educational Resources Information Center

    Johnson, Dale M.; Smith, Blaine

    1987-01-01

    John Saxon's incremental development model has been proclaimed as a superior teaching strategy for mathematics. This study evaluated the Saxon approach and textbook using 276 Algebra I students in experimental and control groups. The groups were compared in cognitive and affective areas. Results are presented. (Author/MT)

  15. Programed Instruction in Elementary Algebra: An Experiment

    ERIC Educational Resources Information Center

    Lial, Margaret L.

    1970-01-01

    Report of an experiment which investigated the use of a programed elementary algebra text as a teaching method. The method was evaluated on the basis of student evaluation of the course and the percentage of students achieving a grade of C or better. Results indicated that the use of programed texts was superior to the traditional approach using…

  16. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. PMID:26124252

  17. Algebraic models of flexible manufacturing systems

    NASA Astrophysics Data System (ADS)

    Leskin, Aleksei Alekseevich

    Various aspects of the use of mathematical methods in the development of flexible manufacturing systems are examined. Attention is given to dynamical and structural models of flexible manufacturing systems developed by using methods of algebraic and differential geometry, topology, polynomial algebra, and extreme value problem theory. The principles of model integration are discussed, and approaches are proposed for solving problems related to the selection of flexible manufacturing equipment, real-time modeling of the manufacturing process, and optimization of local automation systems. The discussion is illustrated by examples.

  18. The Dirac equation and Hestenes' geometric algebra

    NASA Astrophysics Data System (ADS)

    Hamilton, J. Dwayne

    1984-06-01

    Hestenes' geometric algebra and Dirac spinors are reviewed and united into a common mathematical formalism, a unification that establishes the Dirac equation as being manifestly covariant under the Lorentz group, and one that needs no matrix representation of the Dirac algebra. New and simple methods of amplitude or ``trace'' calculations are then described. A number of problems are then considered within the context of the new approach, such as relativistic spin projections, new and covariant C and T-transformations and spinors for massless and Majorana fields.

  19. A modular approach to modeling an isolated power system on a finite voltage bus using a differential algebraic equation solving routine

    NASA Astrophysics Data System (ADS)

    Kipps, Mark R.

    1994-03-01

    The modeling of power systems has been primarily driven by the commercial power utility industry. These models usually involve the assumption that system bus voltage and frequency are constant. However, in applications such as shipboard power systems this infinite bus assumption is not valid. This thesis investigates the modeling of a synchronous generator and various loads in a modular fashion on a finite bus. The simulation presented allows the interconnection of multiple state-space models via a bus voltage model. The major difficulty encountered in building a model which computes bus voltage at each time step is that bus voltage is a function of current and current derivative terms. Bus voltage is also an input to the state equations which produce the current and current derivatives. This creates an algebraic loop which is a form of implicit differential equation. A routine has been developed by Linda Petzold of Lawrence Livermore Laboratory for solving these types of equations. The routine, called Differential Algebraic System Solver (DASSL), has been implemented in a pre-release version of the software Advanced Continuous Simulation Language (ACSL) and has been made available to the Naval Postgraduate School on a trial basis. An isolated power system is modeled using this software and the DASSL routine. The system response to several dynamic situations is studied and the results are presented.

  20. On Griess Algebras

    NASA Astrophysics Data System (ADS)

    Roitman, Michael

    2008-08-01

    In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.

  1. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158

  2. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  3. Systems Engineering Interfaces: A Model Based Approach

    NASA Technical Reports Server (NTRS)

    Fosse, Elyse; Delp, Christopher

    2013-01-01

    Currently: Ops Rev developed and maintains a framework that includes interface-specific language, patterns, and Viewpoints. Ops Rev implements the framework to design MOS 2.0 and its 5 Mission Services. Implementation de-couples interfaces and instances of interaction Future: A Mission MOSE implements the approach and uses the model based artifacts for reviews. The framework extends further into the ground data layers and provides a unified methodology.

  4. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  5. Algebraic geometric codes

    NASA Technical Reports Server (NTRS)

    Shahshahani, M.

    1991-01-01

    The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.

  6. Extended conformal algebras

    NASA Astrophysics Data System (ADS)

    Bouwknegt, Peter

    1988-06-01

    We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.

  7. Abstract numeric relations and the visual structure of algebra.

    PubMed

    Landy, David; Brookes, David; Smout, Ryan

    2014-09-01

    Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition, it has often been assumed that skilled users of these formalisms treat situations in terms of semantic properties encoded in an abstract syntax that governs the use of notation without particular regard to the details of the physical structure of the equation itself (Anderson, 2005; Hegarty, Mayer, & Monk, 1995). We explore how the notational structure of verbal descriptions or algebraic equations (e.g., the spatial proximity of certain words or the visual alignment of numbers and symbols in an equation) plays a role in the process of interpreting or constructing symbolic equations. We propose in particular that construction processes involve an alignment of notational structures across representation systems, biasing reasoners toward the selection of formal notations that maintain the visuospatial structure of source representations. For example, in the statement "There are 5 elephants for every 3 rhinoceroses," the spatial proximity of 5 and elephants and 3 and rhinoceroses will bias reasoners to write the incorrect expression 5E = 3R, because that expression maintains the spatial relationships encoded in the source representation. In 3 experiments, participants constructed equations with given structure, based on story problems with a variety of phrasings. We demonstrate how the notational alignment approach accounts naturally for a variety of previously reported phenomena in equation construction and successfully predicts error patterns that are not accounted for by prior explanations, such as the left to right transcription heuristic. PMID:24820674

  8. Teaching Arithmetic and Algebraic Expressions

    ERIC Educational Resources Information Center

    Subramaniam, K.; Banerjee, Rakhi

    2004-01-01

    A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…

  9. Assessing Elementary Algebra with STACK

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  10. [Use of ternary algebra in the analysis of medical data].

    PubMed

    Bernard, M J

    1976-01-01

    Logical methods are most valuable in the field of Medicine. They are usually based on Boolean algebra and can thus only deal with binary data) (Present)/(Absent)). Use of ternary algebra opens the way to treatment of the triple-state variables ((Present)/(absent)/(Don't know)) frequently encountered in medical context. PMID:816530

  11. Dynamics of three-level Λ-type atom interacting with one mode cavity field with both classical gravity and quantum radiation: Lie algebra approach

    NASA Astrophysics Data System (ADS)

    Abd El-Wahab, N. H.; Abdel Rady, A. S.; Osman, Abdel-Nasser A.; Salah, Ahmed

    2015-10-01

    In this paper, a model is introduced to investigate the interaction between a three-level atom and one-mode of the radiation field. The atomic motion and the classical homogenous gravitational field are taken into consideration. For this purpose, we first introduce a set of new atomic operators obeying an su(3) algebraic structure to derive an effective Hamiltonian for the system under consideration. By solving the Schrödinger equation in the interaction picture, the exact solution is given when the atom and the field are initially prepared in excited state and coherent state, respectively. The influences of the gravity parameter on the collapses-revivals phenomena, the atomic momentum diffusion, the Mandel Q-parameter, the normal squeezing phenomena and the coherent properties for the considered system are examined. It is found that the gravity parameter has important effects on the properties of these phenomena.

  12. Approach of the Azimuthal and Magnetic Quantum Numbers l and m to Representation of a Cubic Deformation of su(2) Algebra

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Hashemzadeh, R.

    It is shown that the space of spherical harmonics Ylm(θ ,φ ) whose 2l - m = p - 1 is given, represent irreducibly a cubic deformation of su(2) algebra, the so-called suΦp(2), with deformation function as Φ p(x) = (27)/(2)x2 + 3(7-3p2)x. The irreducible representation spaces are classified in three different bunches, depending on one of values 3k - 2, 3k - 1 and 3k, with k as a positive integer, to be chosen for p. So, three different methods for generating the spectrum of spherical harmonics are presented by using the cubic deformation of su(2). Moreover, it is shown that p plays the role of deformation parameter.

  13. Heutagogy: An alternative practice based learning approach.

    PubMed

    Bhoyrub, John; Hurley, John; Neilson, Gavin R; Ramsay, Mike; Smith, Margaret

    2010-11-01

    Education has explored and utilised multiple approaches in attempts to enhance the learning and teaching opportunities available to adult learners. Traditional pedagogy has been both directly and indirectly affected by andragogy and transformational learning, consequently widening our understandings and approaches toward view teaching and learning. Within the context of nurse education, a major challenge has been to effectively apply these educational approaches to the complex, unpredictable and challenging environment of practice based learning. While not offered as a panacea to such challenges, heutagogy is offered in this discussion paper as an emerging and potentially highly congruent educational framework to place around practice based learning. Being an emergent theory its known conceptual underpinnings and possible applications to nurse education need to be explored and theoretically applied. Through placing the adult learner at the foreground of grasping learning opportunities as they unpredictability emerge from a sometimes chaotic environment, heutagogy can be argued as offering the potential to minimise many of the well published difficulties of coordinating practice with faculty teaching and learning. PMID:20554249

  14. Algebraic Artful Aids.

    ERIC Educational Resources Information Center

    Glick, David

    1995-01-01

    Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

  15. From Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott

    2007-01-01

    Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

  16. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  17. The Power of Algebra.

