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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, D; Kang, S; Kim, T

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 studiesmore » 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)« less

An algebraic iterative reconstruction technique for differential X-ray phase-contrast computed tomography.

PubMed

Fu, Jian; Schleede, Simone; Tan, Renbo; Chen, Liyuan; Bech, Martin; Achterhold, Klaus; Gifford, Martin; Loewen, Rod; Ruth, Ronald; Pfeiffer, Franz

2013-09-01

Iterative reconstruction has a wide spectrum of proven advantages in the field of conventional X-ray absorption-based computed tomography (CT). In this paper, we report on an algebraic iterative reconstruction technique for grating-based differential phase-contrast CT (DPC-CT). Due to the differential nature of DPC-CT projections, a differential operator and a smoothing operator are added to the iterative reconstruction, compared to the one commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured at a two-grating interferometer setup. Since the algorithm is easy to implement and allows for the extension to various regularization possibilities, we expect a significant impact of the method for improving future medical and industrial DPC-CT applications. Copyright © 2012. Published by Elsevier GmbH.

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.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schlichenmaier, M

Recently, Lax operator algebras appeared as a new class of higher genus current-type algebras. Introduced by Krichever and Sheinman, they were based on Krichever's theory of Lax operators on algebraic curves. These algebras are almost-graded Lie algebras of currents on Riemann surfaces with marked points (in-points, out-points and Tyurin points). In a previous joint article with Sheinman, the author classified the local cocycles and associated almost-graded central extensions in the case of one in-point and one out-point. It was shown that the almost-graded extension is essentially unique. In this article the general case of Lax operator algebras corresponding to several in- andmore » out-points is considered. As a first step they are shown to be almost-graded. The grading is given by splitting the marked points which are non-Tyurin points into in- and out-points. Next, classification results both for local and bounded cocycles are proved. The uniqueness theorem for almost-graded central extensions follows. To obtain this generalization additional techniques are needed which are presented in this article. Bibliography: 30 titles.« less

Generalized algebraic scene-based nonuniformity correction algorithm.

PubMed

Ratliff, Bradley M; Hayat, Majeed M; Tyo, J Scott

2005-02-01

A generalization of a recently developed algebraic scene-based nonuniformity correction algorithm for focal plane array (FPA) sensors is presented. The new technique uses pairs of image frames exhibiting arbitrary one- or two-dimensional translational motion to compute compensator quantities that are then used to remove nonuniformity in the bias of the FPA response. Unlike its predecessor, the generalization does not require the use of either a blackbody calibration target or a shutter. The algorithm has a low computational overhead, lending itself to real-time hardware implementation. The high-quality correction ability of this technique is demonstrated through application to real IR data from both cooled and uncooled infrared FPAs. A theoretical and experimental error analysis is performed to study the accuracy of the bias compensator estimates in the presence of two main sources of error.

Fast and accurate computation of system matrix for area integral model-based algebraic reconstruction technique

NASA Astrophysics Data System (ADS)

Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua

2014-11-01

Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Tongsong, E-mail: jiangtongsong@sina.com; Department of Mathematics, Heze University, Heze, Shandong 274015; Jiang, Ziwu

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

A compressed sensing based approach on Discrete Algebraic Reconstruction Technique.

PubMed

Demircan-Tureyen, Ezgi; Kamasak, Mustafa E

2015-01-01

Discrete tomography (DT) techniques are capable of computing better results, even using less number of projections than the continuous tomography techniques. Discrete Algebraic Reconstruction Technique (DART) is an iterative reconstruction method proposed to achieve this goal by exploiting a prior knowledge on the gray levels and assuming that the scanned object is composed from a few different densities. In this paper, DART method is combined with an initial total variation minimization (TvMin) phase to ensure a better initial guess and extended with a segmentation procedure in which the threshold values are estimated from a finite set of candidates to minimize both the projection error and the total variation (TV) simultaneously. The accuracy and the robustness of the algorithm is compared with the original DART by the simulation experiments which are done under (1) limited number of projections, (2) limited view problem and (3) noisy projections conditions.

A Simple Algebraic Grid Adaptation Scheme with Applications to Two- and Three-dimensional Flow Problems

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.; Lytle, John K.

1989-01-01

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.

Two-step tomographic reconstructions of temperature and species concentration in a flame based on laser absorption measurements with a rotation platform

NASA Astrophysics Data System (ADS)

Xia, Huihui; Kan, Ruifeng; Xu, Zhenyu; He, Yabai; Liu, Jianguo; Chen, Bing; Yang, Chenguang; Yao, Lu; Wei, Min; Zhang, Guangle

2017-03-01

We present a system for accurate tomographic reconstruction of the combustion temperature and H2O vapor concentration of a flame based on laser absorption measurements, in combination with an innovative two-step algebraic reconstruction technique. A total of 11 collimated laser beams generated from outputs of fiber-coupled diode lasers formed a two-dimensional 5 × 6 orthogonal beam grids and measured at two H2O absorption transitions (7154.354/7154.353 cm-1 and 7467.769 cm-1). The measurement system was designed on a rotation platform to achieve a two-folder improvement in spatial resolution. Numerical simulation showed that the proposed two-step algebraic reconstruction technique for temperature and concentration, respectively, greatly improved the reconstruction accuracy of species concentration when compared with a traditional calculation. Experimental results demonstrated the good performances of the measurement system and the two-step reconstruction technique for applications such as flame monitoring and combustion diagnosis.

Linking Computer Algebra Systems and Paper-and-Pencil Techniques To Support the Teaching of Mathematics.

ERIC Educational Resources Information Center

van Herwaarden, Onno A.; Gielen, Joseph L. W.

2002-01-01

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Assessing non-uniqueness: An algebraic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Chiropractic biophysics technique: a linear algebra approach to posture in chiropractic.

PubMed

Harrison, D D; Janik, T J; Harrison, G R; Troyanovich, S; Harrison, D E; Harrison, S O

1996-10-01

This paper discusses linear algebra as applied to human posture in chiropractic, specifically chiropractic biophysics technique (CBP). Rotations, reflections and translations are geometric functions studied in vector spaces in linear algebra. These mathematical functions are termed rigid body transformations and are applied to segmental spinal movement in the literature. Review of the literature indicates that these linear algebra concepts have been used to describe vertebral motion. However, these rigid body movers are presented here as applying to the global postural movements of the head, thoracic cage and pelvis. The unique inverse functions of rotations, reflections and translations provide a theoretical basis for making postural corrections in neutral static resting posture. Chiropractic biophysics technique (CBP) uses these concepts in examination procedures, manual spinal manipulation, instrument assisted spinal manipulation, postural exercises, extension traction and clinical outcome measures.