    ERIC Educational Resources Information Center

    Boiteau, Denise; Stansfield, David

    This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…

  18. Pre-Algebra.

    ERIC Educational Resources Information Center

    Kennedy, John

    This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…

  19. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  20. Acoustic Emission tomography based on simultaneous algebraic reconstruction technique to visualize the damage source location in Q235B steel plate

    NASA Astrophysics Data System (ADS)

    Jiang, Yu; Xu, Feiyun; Xu, Bingsheng

    2015-12-01

    Acoustic Emission (AE) tomography based on Simultaneous Algebraic Reconstruction Technique (SART), which combines the traditional location algorithm with the SART algorithm by using AE events as its signal sources, is a new visualization method for inspecting and locating the internal damages in the structure. In this paper, the proposed method is applied to examine and visualize two man-made damage source locations in the Q235B steel plate to validate its effectiveness. Firstly, the Q235B steel plate with two holes specimen is fabricated and the pencil lead break (PLB) signal is taken as the exciting source for AE tomography.Secondly, A 6-step description of the SART algorithm is provided and the three dimensional(3D)image contained the damage source locations is visualized by using the proposed algorithm in terms of a locally varying wave velocity distribution. It is shown that the AE tomography based on SART has great potential in the application of structure damage detection. Finally, to further improve the quality of 3D imaging, the Median Filter and the Adaptive Median Filter are used to reduce the noises resulting from AE tomography. The experiment results indicate that Median Filter is the optimal method to remove Salt & Pepper noises.

  1. Algebraic Davis Decomposition and Asymmetric Doob Inequalities

    NASA Astrophysics Data System (ADS)

    Hong, Guixiang; Junge, Marius; Parcet, Javier

    2016-04-01

    In this paper we investigate asymmetric forms of Doob maximal inequality. The asymmetry is imposed by noncommutativity. Let {({M}, τ)} be a noncommutative probability space equipped with a filtration of von Neumann subalgebras {({M}_n)_{n ≥ 1}} , whose union {bigcup_{n≥1}{M}_n} is weak-* dense in {{M}} . Let {{E}_n} denote the corresponding family of conditional expectations. As an illustration for an asymmetric result, we prove that for {1 < p < 2} and {x in L_p({M},τ)} one can find {a, b in L_p({M},τ)} and contractions {u_n, v_n in {M}} such that {E}_n(x) = a u_n + v_n b quad and quad max big{ |a|_p,|b|_p big} ≤ c_p |x|_p. Moreover, it turns out that {a u_n} and {v_n b} converge in the row/column Hardy spaces {{H}_p^r({M})} and {{H}_p^c({M})} respectively. In particular, this solves a problem posed by the Defant and Junge in 2004. In the case p = 1, our results establish a noncommutative form of the Davis celebrated theorem on the relation betwe en martingale maximal and square functions in L 1, whose noncommutative form has remained open for quite some time. Given {1 ≤ p ≤ 2} , we also provide new weak type maximal estimates, which imply in turn left/right almost uniform convergence of {{E}_n(x)} in row/column Hardy spaces. This improves the bilateral convergence known so far. Our approach is based on new forms of Davis martingale decomposition which are of independent interest, and an algebraic atomic description for the involved Hardy spaces. The latter results are new even for commutative von Neumann algebras.

  2. Dual algebraic formulation of differential GPS

    NASA Astrophysics Data System (ADS)

    Lannes, A.; Dur, S.

    2003-05-01

    A new approach to differential GPS is presented. The corresponding theoretical framework calls on elementary concepts of algebraic graph theory. The notion of double difference, which is related to that of closure in the sense of Kirchhoff, is revisited in this context. The Moore-Penrose pseudo-inverse of the closure operator plays a key role in the corresponding dual formulation. This approach, which is very attractive from a conceptual point of view, sheds a new light on the Teunissen formulation.

  3. XML algebras for data mining

    NASA Astrophysics Data System (ADS)

    Zhang, Ming; Yao, JingTao

    2004-04-01

    The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.

  4. C*-algebras of holonomy-diffeomorphisms and quantum gravity: I

    NASA Astrophysics Data System (ADS)

    Aastrup, Johannes; Møller Grimstrup, Jesper

    2013-04-01

    A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a quantized Dirac-type operator, the two capturing the kinematics of quantum gravity formulated in terms of Ashtekar variables. We prove that the separable part of the spectrum of the algebra is contained in the space of measurable connections modulo gauge transformations and we give limitations to the non-separable part. The construction of the Dirac-type operator—and thus the application of noncommutative geometry—is motivated by the requirement of diffeomorphism invariance. We conjecture that a semi-finite spectral triple, which is invariant under volume-preserving diffeomorphisms, arises from a GNS construction of a semi-classical state. Key elements of quantum field theory emerge from the construction in a semi-classical limit, as does an almost commutative algebra. Finally, we note that the spectrum of loop quantum gravity emerges from a discretization of our construction. Certain convergence issues are left unresolved. This paper is the first of two where the second paper [1] is concerned with mathematical details and proofs concerning the spectrum of the holonomy-diffeomorphism algebra.

  5. Pilot study on algebra learning among junior secondary students

    NASA Astrophysics Data System (ADS)

    Poon, Kin-Keung; Leung, Chi-Keung

    2010-01-01

    The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers' perceptions of students' ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From the responses of the participating students (N = 815), it was found that students in schools with a higher level of academic achievement had better algebra test results than did those in schools with a lower level of such achievement. Moreover, it was found that a teacher's perception of a student's ability has a correlation with that student's level of achievement. Based on this finding, an instrument that measures teaching effectiveness is discussed. Last but not least, typical errors in algebra are identified, and some ideas for an instructional design based on these findings are discussed.

  6. The Impact of New State Accountability Standards on Algebra I Students

    ERIC Educational Resources Information Center

    Heath, Kyle G.

    2013-01-01

    The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…

  7. On Dunkl angular momenta algebra

    NASA Astrophysics Data System (ADS)

    Feigin, Misha; Hakobyan, Tigran

    2015-11-01

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  8. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  9. Teaching Algebra-Based Concepts to Students with Learning Disabilities: The Effects of Preteaching Using a Gradual Instructional Sequence

    ERIC Educational Resources Information Center

    Watt, Sarah Jean

    2013-01-01

    Research to identify validated instructional approaches to teach math to students with LD and those at-risk for failure in both core and supplemental instructional settings is necessary to assist teachers in closing the achievement gaps that exist across the country. The concrete-to-representational-to-abstract instructional sequence (CRA) has…

  10. Lunar base CELSS: A bioregenerative approach

    NASA Technical Reports Server (NTRS)

    Easterwood, G. W.; Street, J. J.; Sartain, J. B.; Hubbell, D. H.; Robitaille, H. A.

    1992-01-01

    During the twenty-first century, human habitation of a self-sustaining lunar base could become a reality. To achieve this goal, the occupants will have to have food, water, and an adequate atmosphere within a carefully designed environment. Advanced technology will be employed to support terrestrial life-sustaining processes on the Moon. One approach to a life support system based on food production, waste management and utilization, and product synthesis is outlined. Inputs include an atmosphere, water, plants, biodegradable substrates, and manufacutured materials such as fiberglass containment vessels from lunar resources. Outputs include purification of air and water, food, and hydrogen (H2) generated from methane (CH4). Important criteria are as follows: (1) minimize resupply from Earth; and (2) recycle as efficiently as possible.

  11. An Ontology Based Approach to Information Security

    NASA Astrophysics Data System (ADS)

    Pereira, Teresa; Santos, Henrique

    The semantically structure of knowledge, based on ontology approaches have been increasingly adopted by several expertise from diverse domains. Recently ontologies have been moved from the philosophical and metaphysics disciplines to be used in the construction of models to describe a specific theory of a domain. The development and the use of ontologies promote the creation of a unique standard to represent concepts within a specific knowledge domain. In the scope of information security systems the use of an ontology to formalize and represent the concepts of security information challenge the mechanisms and techniques currently used. This paper intends to present a conceptual implementation model of an ontology defined in the security domain. The model presented contains the semantic concepts based on the information security standard ISO/IEC_JTC1, and their relationships to other concepts, defined in a subset of the information security domain.

  12. LP based approach to optimal stable matchings

    SciTech Connect

    Teo, Chung-Piaw; Sethuraman, J.

    1997-06-01

    We study the classical stable marriage and stable roommates problems using a polyhedral approach. We propose a new LP formulation for the stable roommates problem. This formulation is non-empty if and only if the underlying roommates problem has a stable matching. Furthermore, for certain special weight functions on the edges, we construct a 2-approximation algorithm for the optimal stable roommates problem. Our technique uses a crucial geometry of the fractional solutions in this formulation. For the stable marriage problem, we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as convex combination of stable marriage solutions. This leads to a genuinely simple proof of the integrality of the stable marriage polytope. Based on these ideas, we devise a heuristic to solve the optimal stable roommates problem. The heuristic combines the power of rounding and cutting-plane methods. We present some computational results based on preliminary implementations of this heuristic.

  13. Synthetic aperture elastography: a GPU based approach

    NASA Astrophysics Data System (ADS)

    Verma, Prashant; Doyley, Marvin M.

    2014-03-01

    Synthetic aperture (SA) ultrasound imaging system produces highly accurate axial and lateral displacement estimates; however, low frame rates and large data volumes can hamper its clinical use. This paper describes a real-time SA imaging based ultrasound elastography system that we have recently developed to overcome this limitation. In this system, we implemented both beamforming and 2D cross-correlation echo tracking on Nvidia GTX 480 graphics processing unit (GPU). We used one thread per pixel for beamforming; whereas, one block per pixel was used for echo tracking. We compared the quality of elastograms computed with our real-time system relative to those computed using our standard single threaded elastographic imaging methodology. In all studies, we used conventional measures of image quality such as elastographic signal to noise ratio (SNRe). Specifically, SNRe of axial and lateral strain elastograms computed with real-time system were 36 dB and 23 dB, respectively, which was numerically equal to those computed with our standard approach. We achieved a frame rate of 6 frames per second using our GPU based approach for 16 transmits and kernel size of 60 × 60 pixels, which is 400 times faster than that achieved using our standard protocol.

  14. Modern Geometric Algebra: A (Very Incomplete!) Survey

    ERIC Educational Resources Information Center

    Suzuki, Jeff

    2009-01-01

    Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…

  15. Understanding Algebraic Notation from the Students' Perspective.

    ERIC Educational Resources Information Center

    Kinzel, Margaret Tatem

    1999-01-01

    Explores how students interpret algebraic notation and what teachers can do to support appropriate interpretations. Presents two research-based strategies and concludes that in the face of reform and technological advances, finding a definition for symbol sense takes on added significance. Contains 22 references. (ASK)

  16. An Application of Boolean Algebra to Biology

    ERIC Educational Resources Information Center

    McConnell, John W.