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 1. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the student text for part one of a three-part SMSG algebra course for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations;…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 1, Teacher's Commentary. Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part one of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables;…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, subtraction and division…

Practicing Algebraic Skills: A Conceptual Approach

ERIC Educational Resources Information Center

Friedlander, Alex; Arcavi, Abraham

2012-01-01

Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…

Measuring the Readability of Elementary Algebra Using the Cloze Technique.

ERIC Educational Resources Information Center

Kulm, Gerald

The relationship to readability of ten variables characterizing structural properties of mathematical prose was investigated in elementary algebra textbooks. Readability was measured by algebra student's responses to two forms of cloze tests. Linear and currilinear correlations were calculated between each structural variable and the cloze test.…

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; 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 derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

The Co-Emergence of Machine Techniques, Paper-and-Pencil Techniques, and Theoretical Reflection: A Study of CAS Use in Secondary School Algebra

ERIC Educational Resources Information Center

Kieran, Carolyn; Drijvers, Paul

2006-01-01

This paper addresses the dialectical relation between theoretical thinking and technique, as they co-emerge in a combined computer algebra (CAS) and paper-and-pencil environment. The theoretical framework in this ongoing study consists of the instrumental approach to tool use and an adaptation of Chevallard's anthropological theory. The main aim…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 2, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real…

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.

A Novel Image Encryption Based on Algebraic S-box and Arnold Transform

NASA Astrophysics Data System (ADS)

Farwa, Shabieh; Muhammad, Nazeer; Shah, Tariq; Ahmad, Sohail

2017-09-01

Recent study shows that substitution box (S-box) only cannot be reliably used in image encryption techniques. We, in this paper, propose a novel and secure image encryption scheme that utilizes the combined effect of an algebraic substitution box along with the scrambling effect of the Arnold transform. The underlying algorithm involves the application of S-box, which is the most imperative source to create confusion and diffusion in the data. The speciality of the proposed algorithm lies, firstly, in the high sensitivity of our S-box to the choice of the initial conditions which makes this S-box stronger than the chaos-based S-boxes as it saves computational labour by deploying a comparatively simple and direct approach based on the algebraic structure of the multiplicative cyclic group of the Galois field. Secondly the proposed method becomes more secure by considering a combination of S-box with certain number of iterations of the Arnold transform. The strength of the S-box is examined in terms of various performance indices such as nonlinearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. We prove through the most significant techniques used for the statistical analyses of the encrypted image that our image encryption algorithm satisfies all the necessary criteria to be usefully and reliably implemented in image encryption applications.

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.

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…

The structure and Gel'fand patterns inherent in the Heisenberg supergenerator algebra of dual Liouville-space ||kq{K-tilde.}(k1 - kn)[lambda- tilde],scriptn>> tensors and the Cayley algebra of scalar invariants over a (k1 - kn) field

NASA Astrophysics Data System (ADS)

Temme, F. P.

1991-06-01

For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the Sn-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl-kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the Sn partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel'fand pattern algebra of SU(2) and SU(2)×Sn tensor bases over Liouville space is presented together with both the related s-boson algebras and a description of the associated {||2k 0>>} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×Sn induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.

Diagnosing students' misconceptions in algebra: results from an experimental pilot study.

PubMed

Russell, Michael; O'Dwyer, Laura M; Miranda, Helena

2009-05-01

Computer-based diagnostic assessment systems hold potential to help teachers identify sources of poor performance and to connect teachers and students to learning activities designed to help advance students' conceptual understandings. The present article presents findings from a study that examined how students' performance in algebra and their overcoming of common algebraic misconceptions were affected by the use of a diagnostic assessment system that focused on important algebra concepts. This study used a four-group randomized cluster trial design in which teachers were assigned randomly to one of four groups: a "business as usual" control group, a partial intervention group that was provided with access to diagnostic tests results, a partial intervention group that was provided with access to the learning activities, and a full intervention group that was given access to the test results and learning activities. Data were collected from 905 students (6th-12th grade) nested within 44 teachers. We used hierarchical linear modeling techniques to compare the effects of full, partial, and no (control) intervention on students' algebraic ability and misconceptions. The analyses indicate that full intervention had a net positive effect on ability and misconception measures.

Integrand-level reduction of loop amplitudes by computational algebraic geometry methods

NASA Astrophysics Data System (ADS)

Zhang, Yang

2012-09-01

We present an algorithm for the integrand-level reduction of multi-loop amplitudes of renormalizable field theories, based on computational algebraic geometry. This algorithm uses (1) the Gröbner basis method to determine the basis for integrand-level reduction, (2) the primary decomposition of an ideal to classify all inequivalent solutions of unitarity cuts. The resulting basis and cut solutions can be used to reconstruct the integrand from unitarity cuts, via polynomial fitting techniques. The basis determination part of the algorithm has been implemented in the Mathematica package, BasisDet. The primary decomposition part can be readily carried out by algebraic geometry softwares, with the output of the package BasisDet. The algorithm works in both D = 4 and D = 4 - 2 ɛ dimensions, and we present some two and three-loop examples of applications of this algorithm.

A simple method for constructing the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n))

NASA Astrophysics Data System (ADS)

Shariati, A.; Aghamohammadi, A.

1995-12-01

We propose a simple and concise method to construct the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n)). Our technique is based on embedding an n-dimensional quantum space in an n+1-dimensional one as the set xn+1=1. This is possible only if one considers the multiparametric quantum space whose parameters are fixed in a specific way. The quantum group IGLq(n) is then the subset of GLq(n+1), which leaves the xn+1=1 subset invariant. For the deformed universal enveloping algebra Uq(igl(n)), we will show that it can also be embedded in Uq(gl(n+1)), provided one uses the multiparametric deformation of U(gl(n+1)) with a specific choice of its parameters.

Reducing "Math Anxiety" in College Algebra Courses Including Comparisons with Elementary Statistics Courses.

ERIC Educational Resources Information Center

Bankhead, Mike

The high levels of anxiety, apprehension, and apathy of students in college algebra courses caused the instructor to create and test a variety of math teaching techniques designed to boost student confidence and enthusiasm in the subject. Overall, this proposal covers several different techniques, which have been evaluated by both students and the…

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.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Simulations of Coherent Synchrotron Radiation Effects in Electron Machines

NASA Astrophysics Data System (ADS)

Migliorati, M.; Schiavi, A.; Dattoli, G.