    1971-01-01

    Examines the model of interacting nerve systems based on a switching theory, which uses a mathematical structure familiar to many high school students and requires little knowledge of biology. Reviews the basic operation of nerves, and demonstrates how Boolean algebraic statements are applied to synaptic interactions. (PR)

  17. Confluences of the Painlevé equations, Cherednik algebras and q-Askey scheme

    NASA Astrophysics Data System (ADS)

    Mazzocco, Marta

    2016-09-01

    In this paper we produce seven new algebras as confluences of the Cherednik algebra of type \\check {{{{C}1}}} {{C}1} and we characterise their spherical-sub-algebras. The limit of the spherical sub-algebra of the Cherednik algebra of type \\check {{{{C}1}}} {{C}1} is the monodromy manifold of the Painlevé VI equation (Oblomkov 2004 Int. Math. Res. Not. 2004 877–912). Here we prove that by considering the limits of the spherical sub-algebras of our new confluent algebras, one obtains the monodromy manifolds of all other Painlevé differential equations. Moreover, we introduce confluent versions of the Zhedanov algebra and prove that each of them (quotiented by their Casimir) is isomorphic to the corresponding spherical sub-algebra of our new confluent Cherednik algebras. We show that in the basic representation our confluent Zhedanov algebras act as symmetries of certain elements of the q-Askey scheme, thus setting a stepping stone towards the solution of the open problem of finding the corresponding quantum algebra for each element of the q-Askey scheme. These results establish a new link between the theory of the Painlevé equations and the theory of the q-Askey scheme making a step towards the construction of a representation theoretic approach for the Painlevé theory.

  18. An investigation of algebraic quantum dynamics for mesoscopic coupled electric circuits with mutual inductance

    NASA Astrophysics Data System (ADS)

    Pahlavani, H.; Kolur, E. Rahmanpour

    2016-08-01

    Based on the electrical charge discreteness, the Hamiltonian operator for the mutual inductance coupled quantum mesoscopic LC circuits has been found. The persistent current on two driven coupled mesoscopic electric pure L circuits (two quantum loops) has been obtained by using algebraic quantum dynamic approach. The influence of the mutual inductance on energy spectrum and quantum fluctuations of the charge and current for two coupled quantum electric mesoscopic LC circuits have been investigated.

  19. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    SciTech Connect

    Marquette, Ian

    2013-07-15

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.

  20. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  1. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  2. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  3. Vertex Algebras, Kac-Moody Algebras, and the Monster

    NASA Astrophysics Data System (ADS)

    Borcherds, Richard E.

    1986-05-01

    It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.

  4. Peptide Based Radiopharmaceuticals: Specific Construct Approach

    SciTech Connect

    Som, P; Rhodes, B A; Sharma, S S

    1997-10-21

    The objective of this project was to develop receptor based peptides for diagnostic imaging and therapy. A series of peptides related to cell adhesion molecules (CAM) and immune regulation were designed for radiolabeling with 99mTc and evaluated in animal models as potential diagnostic imaging agents for various disease conditions such as thrombus (clot), acute kidney failure, and inflection/inflammation imaging. The peptides for this project were designed by the industrial partner, Palatin Technologies, (formerly Rhomed, Inc.) using various peptide design approaches including a newly developed rational computer assisted drug design (CADD) approach termed MIDAS (Metal ion Induced Distinctive Array of Structures). In this approach, the biological function domain and the 99mTc complexing domain are fused together so that structurally these domains are indistinguishable. This approach allows construction of conformationally rigid metallo-peptide molecules (similar to cyclic peptides) that are metabolically stable in-vivo. All the newly designed peptides were screened in various in vitro receptor binding and functional assays to identify a lead compound. The lead compounds were formulated in a one-step 99mTc labeling kit form which were studied by BNL for detailed in-vivo imaging using various animals models of human disease. Two main peptides usingMIDAS approach evolved and were investigated: RGD peptide for acute renal failure and an immunomodulatory peptide derived from tuftsin (RMT-1) for infection/inflammation imaging. Various RGD based metallopeptides were designed, synthesized and assayed for their efficacy in inhibiting ADP-induced human platelet aggregation. Most of these peptides displayed biological activity in the 1-100 µM range. Based on previous work by others, RGD-I and RGD-II were evaluated in animal models of acute renal failure. These earlier studies showed that after acute ischemic injury the renal cortex displays

  5. The tensor hierarchy algebra

    NASA Astrophysics Data System (ADS)

    Palmkvist, Jakob

    2014-01-01

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  6. The tensor hierarchy algebra

    SciTech Connect

    Palmkvist, Jakob

    2014-01-15

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  7. ECG biometric identification: A compression based approach.

    PubMed

    Bras, Susana; Pinho, Armando J

    2015-08-01

    Using the electrocardiogram signal (ECG) to identify and/or authenticate persons are problems still lacking satisfactory solutions. Yet, ECG possesses characteristics that are unique or difficult to get from other signals used in biometrics: (1) it requires contact and liveliness for acquisition (2) it changes under stress, rendering it potentially useless if acquired under threatening. Our main objective is to present an innovative and robust solution to the above-mentioned problem. To successfully conduct this goal, we rely on information-theoretic data models for data compression and on similarity metrics related to the approximation of the Kolmogorov complexity. The proposed measure allows the comparison of two (or more) ECG segments, without having to follow traditional approaches that require heartbeat segmentation (described as highly influenced by external or internal interferences). As a first approach, the method was able to cluster the data in three groups: identical record, same participant, different participant, by the stratification of the proposed measure with values near 0 for the same participant and closer to 1 for different participants. A leave-one-out strategy was implemented in order to identify the participant in the database based on his/her ECG. A 1NN classifier was implemented, using as distance measure the method proposed in this work. The classifier was able to identify correctly almost all participants, with an accuracy of 99% in the database used. PMID:26737619

  8. New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies

    NASA Astrophysics Data System (ADS)

    Marquette, Ian

    2015-04-01

    Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works.

  9. Surrogate Motherhood: A Trust-Based Approach.

    PubMed

    Beier, Katharina

    2015-12-01

    Because it is often argued that surrogacy should not be treated as contractual, the question arises in which terms this practice might then be couched. In this article, I argue that a phenomenology of surrogacy centering on the notion of trust provides a description that is illuminating from the moral point of view. My thesis is that surrogacy establishes a complex and extended reproductive unit--the "surrogacy triad" consisting of the surrogate mother, the child, and the intending parents--whose constituents are bound together by mutual trustful commitments. Even though a trust-based approach does not provide an ultimate answer to whether surrogacy should be sanctioned or prohibited, it allows for at least some practical suggestions. In particular, I will argue that, under certain conditions, surrogacy is tenable within familial or other significant relationships, and I will stress the necessity of acknowledging the new relationships and moral commitments that result from this practice. PMID:26449234

  10. Nanotechnology-based approaches in anticancer research

    PubMed Central

    Jabir, Nasimudeen R; Tabrez, Shams; Ashraf, Ghulam Md; Shakil, Shazi; Damanhouri, Ghazi A; Kamal, Mohammad A

    2012-01-01

    Cancer is a highly complex disease to understand, because it entails multiple cellular physiological systems. The most common cancer treatments are restricted to chemotherapy, radiation and surgery. Moreover, the early recognition and treatment of cancer remains a technological bottleneck. There is an urgent need to develop new and innovative technologies that could help to delineate tumor margins, identify residual tumor cells and micrometastases, and determine whether a tumor has been completely removed or not. Nanotechnology has witnessed significant progress in the past few decades, and its effect is widespread nowadays in every field. Nanoparticles can be modified in numerous ways to prolong circulation, enhance drug localization, increase drug efficacy, and potentially decrease chances of multidrug resistance by the use of nanotechnology. Recently, research in the field of cancer nanotechnology has made remarkable advances. The present review summarizes the application of various nanotechnology-based approaches towards the diagnostics and therapeutics of cancer. PMID:22927757

  11. VATS-based approach for robotic lobectomy.

    PubMed

    Melfi, Franca M A; Fanucchi, Olivia; Davini, Federico; Mussi, Alfredo

    2014-05-01

    Lobectomy with systematic lymph node sampling or dissection remains the mainstay of treatment of early stage non-small cell lung cancer. The use of video-assisted thoracic surgery (VATS) to perform lobectomy was first reported in 1992. Advantages of VATS include less trauma and pain, shorter chest drainage duration, decreased hospital stay, and preservation of short-term pulmonary function. However, VATS is characterized by loss of binocular vision and a limited maneuverability of thoracoscopic instruments, an unstable camera platform, and poor ergonomics for the surgeon. To overcome these limitations, robotic systems were developed during the last decades. This article reviews the technical aspects of robotic lobectomy using a VATS-based approach. PMID:24780417

  12. Sepsis management: An evidence-based approach.

    PubMed

    Baig, Muhammad Akbar; Shahzad, Hira; Jamil, Bushra; Hussain, Erfan

    2016-03-01

    The Surviving Sepsis Campaign (SSC) guidelines have outlined an early goal directed therapy (EGDT) which demonstrates a standardized approach to ensure prompt and effective management of sepsis. Having said that, there are barriers associated with the application of evidence-based practice, which often lead to an overall poorer adherence to guidelines. Considering the global burden of disease, data from low- to middle-income countries is scarce. Asia is the largest continent but most Asian countries do not have a well-developed healthcare system and compliance rates to resuscitation and management bundles are as low as 7.6% and 3.5%, respectively. Intensive care units are not adequately equipped and financial concerns limit implementation of expensive treatment strategies. Healthcare policy-makers should be notified in order to alleviate financial restrictions and ensure delivery of standard care to septic patients. PMID:26968289

  13. Strategic approaches to planetary base development

    NASA Technical Reports Server (NTRS)

    Roberts, Barney B.

    1992-01-01

    The evolutionary development of a planetary expansionary outpost is considered in the light of both technical and economic issues. The outline of a partnering taxonomy is set forth which encompasses both institutional and temporal issues related to establishing shared interests and investments. The purely technical issues are discussed in terms of the program components which include nonaerospace technologies such as construction engineering. Five models are proposed in which partnership and autonomy for participants are approached in different ways including: (1) the standard customer/provider relationship; (2) a service-provider scenario; (3) the joint venture; (4) a technology joint-development model; and (5) a redundancy model for reduced costs. Based on the assumed characteristics of planetary surface systems the cooperative private/public models are championed with coordinated design by NASA to facilitate outside cooperation.

  14. Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras

    NASA Astrophysics Data System (ADS)

    Paseka, Jan; Riečanová, Zdenka

    2010-12-01

    We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.

  15. Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.

    PubMed

    Sialaros, Michalis; Christianidis, Jean

    2016-06-01

    Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition. PMID:27171890

  16. Changing Practice, Changing Minds, from Arithmetical to Algebraic Thinking: An Application of the Concerns-Based Adoption Model (CBAM)

    ERIC Educational Resources Information Center

    Tunks, Jeanne; Weller, Kirk

    2009-01-01

    This study examines the process of change among grade 4 teachers (students aged 9-10 years) who participated in a yearlong Teacher Quality Grant innovation program. The concerns-based adoption model (CBAM), which informed the design and implementation of the program, was used to examine the process of change. Two questions guided the…

  17. Locally finite dimensional Lie algebras

    NASA Astrophysics Data System (ADS)

    Hennig, Johanna

    We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).

  18. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075

  19. On the cohomology of Leibniz conformal algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Jiao

    2015-04-01

    We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.

  20. Assessing Algebraic Solving Ability: A Theoretical Framework

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  1. Redberry: a computer algebra system designed for tensor manipulation

    NASA Astrophysics Data System (ADS)

    Poslavsky, Stanislav; Bolotin, Dmitry

    2015-05-01

    In this paper we focus on the main aspects of computer-aided calculations with tensors and present a new computer algebra system Redberry which was specifically designed for algebraic tensor manipulation. We touch upon distinctive features of tensor software in comparison with pure scalar systems, discuss the main approaches used to handle tensorial expressions and present the comparison of Redberry performance with other relevant tools.

  2. Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

    SciTech Connect

    Zhang, Hong-Biao Lu, Lu

    2013-12-15

    Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derived naturally from the polynomial su(1, 1) algebras built by us.

  3. How Structure Sense for Algebraic Expressions or Equations Is Related to Structure Sense for Abstract Algebra

    ERIC Educational Resources Information Center

    Novotna, Jarmila; Hoch, Maureen

    2008-01-01

    Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

  4. Higher level twisted Zhu algebras

    SciTech Connect

    Ekeren, Jethro van

    2011-05-15

    The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.

  5. Algebraic special functions and SO(3,2)

    SciTech Connect

    Celeghini, E.; Olmo, M.A. del

    2013-06-15

    A ladder structure of operators is presented for the associated Legendre polynomials and the sphericas harmonics. In both cases these operators belong to the irreducible representation of the Lie algebra so(3,2) with quadratic Casimir equals to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be homomorphic to the space of linear operators acting on the L{sup 2} functions defined on (−1,1)×Z and on the sphere S{sup 2}, respectively. The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining in this way the “algebraic special functions” that are proposed to be the connection between Lie algebras and square-integrable functions so that the space of linear operators on the L{sup 2} functions is homomorphic to the universal enveloping algebra. The passage to the group, by means of the exponential map, shows that the associated Legendre polynomials and the spherical harmonics support the corresponding unitary irreducible representation of the group SO(3,2). -- Highlights: •The algebraic ladder structure is constructed for the associated Legendre polynomials (ALP). •ALP and spherical harmonics support a unitary irreducible SO(3,2)-representation. •A ladder structure is the condition to get a Lie group representation defining “algebraic special functions”. •The “algebraic special functions” connect Lie algebras and L{sup 2} functions.

  6. The arithmetico-geometric sequence: an application of linear algebra

    NASA Astrophysics Data System (ADS)

    Orosi, Greg

    2016-07-01

    In this paper, we present a linear algebra-based derivation of the analytic formula for the sum of the first nth terms of the arithmetico-geometric sequence. Furthermore, the advantage of the derivation is briefly discussed.

  7. Handheld Computer Algebra Systems in the Pre-Algebra Classroom

    ERIC Educational Resources Information Center

    Gantz, Linda Ann Galofaro

    2010-01-01

    This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…

  8. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  9. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  10. Knowledge-based approach to system integration

    NASA Technical Reports Server (NTRS)

    Blokland, W.; Krishnamurthy, C.; Biegl, C.; Sztipanovits, J.

    1988-01-01

    To solve complex problems one can often use the decomposition principle. However, a problem is seldom decomposable into completely independent subproblems. System integration deals with problem of resolving the interdependencies and the integration of the subsolutions. A natural method of decomposition is the hierarchical one. High-level specifications are broken down into lower level specifications until they can be transformed into solutions relatively easily. By automating the hierarchical decomposition and solution generation an integrated system is obtained in which the declaration of high level specifications is enough to solve the problem. We offer a knowledge-based approach to integrate the development and building of control systems. The process modeling is supported by using graphic editors. The user selects and connects icons that represent subprocesses and might refer to prewritten programs. The graphical editor assists the user in selecting parameters for each subprocess and allows the testing of a specific configuration. Next, from the definitions created by the graphical editor, the actual control program is built. Fault-diagnosis routines are generated automatically as well. Since the user is not required to write program code and knowledge about the process is present in the development system, the user is not required to have expertise in many fields.

  11. Evaluating face trustworthiness: a model based approach

    PubMed Central

    Baron, Sean G.; Oosterhof, Nikolaas N.

    2008-01-01

    Judgments of trustworthiness from faces determine basic approach/avoidance responses and approximate the valence evaluation of faces that runs across multiple person judgments. Here, based on trustworthiness judgments and using a computer model for face representation, we built a model for representing face trustworthiness (study 1). Using this model, we generated novel faces with an increased range of trustworthiness and used these faces as stimuli in a functional Magnetic Resonance Imaging study (study 2). Although participants did not engage in explicit evaluation of the faces, the amygdala response changed as a function of face trustworthiness. An area in the right amygdala showed a negative linear response—as the untrustworthiness of faces increased so did the amygdala response. Areas in the left and right putamen, the latter area extended into the anterior insula, showed a similar negative linear response. The response in the left amygdala was quadratic—strongest for faces on both extremes of the trustworthiness dimension. The medial prefrontal cortex and precuneus also showed a quadratic response, but their response was strongest to faces in the middle range of the trustworthiness dimension. PMID:19015102

  12. Pattern recognition tool based on complex network-based approach

    NASA Astrophysics Data System (ADS)

    Casanova, Dalcimar; Backes, André Ricardo; Martinez Bruno, Odemir

    2013-02-01

    This work proposed a generalization of the method proposed by the authors: 'A complex network-based approach for boundary shape analysis'. Instead of modelling a contour into a graph and use complex networks rules to characterize it, here, we generalize the technique. This way, the work proposes a mathematical tool for characterization signals, curves and set of points. To evaluate the pattern description power of the proposal, an experiment of plat identification based on leaf veins image are conducted. Leaf vein is a taxon characteristic used to plant identification proposes, and one of its characteristics is that these structures are complex, and difficult to be represented as a signal or curves and this way to be analyzed in a classical pattern recognition approach. Here, we model the veins as a set of points and model as graphs. As features, we use the degree and joint degree measurements in a dynamic evolution. The results demonstrates that the technique has a good power of discrimination and can be used for plant identification, as well as other complex pattern recognition tasks.

  13. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  14. Algebraic Multigrid Benchmark

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less

  15. Solving stochastic epidemiological models using computer algebra

    NASA Astrophysics Data System (ADS)

    Hincapie, Doracelly; Ospina, Juan

    2011-06-01

    Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.

  16. Concurrency-based approaches to parallel programming

    NASA Technical Reports Server (NTRS)

    Kale, L.V.; Chrisochoides, N.; Kohl, J.; Yelick, K.

    1995-01-01

    The inevitable transition to parallel programming can be facilitated by appropriate tools, including languages and libraries. After describing the needs of applications developers, this paper presents three specific approaches aimed at development of efficient and reusable parallel software for irregular and dynamic-structured problems. A salient feature of all three approaches in their exploitation of concurrency within a processor. Benefits of individual approaches such as these can be leveraged by an interoperability environment which permits modules written using different approaches to co-exist in single applications.

  17. Concurrency-based approaches to parallel programming

    SciTech Connect

    Kale, L.V.; Chrisochoides, N.; Kohl, J.

    1995-07-17

    The inevitable transition to parallel programming can be facilitated by appropriate tools, including languages and libraries. After describing the needs of applications developers, this paper presents three specific approaches aimed at development of efficient and reusable parallel software for irregular and dynamic-structured problems. A salient feature of all three approaches in their exploitation of concurrency within a processor. Benefits of individual approaches such as these can be leveraged by an interoperability environment which permits modules written using different approaches to co-exist in single applications.

  18. Sheaf-theoretic representation of quantum measure algebras

    SciTech Connect

    Zafiris, Elias

    2006-09-15

    We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems.