2007-09-01

Coherent synchrotron radiation (CSR) generated by high intensity electron beams can be a source of undesirable effects limiting the performance of storage rings. The complexity of the physical mechanisms underlying the interplay between the electron beam and the CSR demands for reliable simulation codes. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problems in accelerators. The extension of these methods to the non linear case is ideally suited to treat wakefields - beam interaction. In this paper we report on the development of a numerical code, based on the solution of the Vlasov equation, which includes the non linear contribution due to wakefields. The proposed solution method exploits an algebraic technique that uses the exponential operators. We show that, in the case of CSR wakefields, the integration procedure is capable of reproducing the onset of an instability which leads to microbunching of the beam thus increasing the CSR at short wavelengths. In addition, considerations on the threshold of the instability for Gaussian bunches is also reported.

Simulations of Coherent Synchrotron Radiation Effects in Electron Machines

NASA Astrophysics Data System (ADS)

Migliorati, M.; Schiavi, A.; Dattoli, G.

Coherent synchrotron radiation (CSR) generated by high intensity electron beams can be a source of undesirable effects limiting the performance of storage rings. The complexity of the physical mechanisms underlying the interplay between the electron beam and the CSR demands for reliable simulation codes. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problems in accelerators. The extension of these methods to the non linear case is ideally suited to treat wakefields - beam interaction. In this paper we report on the development of a numerical code, based on the solution of the Vlasov equation, which includes the non linear contribution due to wakefields. The proposed solution method exploits an algebraic technique that uses the exponential operators. We show that, in the case of CSR wakefields, the integration procedure is capable of reproducing the onset of an instability which leads to microbunching of the beam thus increasing the CSR at short wavelengths. In addition, considerations on the threshold of the instability for Gaussian bunches is also reported.

Effect of a Cooperative Learning Technique on the Academic Performance of High School Students in Mathematics

ERIC Educational Resources Information Center

Idowu, Olumuyiwa Ayodeji

2013-01-01

Over the past 2 years, almost 45% of the students attending a local suburban high school failed Algebra 2. The purpose of this study was to compare the impact of a cooperative instructional technique (student teams-achievement divisions [STAD]) to traditional instructional methods on performance in high school algebra. Motivational and cognitive…

Performance improvements in temperature reconstructions of 2-D tunable diode laser absorption spectroscopy (TDLAS)

NASA Astrophysics Data System (ADS)

Choi, Doo-Won; Jeon, Min-Gyu; Cho, Gyeong-Rae; Kamimoto, Takahiro; Deguchi, Yoshihiro; Doh, Deog-Hee

2016-02-01

Performance improvement was attained in data reconstructions of 2-dimensional tunable diode laser absorption spectroscopy (TDLAS). Multiplicative Algebraic Reconstruction Technique (MART) algorithm was adopted for data reconstruction. The data obtained in an experiment for the measurement of temperature and concentration fields of gas flows were used. The measurement theory is based upon the Beer-Lambert law, and the measurement system consists of a tunable laser, collimators, detectors, and an analyzer. Methane was used as a fuel for combustion with air in the Bunsen-type burner. The data used for the reconstruction are from the optical signals of 8-laser beams passed on a cross-section of the methane flame. The performances of MART algorithm in data reconstruction were validated and compared with those obtained by Algebraic Reconstruction Technique (ART) algorithm.

Particle-like structure of coaxial Lie algebras

NASA Astrophysics Data System (ADS)

Vinogradov, A. M.

2018-01-01

This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.

ADART: an adaptive algebraic reconstruction algorithm for discrete tomography.

PubMed

Maestre-Deusto, F Javier; Scavello, Giovanni; Pizarro, Joaquín; Galindo, Pedro L

2011-08-01

In this paper we suggest an algorithm based on the Discrete Algebraic Reconstruction Technique (DART) which is capable of computing high quality reconstructions from substantially fewer projections than required for conventional continuous tomography. Adaptive DART (ADART) goes a step further than DART on the reduction of the number of unknowns of the associated linear system achieving a significant reduction in the pixel error rate of reconstructed objects. The proposed methodology automatically adapts the border definition criterion at each iteration, resulting in a reduction of the number of pixels belonging to the border, and consequently of the number of unknowns in the general algebraic reconstruction linear system to be solved, being this reduction specially important at the final stage of the iterative process. Experimental results show that reconstruction errors are considerably reduced using ADART when compared to original DART, both in clean and noisy environments.

Remote Symbolic Computation of Loci

ERIC Educational Resources Information Center

Abanades, Miguel A.; Escribano, Jesus; Botana, Francisco

2010-01-01

This article presents a web-based tool designed to compute certified equations and graphs of geometric loci specified using standard Dynamic Geometry Systems (DGS). Complementing the graphing abilities of the considered DGS, the equations of the loci produced by the application are remotely computed using symbolic algebraic techniques from the…

ADAM: analysis of discrete models of biological systems using computer algebra.

PubMed

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

A spatial operator algebra for manipulator modeling and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

1991-01-01

A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

Learning to Apply Algebra in the Community for Adults With Intellectual Developmental Disabilities.

PubMed

Rodriguez, Anthony M

2016-02-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This study explores the feasibility of algebra instruction for adults with IDD through an experimental curriculum. Ten individuals with IDD participated in a 6-week course framing mathematics concepts within the context of everyday challenges in handling money. The article explores classroom techniques, discusses student strategies, and proposes possible avenues for future research analyzing mathematics instructional design strategies for individuals with IDD.

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

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…

Undergraduate Mathematics Students' Pronumeral Misconceptions

ERIC Educational Resources Information Center

Bardini, Caroline; Vincent, Jill; Pierce, Robyn; King, Deborah

2014-01-01

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students with high tertiary entrance ranks enrolled in first semester university mathematics were found to have misconceptions relating to…

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.

Teaching Students to Formulate Questions

ERIC Educational Resources Information Center

Jensen-Vallin, Jacqueline

2017-01-01

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

Sixth SIAM conference on applied linear algebra: Final program and abstracts. Final technical report

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1997-12-31

Linear algebra plays a central role in mathematics and applications. The analysis and solution of problems from an amazingly wide variety of disciplines depend on the theory and computational techniques of linear algebra. In turn, the diversity of disciplines depending on linear algebra also serves to focus and shape its development. Some problems have special properties (numerical, structural) that can be exploited. Some are simply so large that conventional approaches are impractical. New computer architectures motivate new algorithms, and fresh ways to look at old ones. The pervasive nature of linear algebra in analyzing and solving problems means that peoplemore » from a wide spectrum--universities, industrial and government laboratories, financial institutions, and many others--share an interest in current developments in linear algebra. This conference aims to bring them together for their mutual benefit. Abstracts of papers presented are included.« less

The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jafarov, E. I.; Van der Jeugt, J.

2013-10-15

We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg–Weyl superalgebra or “the algebra of supersymmetric quantum mechanics,” and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter γ. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C{sub n} with parameter γ{sup 2}. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillatormore » model.« less

Heterogeneous Software System Interoperability Through Computer-Aided Resolution of Modeling Differences

DTIC Science & Technology

2002-06-01

techniques for addressing the software component retrieval problem. Steigerwald [Ste91] introduced the use of algebraic specifications for defining the...provided in terms of a specification written using Luqi’s Prototype Specification Description Language (PSDL) [LBY88] augmented with an algebraic

Zombie states for description of structure and dynamics of multi-electron systems

NASA Astrophysics Data System (ADS)

Shalashilin, Dmitrii V.

2018-05-01

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr

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 upmore » 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.« less

An object-oriented simulator for 3D digital breast tomosynthesis imaging system.

PubMed

Seyyedi, Saeed; Cengiz, Kubra; Kamasak, Mustafa; Yildirim, Isa

2013-01-01

Digital breast tomosynthesis (DBT) is an innovative imaging modality that provides 3D reconstructed images of breast to detect the breast cancer. Projections obtained with an X-ray source moving in a limited angle interval are used to reconstruct 3D image of breast. Several reconstruction algorithms are available for DBT imaging. Filtered back projection algorithm has traditionally been used to reconstruct images from projections. Iterative reconstruction algorithms such as algebraic reconstruction technique (ART) were later developed. Recently, compressed sensing based methods have been proposed in tomosynthesis imaging problem. We have developed an object-oriented simulator for 3D digital breast tomosynthesis (DBT) imaging system using C++ programming language. The simulator is capable of implementing different iterative and compressed sensing based reconstruction methods on 3D digital tomosynthesis data sets and phantom models. A user friendly graphical user interface (GUI) helps users to select and run the desired methods on the designed phantom models or real data sets. The simulator has been tested on a phantom study that simulates breast tomosynthesis imaging problem. Results obtained with various methods including algebraic reconstruction technique (ART) and total variation regularized reconstruction techniques (ART+TV) are presented. Reconstruction results of the methods are compared both visually and quantitatively by evaluating performances of the methods using mean structural similarity (MSSIM) values.

An Object-Oriented Simulator for 3D Digital Breast Tomosynthesis Imaging System

PubMed Central

Cengiz, Kubra

2013-01-01

Digital breast tomosynthesis (DBT) is an innovative imaging modality that provides 3D reconstructed images of breast to detect the breast cancer. Projections obtained with an X-ray source moving in a limited angle interval are used to reconstruct 3D image of breast. Several reconstruction algorithms are available for DBT imaging. Filtered back projection algorithm has traditionally been used to reconstruct images from projections. Iterative reconstruction algorithms such as algebraic reconstruction technique (ART) were later developed. Recently, compressed sensing based methods have been proposed in tomosynthesis imaging problem. We have developed an object-oriented simulator for 3D digital breast tomosynthesis (DBT) imaging system using C++ programming language. The simulator is capable of implementing different iterative and compressed sensing based reconstruction methods on 3D digital tomosynthesis data sets and phantom models. A user friendly graphical user interface (GUI) helps users to select and run the desired methods on the designed phantom models or real data sets. The simulator has been tested on a phantom study that simulates breast tomosynthesis imaging problem. Results obtained with various methods including algebraic reconstruction technique (ART) and total variation regularized reconstruction techniques (ART+TV) are presented. Reconstruction results of the methods are compared both visually and quantitatively by evaluating performances of the methods using mean structural similarity (MSSIM) values. PMID:24371468

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.

Constructing Meanings and Utilities within Algebraic Tasks

ERIC Educational Resources Information Center

Ainley, Janet; Bills, Liz; Wilson, Kirsty

2004-01-01

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

Teaching Algebraic Equations to Middle School Students with Intellectual Disabilities

ERIC Educational Resources Information Center

Baker, Joshua N.; Rivera, Christopher J.; Morgan, Joseph John; Reese, Noelle

2015-01-01

The purpose of this study was to replicate similar instructional techniques of Jimenez, Browder, and Courtade (2008) using a single-subject multiple-probe across participants design to investigate the effects of task analytic instruction coupled with semi-concrete representations to teach linear algebraic equations to middle school students with…

Generalized Heisenberg algebra and (non linear) pseudo-bosons

NASA Astrophysics Data System (ADS)

Bagarello, F.; Curado, E. M. F.; Gazeau, J. P.

2018-04-01

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given physical system. We also discuss relations with nonlinear pseudo-bosons. Several examples are discussed.

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;…

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Computing Gröbner Bases within Linear Algebra

NASA Astrophysics Data System (ADS)

Suzuki, Akira

In this paper, we present an alternative algorithm to compute Gröbner bases, which is based on computations on sparse linear algebra. Both of S-polynomial computations and monomial reductions are computed in linear algebra simultaneously in this algorithm. So it can be implemented to any computational system which can handle linear algebra. For a given ideal in a polynomial ring, it calculates a Gröbner basis along with the corresponding term order appropriately.

Triangles with Integer Side Lengths and Rational Internal Radius P and External Radius R

ERIC Educational Resources Information Center

Zelator, Konstantine

2005-01-01

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

PubMed Central

2011-01-01

Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics. PMID:21774817

Research issues of geometry-based visual languages and some solutions

NASA Astrophysics Data System (ADS)

Green, Thorn G.

This dissertation addresses the problem of how to design visual language systems that are based upon Geometric Algebra, and provide a visual coupling of algebraic expressions and geometric depictions. This coupling of algebraic expressions and geometric depictions provides a new means for expressing both mathematical and geometric relationships present in mathematics, physics, and Computer-Aided Geometric Design (CAGD). Another significant feature of such a system is that the result of changing a parameter (by dragging the mouse) can be seen immediately in the depiction(s) of all expressions that use that parameter. This greatly aides the cognition of the relationships between variables. Systems for representing such a coupling of algebra and geometry have characteristics of both visual language systems, and systems for scientific visualization. Instead of using a parsing or dataflow paradigm for the visual language representation, the systems instead represent equations as manipulatible constrained diagrams for their visualization. This requires that the design of such a system have (but is not limited to) a means for parsing equations entered by the user, a scheme for producing a visual representation of these equations; techniques for maintaining the coupling between the expressions entered and the diagrams displayed; algorithms for maintaining the consistency of the diagrams; and, indexing capabilities that are efficient enough to allow diagrams to be created, and manipulated in a short enough period of time. The author proposes solutions for how such a design can be realized.