  19. Using computer algebra and SMT solvers in algebraic biology

    NASA Astrophysics Data System (ADS)

    Pineda Osorio, Mateo

    2014-05-01

    Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks are approached with the help of SMT Solvers and the use of computer algebra. Software such as Maple and Z3 was used in this case. The number of stationary states for each network was calculated. The network studied here corresponds to the immune system under the effects of drastic mood changes. Mood is considered as a Boolean variable that affects the entire dynamics of the immune system, changing the Boolean satisfiability and the number of stationary states of the immune network. Results obtained show Z3's great potential as a SMT Solver. Some of these results were verified in Maple, even though it showed not to be as suitable for the problem approach. The solving code was constructed using Z3-Python and Z3-SMT-LiB. Results obtained are important in biology systems and are expected to help in the design of immune therapies. As a future line of research, more complex Boolean network representations of the immune system as well as the whole psychological apparatus are suggested.

  20. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  1. Algebraic Squares: Complete and Incomplete.

    ERIC Educational Resources Information Center

    Gardella, Francis J.

    2000-01-01

    Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

  2. The Algebra of the Arches

    ERIC Educational Resources Information Center

    Buerman, Margaret

    2007-01-01

    Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

  3. Online Algebraic Tools for Teaching

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2011-01-01

    Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

  4. Condensing Algebra for Technical Mathematics.

    ERIC Educational Resources Information Center

    Greenfield, Donald R.

    Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…

  5. Algebra: Grades 8-12.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…

  6. Learning Algebra from Worked Examples

    ERIC Educational Resources Information Center

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…

  7. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  8. Topological insulators and C*-algebras: Theory and numerical practice

    SciTech Connect

    Hastings, Matthew B.; Loring, Terry A.

    2011-07-15

    Research Highlights: > We classify topological insulators using C* algebras. > We present new K-theory invariants. > We develop efficient numerical algorithms based on this technique. > We observe unexpected quantum phase transitions using our algorithm. - Abstract: We apply ideas from C*-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12{sup 3}, averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an 'order parameter' for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C*-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.

  9. Prognostics and Health Management for Complex system Based on Fusion of Model-based approach and Data-driven approach

    NASA Astrophysics Data System (ADS)

    Hong-feng, Wang

    Prognostics and Health Management has been becoming an effective technology to increasing efficiency and reducing cost for complex system. As for the two major categories methods, both model-based approaches and datadriven approaches have merits and drawbacks. A kind of fusion approaches that integrate model-based approaches and data-driven approaches is presented in this paper and fusion structure is detailed to make full use of their advantages and overcome their limitations.

  10. Reuse: A knowledge-based approach

    NASA Technical Reports Server (NTRS)

    Iscoe, Neil; Liu, Zheng-Yang; Feng, Guohui

    1992-01-01

    This paper describes our research in automating the reuse process through the use of application domain models. Application domain models are explicit formal representations of the application knowledge necessary to understand, specify, and generate application programs. Furthermore, they provide a unified repository for the operational structure, rules, policies, and constraints of a specific application area. In our approach, domain models are expressed in terms of a transaction-based meta-modeling language. This paper has described in detail the creation and maintenance of hierarchical structures. These structures are created through a process that includes reverse engineering of data models with supplementary enhancement from application experts. Source code is also reverse engineered but is not a major source of domain model instantiation at this time. In the second phase of the software synthesis process, program specifications are interactively synthesized from an instantiated domain model. These specifications are currently integrated into a manual programming process but will eventually be used to derive executable code with mechanically assisted transformations. This research is performed within the context of programming-in-the-large types of systems. Although our goals are ambitious, we are implementing the synthesis system in an incremental manner through which we can realize tangible results. The client/server architecture is capable of supporting 16 simultaneous X/Motif users and tens of thousands of attributes and classes. Domain models have been partially synthesized from five different application areas. As additional domain models are synthesized and additional knowledge is gathered, we will inevitably add to and modify our representation. However, our current experience indicates that it will scale and expand to meet our modeling needs.

  11. Invariants of triangular Lie algebras

    NASA Astrophysics Data System (ADS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-07-01

    Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.

  12. Translating cosmological special relativity into geometric algebra

    NASA Astrophysics Data System (ADS)

    Horn, Martin Erik

    2012-11-01

    Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.

  13. Zeta functional equation on Jordan algebras of type II

    NASA Astrophysics Data System (ADS)

    Kayoya, J. B.

    2005-02-01

    Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II.

  14. Nanotechnology based approaches in cancer therapeutics

    NASA Astrophysics Data System (ADS)

    Kumer Biswas, Amit; Reazul Islam, Md; Sadek Choudhury, Zahid; Mostafa, Asif; Fahim Kadir, Mohammad

    2014-12-01

    The current decades are marked not by the development of new molecules for the cure of various diseases but rather the development of new delivery methods for optimum treatment outcome. Nanomedicine is perhaps playing the biggest role in this concern. Nanomedicine offers numerous advantages over conventional drug delivery approaches and is particularly the hot topic in anticancer research. Nanoparticles (NPs) have many unique criteria that enable them to be incorporated in anticancer therapy. This topical review aims to look at the properties and various forms of NPs and their use in anticancer treatment, recent development of the process of identifying new delivery approaches as well as progress in clinical trials with these newer approaches. Although the outcome of cancer therapy can be increased using nanomedicine there are still many disadvantages of using this approach. We aim to discuss all these issues in this review.

  15. Minimally invasive surgery of the anterior skull base: transorbital approaches

    PubMed Central

    Gassner, Holger G.; Schwan, Franziska; Schebesch, Karl-Michael

    2016-01-01

    Minimally invasive approaches are becoming increasingly popular to access the anterior skull base. With interdisciplinary cooperation, in particular endonasal endoscopic approaches have seen an impressive expansion of indications over the past decades. The more recently described transorbital approaches represent minimally invasive alternatives with a differing spectrum of access corridors. The purpose of the present paper is to discuss transorbital approaches to the anterior skull base in the light of the current literature. The transorbital approaches allow excellent exposure of areas that are difficult to reach like the anterior and posterior wall of the frontal sinus; working angles may be more favorable and the paranasal sinus system can be preserved while exposing the skull base. Because of their minimal morbidity and the cosmetically excellent results, the transorbital approaches represent an important addition to established endonasal endoscopic and open approaches to the anterior skull base. Their execution requires an interdisciplinary team approach. PMID:27453759

  16. The Impact of the One to One Laptop Initiative on High School Students' Academic Performance in Algebra I and English I--A Meta-Analytic Approach

    ERIC Educational Resources Information Center

    Dennis, Quincita

    2014-01-01

    This study examined the effectiveness of using laptops to teach and deliver instruction to students. The meta-analytic approach was employed to compare the means of End-of Course Test scores from North Carolina one-to-one high schools during the traditional teaching period and the laptop teaching period in order to determine if there are…

  17. Cosmological Singularities, Billiards and Lorentzian Kac-Moody Algebras

    NASA Astrophysics Data System (ADS)

    Damour, T.

    The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically simplified by the use of the Arnowitt-Deser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solution is describable, at each (generic) spatial point, as a billiard motion in an auxiliary Lorentzian space. For certain Einstein-matter systems, notably for pure Einstein gravity in any spacetime dimension D and for the particular Einstein-matter systems arising in String theory, the billiard tables describing asymptotic cosmological behaviour are found to be identical to the Weyl chambers of some Lorentzian Kac-Moody algebras. In the case of the bosonic sector of supergravity in 11 dimensional spacetime the underlying Lorentzian algebra is that of the hyperbolic Kac-Moody group E(10), and there exists some evidence of a correspondence between the general solution of the Einstein-three-form system and a null geodesic in the infinite dimensional coset space E(10)/K (E(10)), where K (E(10)) is the maximal compact subgroup of E(10).

  18. Constraint algebra in bigravity

    SciTech Connect

    Soloviev, V. O.

    2015-07-15

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  19. Student Perceptions of the Flipped Classroom in College Algebra

    ERIC Educational Resources Information Center

    Ogden, Lori

    2015-01-01

    The flipped classroom approach was implemented across three semesters of a College Algebra course. This paper is part of a larger design and development research study and focuses on student perceptions of the flipped classroom teaching approach. Qualitative methodology was used to describe how students perceived the instruction of their College…

  20. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  1. Emphasizing language and visualization in teaching linear algebra

    NASA Astrophysics Data System (ADS)

    Hannah, John; Stewart, Sepideh; Thomas, Mike

    2013-06-01

    Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his approach in both lectures and tutorials, and how he employed visualization and an emphasis on language to encourage conceptual thinking. We use Tall's framework of three worlds of mathematical thinking to reflect on the effect of these activities in students' learning. An analysis of students' attitudes to the course and their test and examination results help to answer questions about the value of such an approach, suggesting ways forward in teaching linear algebra.

  2. The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

    ERIC Educational Resources Information Center

    O'Hanlon, Angela L.

    2011-01-01

    The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…

  3. Fault Detection in Differential Algebraic Equations

    NASA Astrophysics Data System (ADS)

    Scott, Jason Roderick

    Fault detection and identification (FDI) is important in almost all real systems. Fault detection is the supervision of technical processes aimed at detecting undesired or unpermitted states (faults) and taking appropriate actions to avoid dangerous situations, or to ensure efficiency in a system. This dissertation develops and extends fault detection techniques for systems modeled by differential algebraic equations (DAEs). First, a passive, observer-based approach is developed and linear filters are constructed to identify faults by filtering residual information. The method presented here uses the least squares completion to compute an ordinary differential equation (ODE) that contains the solution of the DAE and applies the observer directly to this ODE. While observers have been applied to ODE models for the purpose of fault detection in the past, the use of observers on completions of DAEs is a new idea. Moreover, the resulting residuals are modified requiring additional analysis. Robustness with respect to disturbances is also addressed by a novel frequency filtering technique. Active detection, as opposed to passive detection where outputs are passively monitored, allows the injection of an auxiliary control signal to test the system. These algorithms compute an auxiliary input signal guaranteeing fault detection, assuming bounded noise. In the second part of this dissertation, a novel active detection approach for DAE models is developed by taking linear transformations of the DAEs and solving a bi-layer optimization problem. An efficient real-time detection algorithm is also provided, as is the extension to model uncertainty. The existence of a class of problems where the algorithm breaks down is revealed and an alternative algorithm that finds a nearly minimal auxiliary signal is presented. Finally, asynchronous signal design, that is, applying the test signal on a different interval than the observation window, is explored and discussed.