Mastering algebra retrains the visual system to perceive hierarchical structure in equations.

PubMed

Marghetis, Tyler; Landy, David; Goldstone, Robert L

2016-01-01

Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

Generalized Quantum Field Theory Based on a Nonlinear Deformed Heisenberg Algebra

NASA Astrophysics Data System (ADS)

Ribeiro-Silva, C. I.; Oliveira-Neto, N. M.

We consider a quantum field theory based on a nonlinear Heisenberg algebra which describes phenomenologically a composite particle. Perturbative computation, considering the λϕ4 interaction was done and we also performed some comparison with a quantum field theory based on the q-oscillator algebra.

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…

A spatial operator algebra for manipulator modeling and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, Kenneth; Jain, Abhinandan

1989-01-01

A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

Teaching materials of algebraic equation

NASA Astrophysics Data System (ADS)

Widodo, S. A.; Prahmana, R. C. I.; Purnami, A. S.; Turmudi

2017-12-01

The purpose of this paper is to know the effectiveness of teaching materials algebraic equation. This type of research used experimental method. The population in this study is all students of mathematics education who take numerical method in sarjanawiyata tamansiswa of university; the sample is taken using cluster random sampling. Instrument used in this research is test and questionnaire. The test is used to know the problem solving ability and achievement, while the questionnaire is used to know the student's response on the teaching materials. Data Analysis technique of quantitative used Wilcoxon test, while the qualitative data used grounded theory. Based on the results of the test can be concluded that the development of teaching materials can improve the ability to solve problems and achievement.

A novel encryption scheme for high-contrast image data in the Fresnelet domain

PubMed Central

Bibi, Nargis; Farwa, Shabieh; Jahngir, Adnan; Usman, Muhammad

2018-01-01

In this paper, a unique and more distinctive encryption algorithm is proposed. This is based on the complexity of highly nonlinear S box in Flesnelet domain. The nonlinear pattern is transformed further to enhance the confusion in the dummy data using Fresnelet technique. The security level of the encrypted image boosts using the algebra of Galois field in Fresnelet domain. At first level, the Fresnelet transform is used to propagate the given information with desired wavelength at specified distance. It decomposes given secret data into four complex subbands. These complex sub-bands are separated into two components of real subband data and imaginary subband data. At second level, the net subband data, produced at the first level, is deteriorated to non-linear diffused pattern using the unique S-box defined on the Galois field F28. In the diffusion process, the permuted image is substituted via dynamic algebraic S-box substitution. We prove through various analysis techniques that the proposed scheme enhances the cipher security level, extensively. PMID:29608609

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Identification of control targets in Boolean molecular network models via computational algebra.

PubMed

Murrugarra, David; Veliz-Cuba, Alan; Aguilar, Boris; Laubenbacher, Reinhard

2016-09-23

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

Sensitivity calculations for iteratively solved problems

NASA Technical Reports Server (NTRS)

Haftka, R. T.

1985-01-01

The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by-element preconditioned conjugate gradient iterative solution technique applied to truss examples.

Category-theoretic models of algebraic computer systems

NASA Astrophysics Data System (ADS)

Kovalyov, S. P.

2016-01-01

A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.

Construction of Ligand Group Orbitals for Polyatomics and Transition-Metal Complexes Using an Intuitive Symmetry-Based Approach

ERIC Educational Resources Information Center

Johnson, Adam R.

2013-01-01

A molecular orbital (MO) diagram, especially its frontier orbitals, explains the bonding and reactivity for a chemical compound. It is therefore important for students to learn how to construct one. The traditional methods used to derive these diagrams rely on linear algebra techniques to combine ligand orbitals into symmetry-adapted linear…

Study of coherent synchrotron radiation effects by means of a new simulation code based on the non-linear extension of the operator splitting method

NASA Astrophysics Data System (ADS)

Dattoli, G.; Migliorati, M.; Schiavi, A.

2007-05-01

The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high-intensity electron accelerators. The complexity of the physical mechanisms underlying the onset of instabilities due to CSR demands for accurate descriptions, capable of including the large number of features of an actual accelerating device. A code devoted to the analysis of these types of problems should be fast and reliable, conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problems in accelerators. The extension of these methods to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique that uses the exponential operators. We show that the integration procedure is capable of reproducing the onset of instability and the effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, considerations on the threshold of the instability are also developed.

Incomplete projection reconstruction of computed tomography based on the modified discrete algebraic reconstruction technique

NASA Astrophysics Data System (ADS)

Yang, Fuqiang; Zhang, Dinghua; Huang, Kuidong; Gao, Zongzhao; Yang, YaFei

2018-02-01

Based on the discrete algebraic reconstruction technique (DART), this study aims to address and test a new improved algorithm applied to incomplete projection data to generate a high quality reconstruction image by reducing the artifacts and noise in computed tomography. For the incomplete projections, an augmented Lagrangian based on compressed sensing is first used in the initial reconstruction for segmentation of the DART to get higher contrast graphics for boundary and non-boundary pixels. Then, the block matching 3D filtering operator was used to suppress the noise and to improve the gray distribution of the reconstructed image. Finally, simulation studies on the polychromatic spectrum were performed to test the performance of the new algorithm. Study results show a significant improvement in the signal-to-noise ratios (SNRs) and average gradients (AGs) of the images reconstructed from incomplete data. The SNRs and AGs of the new images reconstructed by DART-ALBM were on average 30%-40% and 10% higher than the images reconstructed by DART algorithms. Since the improved DART-ALBM algorithm has a better robustness to limited-view reconstruction, which not only makes the edge of the image clear but also makes the gray distribution of non-boundary pixels better, it has the potential to improve image quality from incomplete projections or sparse projections.

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.

Z2×Z2 generalizations of 𝒩 =2 super Schrödinger algebras and their representations

NASA Astrophysics Data System (ADS)

Aizawa, N.; Segar, J.

2017-11-01

We generalize the real and chiral N =2 super Schrödinger algebras to Z2×Z2-graded Lie superalgebras. This is done by D-module presentation, and as a consequence, the D-module presentations of Z2×Z2-graded superalgebras are identical to the ones of super Schrödinger algebras. We then generalize the calculus over the Grassmann number to Z2×Z2 setting. Using it and the standard technique of Lie theory, we obtain a vector field realization of Z2×Z2-graded superalgebras. A vector field realization of the Z2×Z2 generalization of N =1 super Schrödinger algebra is also presented.