  4. Distance geometry and geometric algebra

    NASA Astrophysics Data System (ADS)

    Dress, Andreas W. M.; Havel, Timothy F.

    1993-10-01

    As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)

  5. Loop Virasoro Lie conformal algebra

    SciTech Connect

    Wu, Henan Chen, Qiufan; Yue, Xiaoqing

    2014-01-15

    The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

  6. Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

    PubMed Central

    Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

    2016-01-01

    This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

  7. Hopf algebras and Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Weinzierl, Stefan

    2016-06-01

    In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.

  8. Invariants of triangular Lie algebras with one nil-independent diagonal element

    NASA Astrophysics Data System (ADS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-08-01

    The invariants of solvable triangular Lie algebras with one nil-independent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan's method of moving frames and the special technique developed for triangular and closed algebras in Boyko et al (J. Phys. A: Math. Theor. 2007 40 7557). The conjecture of Tremblay and Winternitz (J. Phys. A: Math. Gen. 2001 34 9085) on the number and form of elements in the bases is completed and proved.

  9. Assessment of polytechnic students' understanding of basic algebra

    NASA Astrophysics Data System (ADS)

    Mokmin, Nur Azlina Mohamed; Masood, Mona

    2015-12-01

    It is important for engineering students to excel in algebra. Previous studies show that the algebraic fraction is a subtopic of algebra that was found to be the most challenging for engineering students. This study is done with 191 first semester engineering students who have enrolled in engineering programs in Malaysian polytechnic. The respondents are divided into Group 1 (Distinction) and Group 2 (Credit) based on their Mathematics SPM result. A computer application is developed for this study to assess student information and understanding of the algebraic fraction topic. The result is analyzed using SPSS and Microsoft Excel. The test results show that there are significant differences between Group 1 and Group 2 and that most of the students scored below the minimum requirement.

  10. On explicit algebraic stress models for complex turbulent flows

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Speziale, C. G.

    1992-01-01

    Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

  11. Boolean Operations with Prism Algebraic Patches.

    PubMed

    Bajaj, Chandrajit; Paoluzzi, Alberto; Portuesi, Simone; Lei, Na; Zhao, Wenqi

    2008-01-01

    In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C(1)-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation. PMID:21516262

  12. Assessment of Person Fit Using Resampling-Based Approaches

    ERIC Educational Resources Information Center

    Sinharay, Sandip

    2016-01-01

    De la Torre and Deng suggested a resampling-based approach for person-fit assessment (PFA). The approach involves the use of the [math equation unavailable] statistic, a corrected expected a posteriori estimate of the examinee ability, and the Monte Carlo (MC) resampling method. The Type I error rate of the approach was closer to the nominal level…

  13. Evaluating a pivot-based approach for bilingual lexicon extraction.

    PubMed

    Kim, Jae-Hoon; Kwon, Hong-Seok; Seo, Hyeong-Won

    2015-01-01

    A pivot-based approach for bilingual lexicon extraction is based on the similarity of context vectors represented by words in a pivot language like English. In this paper, in order to show validity and usability of the pivot-based approach, we evaluate the approach in company with two different methods for estimating context vectors: one estimates them from two parallel corpora based on word association between source words (resp., target words) and pivot words and the other estimates them from two parallel corpora based on word alignment tools for statistical machine translation. Empirical results on two language pairs (e.g., Korean-Spanish and Korean-French) have shown that the pivot-based approach is very promising for resource-poor languages and this approach observes its validity and usability. Furthermore, for words with low frequency, our method is also well performed. PMID:25983745

  14. Evaluating a Pivot-Based Approach for Bilingual Lexicon Extraction

    PubMed Central

    Kim, Jae-Hoon; Kwon, Hong-Seok; Seo, Hyeong-Won

    2015-01-01

    A pivot-based approach for bilingual lexicon extraction is based on the similarity of context vectors represented by words in a pivot language like English. In this paper, in order to show validity and usability of the pivot-based approach, we evaluate the approach in company with two different methods for estimating context vectors: one estimates them from two parallel corpora based on word association between source words (resp., target words) and pivot words and the other estimates them from two parallel corpora based on word alignment tools for statistical machine translation. Empirical results on two language pairs (e.g., Korean-Spanish and Korean-French) have shown that the pivot-based approach is very promising for resource-poor languages and this approach observes its validity and usability. Furthermore, for words with low frequency, our method is also well performed. PMID:25983745

  15. The Effect of Instruction with Graphing Calculators on How General Mathematics Students Naturalistically Solve Algebraic Problems.

    ERIC Educational Resources Information Center

    Merriweather, Michelle; Tharp, Marcia L.

    1999-01-01

    Focuses on changes in attitude toward mathematics and calculator use and changes in how general mathematics students naturalistically solve algebraic problems. Uses a survey to determine whether a student is rule-based. Concludes that the rule-based students used an equation to solve the algebraic word problem whereas the non-rule-based students…

  16. Sequential products on effect algebras

    NASA Astrophysics Data System (ADS)

    Gudder, Stan; Greechie, Richard

    2002-02-01

    A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.

  17. Curvature calculations with spacetime algebra

    SciTech Connect

    Hestenes, D.

    1986-06-01

    A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.

  18. GCD, LCM, and Boolean Algebra?

    ERIC Educational Resources Information Center

    Cohen, Martin P.; Juraschek, William A.

    1976-01-01

    This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)

  19. Cartooning in Algebra and Calculus

    ERIC Educational Resources Information Center

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  20. Ada Linear-Algebra Program

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  1. Maximizing algebraic connectivity in air transportation networks

    NASA Astrophysics Data System (ADS)

    Wei, Peng

    In air transportation networks the robustness of a network regarding node and link failures is a key factor for its design. An experiment based on the real air transportation network is performed to show that the algebraic connectivity is a good measure for network robustness. Three optimization problems of algebraic connectivity maximization are then formulated in order to find the most robust network design under different constraints. The algebraic connectivity maximization problem with flight routes addition or deletion is first formulated. Three methods to optimize and analyze the network algebraic connectivity are proposed. The Modified Greedy Perturbation Algorithm (MGP) provides a sub-optimal solution in a fast iterative manner. The Weighted Tabu Search (WTS) is designed to offer a near optimal solution with longer running time. The relaxed semi-definite programming (SDP) is used to set a performance upper bound and three rounding techniques are discussed to find the feasible solution. The simulation results present the trade-off among the three methods. The case study on two air transportation networks of Virgin America and Southwest Airlines show that the developed methods can be applied in real world large scale networks. The algebraic connectivity maximization problem is extended by adding the leg number constraint, which considers the traveler's tolerance for the total connecting stops. The Binary Semi-Definite Programming (BSDP) with cutting plane method provides the optimal solution. The tabu search and 2-opt search heuristics can find the optimal solution in small scale networks and the near optimal solution in large scale networks. The third algebraic connectivity maximization problem with operating cost constraint is formulated. When the total operating cost budget is given, the number of the edges to be added is not fixed. Each edge weight needs to be calculated instead of being pre-determined. It is illustrated that the edge addition and the

  2. Algebraic Proof of the Distributive Law for Vector Multiplication

    NASA Astrophysics Data System (ADS)

    Korn, Charles

    2014-03-01

    Courses in first year mechanics generally start with an introduction to vector methods which include scalar and vector multiplication1. While the demonstration of the validity of the distributive law for scalar multiplication is straightforward, this is not so for vector multiplication. The latter requires complicated geometrical visualization, so its proof is often skipped1. Neither the commutative nor associative law holds for vector multiplication, so there is no a priori reason that the distributive law should hold. In this paper we present an algebraic approach to the proof that requires no geometric visualization. It is based on two relations: (1) the distributive law for scalar multiplication and (2) a*(bxc) =c*(axb) =b*(cxa). 1. e.g. C. Kittlel, W.D. Knight, M.A. Ruderman, Mechanics, Berkeley Physics Course Vol. 1, 2nd ed. McGraw Hill, pp34-39.

  3. ALGEBRA v.1.27

    2005-04-11

    The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.

  4. From Function to Equations: Introduction of Algebraic Thinking to 13 Year-Old Students

    ERIC Educational Resources Information Center

    Farmaki, Vasiliki; Klaoudatos, Nikos; Verikios, Petros

    2004-01-01

    The various difficulties and cognitive obstacles that students face when they are introduced to algebra are well documented and described in the relevant bibliography. If it is possible, in order to avoid these difficulties, we have adopted the functional approach widening the meaning of algebraic thinking. In this paper, which is part of wider…

  5. Maple (Computer Algebra System) in Teaching Pre-Calculus: Example of Absolute Value Function

    ERIC Educational Resources Information Center

    Tuluk, Güler

    2014-01-01

    Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…

  6. Cognitive Tutor[R] Algebra I. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2009

    2009-01-01

    The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then customizes prompts…

  7. A Strength-Based Approach to Teacher Professional Development

    ERIC Educational Resources Information Center

    Zwart, Rosanne C.; Korthagen, Fred A. J.; Attema-Noordewier, Saskia

    2015-01-01

    Based on positive psychology, self-determination theory and a perspective on teacher quality, this study proposes and examines a strength-based approach to teacher professional development. A mixed method pre-test/post-test design was adopted to study perceived outcomes of the approach for 93 teachers of six primary schools in the Netherlands and…

  8. EFL Reading Instruction: Communicative Task-Based Approach

    ERIC Educational Resources Information Center

    Sidek, Harison Mohd

    2012-01-01

    The purpose of this study was to examine the overarching framework of EFL (English as a Foreign Language) reading instructional approach reflected in an EFL secondary school curriculum in Malaysia. Based on such analysis, a comparison was made if Communicative Task-Based Language is the overarching instructional approach for the Malaysian EFL…

  9. Generic, Type-Safe and Object Oriented Computer Algebra Software

    NASA Astrophysics Data System (ADS)

    Kredel, Heinz; Jolly, Raphael

    Advances in computer science, in particular object oriented programming, and software engineering have had little practical impact on computer algebra systems in the last 30 years. The software design of existing systems is still dominated by ad-hoc memory management, weakly typed algorithm libraries and proprietary domain specific interactive expression interpreters. We discuss a modular approach to computer algebra software: usage of state-of-the-art memory management and run-time systems (e.g. JVM) usage of strongly typed, generic, object oriented programming languages (e.g. Java) and usage of general purpose, dynamic interactive expression interpreters (e.g. Python) To illustrate the workability of this approach, we have implemented and studied computer algebra systems in Java and Scala. In this paper we report on the current state of this work by presenting new examples.