Lamb-Wave-Based Tomographic Imaging Techniques for Hole-Edge Corrosion Monitoring in Plate Structures

PubMed Central

Wang, Dengjiang; Zhang, Weifang; Wang, Xiangyu; Sun, Bo

2016-01-01

This study presents a novel monitoring method for hole-edge corrosion damage in plate structures based on Lamb wave tomographic imaging techniques. An experimental procedure with a cross-hole layout using 16 piezoelectric transducers (PZTs) was designed. The A0 mode of the Lamb wave was selected, which is sensitive to thickness-loss damage. The iterative algebraic reconstruction technique (ART) method was used to locate and quantify the corrosion damage at the edge of the hole. Hydrofluoric acid with a concentration of 20% was used to corrode the specimen artificially. To estimate the effectiveness of the proposed method, the real corrosion damage was compared with the predicted corrosion damage based on the tomographic method. The results show that the Lamb-wave-based tomographic method can be used to monitor the hole-edge corrosion damage accurately. PMID:28774041

Sign Lines, Asymptotes, and Tangent Carriers--An Introduction to Curve Sketching.

ERIC Educational Resources Information Center

Spikell, Mark A.; Deane, William R.

This paper discusses methods of sketching various types of algebraic functions from an analysis of the portions of the plane where the curve will be found and where it will not be found. The discussion is limited to rational functions. Methods and techniques presented are applicable to the secondary mathematics curriculum from algebra through…

Solution of Algebraic Equations in the Analysis, Design, and Optimization of Continuous Ultrafiltration

ERIC Educational Resources Information Center

Foley, Greg

2011-01-01

Continuous feed and bleed ultrafiltration, modeled with the gel polarization model for the limiting flux, is shown to provide a rich source of non-linear algebraic equations that can be readily solved using numerical and graphical techniques familiar to undergraduate students. We present a variety of numerical problems in the design, analysis, and…

A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy (II)

ERIC Educational Resources Information Center

Bradford, Russell; Davenport, James H.; Sangwin, Chris

2010-01-01

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

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…

A fast multi-resolution approach to tomographic PIV

NASA Astrophysics Data System (ADS)

Discetti, Stefano; Astarita, Tommaso

2012-03-01

Tomographic particle image velocimetry (Tomo-PIV) is a recently developed three-component, three-dimensional anemometric non-intrusive measurement technique, based on an optical tomographic reconstruction applied to simultaneously recorded images of the distribution of light intensity scattered by seeding particles immersed into the flow. Nowadays, the reconstruction process is carried out mainly by iterative algebraic reconstruction techniques, well suited to handle the problem of limited number of views, but computationally intensive and memory demanding. The adoption of the multiplicative algebraic reconstruction technique (MART) has become more and more accepted. In the present work, a novel multi-resolution approach is proposed, relying on the adoption of a coarser grid in the first step of the reconstruction to obtain a fast estimation of a reliable and accurate first guess. A performance assessment, carried out on three-dimensional computer-generated distributions of particles, shows a substantial acceleration of the reconstruction process for all the tested seeding densities with respect to the standard method based on 5 MART iterations; a relevant reduction in the memory storage is also achieved. Furthermore, a slight accuracy improvement is noticed. A modified version, improved by a multiplicative line of sight estimation of the first guess on the compressed configuration, is also tested, exhibiting a further remarkable decrease in both memory storage and computational effort, mostly at the lowest tested seeding densities, while retaining the same performances in terms of accuracy.

Accelerating simultaneous algebraic reconstruction technique with motion compensation using CUDA-enabled GPU.

PubMed

Pang, Wai-Man; Qin, Jing; Lu, Yuqiang; Xie, Yongming; Chui, Chee-Kong; Heng, Pheng-Ann

2011-03-01

To accelerate the simultaneous algebraic reconstruction technique (SART) with motion compensation for speedy and quality computed tomography reconstruction by exploiting CUDA-enabled GPU. Two core techniques are proposed to fit SART into the CUDA architecture: (1) a ray-driven projection along with hardware trilinear interpolation, and (2) a voxel-driven back-projection that can avoid redundant computation by combining CUDA shared memory. We utilize the independence of each ray and voxel on both techniques to design CUDA kernel to represent a ray in the projection and a voxel in the back-projection respectively. Thus, significant parallelization and performance boost can be achieved. For motion compensation, we rectify each ray's direction during the projection and back-projection stages based on a known motion vector field. Extensive experiments demonstrate the proposed techniques can provide faster reconstruction without compromising image quality. The process rate is nearly 100 projections s (-1), and it is about 150 times faster than a CPU-based SART. The reconstructed image is compared against ground truth visually and quantitatively by peak signal-to-noise ratio (PSNR) and line profiles. We further evaluate the reconstruction quality using quantitative metrics such as signal-to-noise ratio (SNR) and mean-square-error (MSE). All these reveal that satisfactory results are achieved. The effects of major parameters such as ray sampling interval and relaxation parameter are also investigated by a series of experiments. A simulated dataset is used for testing the effectiveness of our motion compensation technique. The results demonstrate our reconstructed volume can eliminate undesirable artifacts like blurring. Our proposed method has potential to realize instantaneous presentation of 3D CT volume to physicians once the projection data are acquired.

Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.

ERIC Educational Resources Information Center

Natour, Denise M.

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Teacher Actions to Facilitate Early Algebraic Reasoning

ERIC Educational Resources Information Center

Hunter, Jodie

2015-01-01

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

SEGMENTATION OF MITOCHONDRIA IN ELECTRON MICROSCOPY IMAGES USING ALGEBRAIC CURVES.

PubMed

Seyedhosseini, Mojtaba; Ellisman, Mark H; Tasdizen, Tolga

2013-01-01

High-resolution microscopy techniques have been used to generate large volumes of data with enough details for understanding the complex structure of the nervous system. However, automatic techniques are required to segment cells and intracellular structures in these multi-terabyte datasets and make anatomical analysis possible on a large scale. We propose a fully automated method that exploits both shape information and regional statistics to segment irregularly shaped intracellular structures such as mitochondria in electron microscopy (EM) images. The main idea is to use algebraic curves to extract shape features together with texture features from image patches. Then, these powerful features are used to learn a random forest classifier, which can predict mitochondria locations precisely. Finally, the algebraic curves together with regional information are used to segment the mitochondria at the predicted locations. We demonstrate that our method outperforms the state-of-the-art algorithms in segmentation of mitochondria in EM images.