  10. Algebraic Flux Correction II

    NASA Astrophysics Data System (ADS)

    Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel

    Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.

  11. Component design bases - A template approach

    SciTech Connect

    Pabst, L.F. ); Strickland, K.M. )

    1991-01-01

    A well-documented nuclear plant design basis can enhance plant safety and availability. Older plants, however, often lack historical evidence of the original design intent, particularly for individual components. Most plant documentation describes the actual design (what is) rather than the bounding limits of the design. Without knowledge of these design limits, information from system descriptions and equipment specifications is often interpreted as inviolate design requirements. Such interpretations may lead to unnecessary design conservatism in plant modifications and unnecessary restrictions on plant operation. In 1986, Florida Power and Light Company's (FP and L's) Turkey Point plant embarked on one of the first design basis reconstitution programs in the United States to catalog the true design requirements. As the program developed, design basis users expressed a need for additional information at the component level. This paper outlines a structured (template) approach to develop useful component design basis information (including the WHYs behind the design).

  12. Context-Based Chemistry: The Salters Approach

    ERIC Educational Resources Information Center

    Bennett, Judith; Lubben, Fred

    2006-01-01

    This paper describes briefly the development and key features of one of the major context-based courses for upper high school students, Salters Advanced Chemistry. It goes on to consider the research evidence on the impact of the course, focusing on teachers' views, and, in particular, on students' affective and cognitive responses. The research…

  13. PBL Approach in Web-Based Instruction

    ERIC Educational Resources Information Center

    ChanLin, Lih-Juan; Chan, Kung-Chi

    2004-01-01

    Web-Based Instruction is increasingly being recognized as a means of teaching and learning. In dietetics, the interactions between drugs and nutrients are complex due to the wide variety of drugs and their mechanism and interactions with nutrients. How to help student professionals acquired necessary skills and knowledge is important in a dietetic…

  14. A model-based multisensor data fusion knowledge management approach

    NASA Astrophysics Data System (ADS)

    Straub, Jeremy

    2014-06-01

    A variety of approaches exist for combining data from multiple sensors. The model-based approach combines data based on its support for or refutation of elements of the model which in turn can be used to evaluate an experimental thesis. This paper presents a collection of algorithms for mapping various types of sensor data onto a thesis-based model and evaluating the truth or falsity of the thesis, based on the model. The use of this approach for autonomously arriving at findings and for prioritizing data are considered. Techniques for updating the model (instead of arriving at a true/false assertion) are also discussed.

  15. Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang

    2015-04-01

    In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

  16. Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.

    ERIC Educational Resources Information Center

    Stoutemyer, David R.

    1983-01-01

    Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)

  17. Multifractal vector fields and stochastic Clifford algebra

    NASA Astrophysics Data System (ADS)

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  18. Multifractal vector fields and stochastic Clifford algebra

    SciTech Connect

    Schertzer, Daniel Tchiguirinskaia, Ioulia

    2015-12-15

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  19. Heisenberg uncertainty in reduced power algebras

    NASA Astrophysics Data System (ADS)

    Rosinger, Elemér E.

    2012-12-01

    The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far wider frameworks of scalars, namely, within one or the other of the infinitely many reduced power algebras which can replace the usual real numbers R, or complex numbers C. Three possible major advantages in Physics of such a reformulation are: 1) the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics", 2) the possibilitiy to have infinitely many "levels of precision" instead of the only one existing at present, 3) the possibility to model "hierarchies of Planck constants", [2]. Last and not least, the scalars given by reduced power algebras contain as a particular case those obtained by Nonstandard Analysis, yet they are far more simple and easy to deal with, being in fact on the level of a first course in Algebra. A detailed version of this paper can be found in arxiv:0901.4825.

  20. Multifractal vector fields and stochastic Clifford algebra.

    PubMed

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality. PMID:26723166

  1. CULA: hybrid GPU accelerated linear algebra routines

    NASA Astrophysics Data System (ADS)

    Humphrey, John R.; Price, Daniel K.; Spagnoli, Kyle E.; Paolini, Aaron L.; Kelmelis, Eric J.

    2010-04-01

    The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/watt ratio. High-level linear algebra operations are computationally intense, often requiring O(N3) operations and would seem a natural fit for the processing power of the GPU. Our work is on CULA, a GPU accelerated implementation of linear algebra routines. We present results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with applications like system solution and least squares. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally.

  2. [Evidence-based medicine: an epistemological approach].

    PubMed

    Henao, Daniel Eduardo; Jaimes, Fabián Alberto

    2009-03-01

    Evidence-based medicine gathers physician's experience and the best scientific evidence to make medical decisions. This proposal has been widely promulgated by medical opinion leaders. Despite a large literature supporting this practice, a formal discussion has not been established regarding its epistemological consequences in daily medical work. The main proposal of evidence-based medicine consists of choosing the best medical decision according to the best available results from scientific studies. Herein, the goal was to highlight inappropriate application of the scientific method used by physics to clinical science. The inaccuracy resides in describing health and disease in strictly numeric equivalents that can be homogenized on a continuous scale. Finally, the authors consider each diseased human being as a complex system, unique and particular, and that this being is defined by an historical background as well as current actual context. Therefore, evidence-based medicine possesses certain limitations that must be recognized in order to to provide better health care to patients. PMID:19753837

  3. Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces

    SciTech Connect

    Koibuchi, H. )

    1991-10-10

    In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.

  4. Wavelet-based approach to character skeleton.

    PubMed

    You, Xinge; Tang, Yuan Yan

    2007-05-01

    Character skeleton plays a significant role in character recognition. The strokes of a character may consist of two regions, i.e., singular and regular regions. The intersections and junctions of the strokes belong to singular region, while the straight and smooth parts of the strokes are categorized to regular region. Therefore, a skeletonization method requires two different processes to treat the skeletons in theses two different regions. All traditional skeletonization algorithms are based on the symmetry analysis technique. The major problems of these methods are as follows. 1) The computation of the primary skeleton in the regular region is indirect, so that its implementation is sophisticated and costly. 2) The extracted skeleton cannot be exactly located on the central line of the stroke. 3) The captured skeleton in the singular region may be distorted by artifacts and branches. To overcome these problems, a novel scheme of extracting the skeleton of character based on wavelet transform is presented in this paper. This scheme consists of two main steps, namely: a) extraction of primary skeleton in the regular region and b) amendment processing of the primary skeletons and connection of them in the singular region. A direct technique is used in the first step, where a new wavelet-based symmetry analysis is developed for finding the central line of the stroke directly. A novel method called smooth interpolation is designed in the second step, where a smooth operation is applied to the primary skeleton, and, thereafter, the interpolation compensation technique is proposed to link the primary skeleton, so that the skeleton in the singular region can be produced. Experiments are conducted and positive results are achieved, which show that the proposed skeletonization scheme is applicable to not only binary image but also gray-level image, and the skeleton is robust against noise and affine transform. PMID:17491454

  5. Arts-based and creative approaches to dementia care.

    PubMed

    McGreevy, Jessica

    2016-02-01

    This article presents a review of arts-based and creative approaches to dementia care as an alternative to antipsychotic medications. While use of antipsychotics may be appropriate for some people, the literature highlights the success of creative approaches and the benefits of their lack of negative side effects associated with antipsychotics. The focus is the use of biographical approaches, music, dance and movement to improve wellbeing, enhance social networks, support inclusive practice and enable participation. Staff must be trained to use these approaches. A case study is presented to demonstrate how creative approaches can be implemented in practice and the outcomes that can be expected when used appropriately. PMID:26938607

  6. Differentiating between rights-based and relational ethical approaches.

    PubMed

    Trobec, Irena; Herbst, Majda; Zvanut, Bostjan

    2009-05-01

    When forced treatment in mental health care is under consideration, two approaches guide clinicians in their actions: the dominant rights-based approach and the relational ethical approach. We hypothesized that nurses with bachelor's degrees differentiate better between the two approaches than nurses without a degree. To test this hypothesis a survey was performed in major Slovenian health institutions. We found that nurses emphasize the importance of ethics and personal values, but 55.4% of all the nurse participants confused the two approaches. The results confirmed our hypothesis and indicate the importance of nurses' formal education, especially when caring for patients with mental illness. PMID:19372123

  7. Ameliorated GA approach for base station planning

    NASA Astrophysics Data System (ADS)

    Wang, Andong; Sun, Hongyue; Wu, Xiaomin

    2011-10-01

    In this paper, we aim at locating base station (BS) rationally to satisfy the most customs by using the least BSs. An ameliorated GA is proposed to search for the optimum solution. In the algorithm, we mesh the area to be planned according to least overlap length derived from coverage radius, bring into isometric grid encoding method to represent BS distribution as well as its number and develop select, crossover and mutation operators to serve our unique necessity. We also construct our comprehensive object function after synthesizing coverage ratio, overlap ratio, population and geographical conditions. Finally, after importing an electronic map of the area to be planned, a recommended strategy draft would be exported correspondingly. We eventually import HongKong, China to simulate and yield a satisfactory solution.