Hurwitz Algebras and the Octonion Algebra

NASA Astrophysics Data System (ADS)

Burdik, Čestmir; Catto, Sultan

2018-02-01

We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.

Surface defects and chiral algebras

NASA Astrophysics Data System (ADS)

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng

2017-05-01

We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. In each case we find perfect agreement with the predicted characters.

A new art code for tomographic interferometry

NASA Technical Reports Server (NTRS)

Tan, H.; Modarress, D.

1987-01-01

A new algebraic reconstruction technique (ART) code based on the iterative refinement method of least squares solution for tomographic reconstruction is presented. Accuracy and the convergence of the technique is evaluated through the application of numerically generated interferometric data. It was found that, in general, the accuracy of the results was superior to other reported techniques. The iterative method unconditionally converged to a solution for which the residual was minimum. The effects of increased data were studied. The inversion error was found to be a function of the input data error only. The convergence rate, on the other hand, was affected by all three parameters. Finally, the technique was applied to experimental data, and the results are reported.

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…

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…

Designing Spreadsheet-Based Tasks for Purposeful Algebra

ERIC Educational Resources Information Center

Ainley, Janet; Bills, Liz; Wilson, Kirsty

2005-01-01

We describe the design of a sequence of spreadsheet-based pedagogic tasks for the introduction of algebra in the early years of secondary schooling within the Purposeful Algebraic Activity project. This design combines two relatively novel features to bring a different perspective to research in the use of spreadsheets for the learning and…

Optical systolic solutions of linear algebraic equations

NASA Technical Reports Server (NTRS)

Neuman, C. P.; Casasent, D.

1984-01-01

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

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…

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…

Reduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizations

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, R.

2018-03-01

A procedure for the construction of nonlinear realizations of Lie algebras in the context of Vessiot-Guldberg-Lie algebras of first-order systems of ordinary differential equations (ODEs) is proposed. The method is based on the reduction of invariants and projection of lowest-dimensional (irreducible) representations of Lie algebras. Applications to the description of parameterized first-order systems of ODEs related by contraction of Lie algebras are given. In particular, the kinematical Lie algebras in (2 + 1)- and (3 + 1)-dimensions are realized simultaneously as Vessiot-Guldberg-Lie algebras of parameterized nonlinear systems in R3 and R4, respectively.

A Method for Using Adjacency Matrices to Analyze the Connections Students Make within and between Concepts: The Case of Linear Algebra

ERIC Educational Resources Information Center

Selinski, Natalie E.; Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

2014-01-01

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…

An analysis of thermal response factors and how to reduce their computational time requirement

NASA Technical Reports Server (NTRS)

Wiese, M. R.

1982-01-01

Te RESFAC2 version of the Thermal Response Factor Program (RESFAC) is the result of numerous modifications and additions to the original RESFAC. These modifications and additions have significantly reduced the program's computational time requirement. As a result of this work, the program is more efficient and its code is both readable and understandable. This report describes what a thermal response factor is; analyzes the original matrix algebra calculations and root finding techniques; presents a new root finding technique and streamlined matrix algebra; supplies ten validation cases and their results.

Contiguity and Entire Separability of States on von Neumann Algebras

NASA Astrophysics Data System (ADS)

Haliullin, Samigulla

2017-12-01

We introduce the notions of the contiguity and entirely separability for two sequences of states on von Neumann algebras. The ultraproducts technique allows us to reduce the study of the contiguity to investigation of the equivalence for two states. Here we apply the Ocneanu ultraproduct and the Groh-Raynaud ultraproduct (see Ocneanu (1985), Groh (J. Operator Theory, 11, 2, 395-404 1984), Raynaud (J. Operator Theory, 48, 1, 41-68, 2002), Ando and Haagerup (J. Funct. Anal., 266, 12, 6842-6913, 2014)), as well as the technique developed in Mushtari and Haliullin (Lobachevskii J. Math., 35, 2, 138-146, 2014).

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

DOE PAGES

Günaydin, Murat; Lüst, Dieter; Malek, Emanuel

2016-11-07

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginarymore » octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s.« less

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Günaydin, Murat; Lüst, Dieter; Malek, Emanuel

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginarymore » octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s.« less

A Modeling-Based College Algebra Course and Its Effect on Student Achievement

ERIC Educational Resources Information Center

Ellington, Aimee J.

2005-01-01

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

Tomographic PIV: particles versus blobs

NASA Astrophysics Data System (ADS)

Champagnat, Frédéric; Cornic, Philippe; Cheminet, Adam; Leclaire, Benjamin; Le Besnerais, Guy; Plyer, Aurélien

2014-08-01

We present an alternative approach to tomographic particle image velocimetry (tomo-PIV) that seeks to recover nearly single voxel particles rather than blobs of extended size. The baseline of our approach is a particle-based representation of image data. An appropriate discretization of this representation yields an original linear forward model with a weight matrix built with specific samples of the system’s point spread function (PSF). Such an approach requires only a few voxels to explain the image appearance, therefore it favors much more sparsely reconstructed volumes than classic tomo-PIV. The proposed forward model is general and flexible and can be embedded in a classical multiplicative algebraic reconstruction technique (MART) or a simultaneous multiplicative algebraic reconstruction technique (SMART) inversion procedure. We show, using synthetic PIV images and by way of a large exploration of the generating conditions and a variety of performance metrics, that the model leads to better results than the classical tomo-PIV approach, in particular in the case of seeding densities greater than 0.06 particles per pixel and of PSFs characterized by a standard deviation larger than 0.8 pixels.

Matrix Algebra for GPU and Multicore Architectures (MAGMA) for Large Petascale Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dongarra, Jack J.; Tomov, Stanimire

2014-03-24

The goal of the MAGMA project is to create a new generation of linear algebra libraries that achieve the fastest possible time to an accurate solution on hybrid Multicore+GPU-based systems, using all the processing power that future high-end systems can make available within given energy constraints. Our efforts at the University of Tennessee achieved the goals set in all of the five areas identified in the proposal: 1. Communication optimal algorithms; 2. Autotuning for GPU and hybrid processors; 3. Scheduling and memory management techniques for heterogeneity and scale; 4. Fault tolerance and robustness for large scale systems; 5. Building energymore » efficiency into software foundations. The University of Tennessee’s main contributions, as proposed, were the research and software development of new algorithms for hybrid multi/many-core CPUs and GPUs, as related to two-sided factorizations and complete eigenproblem solvers, hybrid BLAS, and energy efficiency for dense, as well as sparse, operations. Furthermore, as proposed, we investigated and experimented with various techniques targeting the five main areas outlined.« less

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

PubMed Central

Kerfriden, P.; Goury, O.; Rabczuk, T.; Bordas, S.P.A.