  8. Engineering application based on fuzzy approach

    NASA Astrophysics Data System (ADS)

    Pislaru, Marius; Avasilcai, Silvia; Trandabat, Alexandru

    2011-12-01

    The article focus on an application of chemical engineering. A fuzzy modeling methodology designed to determinate two relevant characteristics of a chemical compound (ferrocenylsiloxane polyamide) for self-assembling - surface tension and maximum UV absorbance measured as temperature and concentration functions. One of the most important parts of a fuzzy rule-based inference system for the polyamide solution characteristics determinations is that it allows to interpret the knowledge contained in the model and also to improve it with a-priori knowledge. The results obtained through proposed method are highly accurate and its can be optimized by utilizing the available information during the modeling process. The results showed that it is feasible in theory and reliable on calculation applying Mamdani fuzzy inference system to the estimation of optical and surface properties of a polyamide solution.

  9. Engineering application based on fuzzy approach

    NASA Astrophysics Data System (ADS)

    Pislaru, Marius; Avasilcai, Silvia; Trandabat, Alexandru

    2012-01-01

    The article focus on an application of chemical engineering. A fuzzy modeling methodology designed to determinate two relevant characteristics of a chemical compound (ferrocenylsiloxane polyamide) for self-assembling - surface tension and maximum UV absorbance measured as temperature and concentration functions. One of the most important parts of a fuzzy rule-based inference system for the polyamide solution characteristics determinations is that it allows to interpret the knowledge contained in the model and also to improve it with a-priori knowledge. The results obtained through proposed method are highly accurate and its can be optimized by utilizing the available information during the modeling process. The results showed that it is feasible in theory and reliable on calculation applying Mamdani fuzzy inference system to the estimation of optical and surface properties of a polyamide solution.

  10. Multiresolution approach based on projection matrices

    SciTech Connect

    Vargas, Javier; Quiroga, Juan Antonio

    2009-03-01

    Active triangulation measurement systems with a rigid geometric configuration are inappropriate for scanning large objects with low measuring tolerances. The reason is that the ratio between the depth recovery error and the lateral extension is a constant that depends on the geometric setup. As a consequence, measuring large areas with low depth recovery error requires the use of multiresolution techniques. We propose a multiresolution technique based on a camera-projector system previously calibrated. The method consists of changing the camera or projector's parameters in order to increase the system depth sensitivity. A subpixel retroprojection error in the self-calibration process and a decrease of approximately one order of magnitude in the depth recovery error can be achieved using the proposed method.

  11. Systems-based approaches toward wound healing

    PubMed Central

    Buganza-Tepole, Adrian; Kuhl, Ellen

    2013-01-01

    Wound healing in the pediatric patient is of utmost clinical and social importance, since hypertrophic scarring can have aesthetic and psychological sequelae, from early childhood to late adolescence. Wound healing is a well-orchestrated reparative response affecting the damaged tissue at the cellular, tissue, organ, and system scales. While tremendous progress has been made towards understanding wound healing at the individual temporal and spatial scales, its effects across the scales remain severely understudied and poorly understood. Here we discuss the critical need for systems-based computational modeling of wound healing across the scales, from short-term to long-term and from small to large. We illustrate the state of the art in systems modeling by means of three key signaling mechanisms: oxygen tension regulating angiogenesis and revascularization; TGF-β kinetics controlling collagen deposition; and mechanical stretch stimulating cellular mitosis and extracellular matrix remodeling. The complex network of biochemical and biomechanical signaling mechanisms and the multi-scale character of the healing process make systems modeling an integral tool in exploring personalized strategies for wound repair. A better mechanistic understanding of wound healing in the pediatric patient could open new avenues in treating children with skin disorders such as birth defects, skin cancer, wounds, and burn injuries. PMID:23314298

  12. Enuresis in children: a case based approach.

    PubMed

    Baird, Drew C; Seehusen, Dean A; Bode, David V

    2014-10-15

    Enuresis is defined as intermittent urinary incontinence during sleep in a child at least five years of age. Approximately 5% to 10% of all seven-year-olds have enuresis, and an estimated 5 to 7 million children in the United States have enuresis. The pathophysiology of primary nocturnal enuresis involves the inability to awaken from sleep in response to a full bladder, coupled with excessive nighttime urine production or a decreased functional capacity of the bladder. Initial evaluation should include a history, physical examination, and urinalysis. Several conditions, such as constipation, obstructive sleep apnea, diabetes mellitus, diabetes insipidus, chronic kidney disease, and psychiatric disorders, are associated with enuresis. If identified, these conditions should be evaluated and treated. Treatment of primary monosymptomatic enuresis (i.e., the only symptom is nocturnal bed-wetting in a child who has never been dry) begins with counseling the child and parents on effective behavioral modifications. First-line treatments for enuresis include bed alarm therapy and desmopressin. The choice of therapy is based on the child's age and nighttime voiding patterns, and the desires of the child and family. Referral to a pediatric urologist is indicated for children with primary enuresis refractory to standard and combination therapies, and for children with some secondary causes of enuresis, including urinary tract malformations, recurrent urinary tract infections, or neurologic disorders. PMID:25369644

  13. Ternary generalization of Heisenberg's algebra

    NASA Astrophysics Data System (ADS)

    Kerner, Richard

    2015-06-01

    A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.

  14. Getting from Arithmetic to Algebra: Balanced Assessments for the Transition

    ERIC Educational Resources Information Center

    Schwartz, Judah L.; Kenney, Joan M.

    2012-01-01

    In this innovative book, two experienced educators present a fresh and engaging approach to mathematics learning in the middle grades with the transition from arithmetic to algebra. The authors provide a collection of balanced, multi-dimensional assessment tasks designed to evaluate students' ability to work with mathematical objects and perform…

  15. Using Enactivism as a Methodology to Characterise Algebraic Learning

    ERIC Educational Resources Information Center

    Lozano, Maria-Dolores

    2015-01-01

    My purpose in this paper is to illustrate the way in which an enactivist methodological approach guided me as I conducted a two-case longitudinal study where the learning of algebra was explored in different contexts throughout time. Three groups of students in two different schools in the city of Puebla, Mexico, were followed from the last year…

  16. L'algebra dei transiti planetari sul Sole

    NASA Astrophysics Data System (ADS)

    Sigismondi, Costantino

    2016-05-01

    The periodicity of Mercury and Venus' transits is regulated by the resonances of the orbital periods of these planets with the Earth's one. A simple algebraic approach is presented for explaining the resonance of 243 years of Venus and the one of 46 years for Mercury and the transits in May and November for Mercury and June and December for Venus.

  17. Cognitive Load and Modelling of an Algebra Problem

    ERIC Educational Resources Information Center

    Chinnappan, Mohan

    2010-01-01

    In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

  18. Optimal Discretization Resolution in Algebraic Image Reconstruction

    NASA Astrophysics Data System (ADS)

    Sharif, Behzad; Kamalabadi, Farzad

    2005-11-01

    In this paper, we focus on data-limited tomographic imaging problems where the underlying linear inverse problem is ill-posed. A typical regularized reconstruction algorithm uses algebraic formulation with a predetermined discretization resolution. If the selected resolution is too low, we may loose useful details of the underlying image and if it is too high, the reconstruction will be unstable and the representation will fit irrelevant features. In this work, two approaches are introduced to address this issue. The first approach is using Mallow's CL method or generalized cross-validation. For each of the two methods, a joint estimator of regularization parameter and discretization resolution is proposed and their asymptotic optimality is investigated. The second approach is a Bayesian estimator of the model order using a complexity-penalizing prior. Numerical experiments focus on a space imaging application from a set of limited-angle tomographic observations.

  19. Selection and identity rules for subductions of type A quantum Iwahori-Hecke algebras

    SciTech Connect

    Chilla, Vincenzo

    2007-11-15

    This paper is concerned with the subduction problem of type A quantum Iwahori-Hecke algebras CH(S{sub f},q{sup 2}) with a real deformation parameter q, i.e., the problem of decomposing irreducible representations of such algebras as direct sum of irreducible representations of the subalgebras CH(S{sub f{sub 1}},q{sup 2})xCH(S{sub f{sub 2}},q{sup 2}), with f{sub 1}+f{sub 2}=f. After giving a suitable combinatorial description for the subduction issue, we provide a selection rule, based on the Richardson-Littlewood criterion, which allows to determine the vanishing coupling coefficients between standard basis vectors for such representations, and we also present an equivariance condition for the subduction coefficients. Such results extend those ones corresponding to the subduction problem in symmetric group algebras CS{sub f}{down_arrow}CS{sub f{sub 1}}xCS{sub f{sub 2}} which are obtained by q approaching the value of 1.

  20. Algebraic theory of recombination spaces.

    PubMed

    Stadler, P F; Wagner, G P

    1997-01-01

    A new mathematical representation is proposed for the configuration space structure induced by recombination, which we call "P-structure." It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "genotypes" the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier decomposition of fitness landscapes into a superposition of "elementary landscapes." This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination, the elementary landscapes are exactly the p-spin functions (Walsh functions), that is, the same as the elementary landscapes of the string point mutation spaces (i.e., the hypercube). This supports the notion of a strong homomorphism between string mutation and recombination spaces. However, the effective nearest neighbor correlations on these elementary landscapes differ between mutation and recombination and among different recombination operators. On average, the nearest neighbor correlation is higher for one-point recombination than for uniform recombination. For one-point recombination, the correlations are higher for elementary landscapes with fewer interacting sites as well as for sites that have closer linkage, confirming the qualitative predictions of the Schema Theorem. We conclude that the algebraic approach to fitness landscape analysis can be extended to recombination spaces and provides an effective way to analyze the relative hardness of a landscape for a given recombination operator. PMID:10021760