2013-01-01

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. PMID:23750055

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Yifei; Zuo, Jian -Min

A diffraction-based technique is developed for the determination of three-dimensional nanostructures. The technique employs high-resolution and low-dose scanning electron nanodiffraction (SEND) to acquire three-dimensional diffraction patterns, with the help of a special sample holder for large-angle rotation. Grains are identified in three-dimensional space based on crystal orientation and on reconstructed dark-field images from the recorded diffraction patterns. Application to a nanocrystalline TiN thin film shows that the three-dimensional morphology of columnar TiN grains of tens of nanometres in diameter can be reconstructed using an algebraic iterative algorithm under specified prior conditions, together with their crystallographic orientations. The principles can bemore » extended to multiphase nanocrystalline materials as well. Furthermore, the tomographic SEND technique provides an effective and adaptive way of determining three-dimensional nanostructures.« less

Communication Avoiding and Overlapping for Numerical Linear Algebra

DTIC Science & Technology

2012-05-08

future exascale systems, communication cost must be avoided or overlapped. Communication-avoiding 2.5D algorithms improve scalability by reducing...linear algebra problems to future exascale systems, communication cost must be avoided or overlapped. Communication-avoiding 2.5D algorithms improve...will continue to grow relative to the cost of computation. With exascale computing as the long-term goal, the community needs to develop techniques

On the structure of quantum L∞ algebras

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Fuchs, Michael; Traube, Matthias

2017-10-01

It is believed that any classical gauge symmetry gives rise to an L∞ algebra. Based on the recently realized relation between classical W algebras and L∞ algebras, we analyze how this generalizes to the quantum case. Guided by the existence of quantum W algebras, we provide a physically well motivated definition of quantum L∞ algebras describing the consistency of global symmetries in quantum field theories. In this case we are restricted to only two non-trivial graded vector spaces X 0 and X -1 containing the symmetry variations and the symmetry generators. This quantum L∞ algebra structure is explicitly exemplified for the quantum W_3 algebra. The natural quantum product between fields is the normal ordered one so that, due to contractions between quantum fields, the higher L∞ relations receive off-diagonal quantum corrections. Curiously, these are not present in the loop L∞ algebra of closed string field theory.

Operator algebra as an application of logarithmic representation of infinitesimal generators

NASA Astrophysics Data System (ADS)

Iwata, Yoritaka

2018-02-01

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.

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…

Algebraic grid generation for coolant passages of turbine blades with serpentine channels and pin fins

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.

1991-01-01

In order to study numerically details of the flow and heat transfer within coolant passages of turbine blades, a method must first be developed to generate grid systems within the very complicated geometries involved. In this study, a grid generation package was developed that is capable of generating the required grid systems. The package developed is based on an algebraic grid generation technique that permits the user considerable control over how grid points are to be distributed in a very explicit way. These controls include orthogonality of grid lines next to boundary surfaces and ability to cluster about arbitrary points, lines, and surfaces. This paper describes that grid generation package and shows how it can be used to generate grid systems within complicated-shaped coolant passages via an example.

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Surface defects and chiral algebras

DOE PAGES

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng

2017-05-26

Here, we investigate superconformal surface defects in four-dimensional N = 2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfield-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. We find perfect agreement with the predicted characters, in eachmore » case.« less

Surface defects and chiral algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng

Here, we investigate superconformal surface defects in four-dimensional N = 2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfield-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. We find perfect agreement with the predicted characters, in eachmore » case.« less

Optimization techniques for integrating spatial data

USGS Publications Warehouse

Herzfeld, U.C.; Merriam, D.F.

1995-01-01

Two optimization techniques ta predict a spatial variable from any number of related spatial variables are presented. The applicability of the two different methods for petroleum-resource assessment is tested in a mature oil province of the Midcontinent (USA). The information on petroleum productivity, usually not directly accessible, is related indirectly to geological, geophysical, petrographical, and other observable data. This paper presents two approaches based on construction of a multivariate spatial model from the available data to determine a relationship for prediction. In the first approach, the variables are combined into a spatial model by an algebraic map-comparison/integration technique. Optimal weights for the map comparison function are determined by the Nelder-Mead downhill simplex algorithm in multidimensions. Geologic knowledge is necessary to provide a first guess of weights to start the automatization, because the solution is not unique. In the second approach, active set optimization for linear prediction of the target under positivity constraints is applied. Here, the procedure seems to select one variable from each data type (structure, isopachous, and petrophysical) eliminating data redundancy. Automating the determination of optimum combinations of different variables by applying optimization techniques is a valuable extension of the algebraic map-comparison/integration approach to analyzing spatial data. Because of the capability of handling multivariate data sets and partial retention of geographical information, the approaches can be useful in mineral-resource exploration. ?? 1995 International Association for Mathematical Geology.

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…

From No to Yes: The Impact of an Intervention on The Persistence of Algebraic Misconceptions among Secondary School Algebra Students

ERIC Educational Resources Information Center

Zielinski, Susan F.

2017-01-01

Many students enter high school with persistent algebraic misconceptions that limit their success in mathematics and, by extension, limit potential educational attainment and future earnings. The purpose of this study was to assess the effectiveness of a warm conceptual change based intervention on remediating algebraic misconceptions held by…

Human motion planning based on recursive dynamics and optimal control techniques

NASA Technical Reports Server (NTRS)

Lo, Janzen; Huang, Gang; Metaxas, Dimitris

2002-01-01

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

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 weight assignment can not be studied separately for the problem with operating cost constraint. Therefore a relaxed SDP method with golden section search is developed to solve both at the same time. The cluster decomposition is utilized to solve large scale networks.

A simplified formalism of the algebra of partially transposed permutation operators with applications

NASA Astrophysics Data System (ADS)

Mozrzymas, Marek; Studziński, Michał; Horodecki, Michał

2018-03-01

Herein we continue the study of the representation theory of the algebra of permutation operators acting on the n -fold tensor product space, partially transposed on the last subsystem. We develop the concept of partially reduced irreducible representations, which allows us to significantly simplify previously proved theorems and, most importantly, derive new results for irreducible representations of the mentioned algebra. In our analysis we are able to reduce the complexity of the central expressions by getting rid of sums over all permutations from the symmetric group, obtaining equations which are much more handy in practical applications. We also find relatively simple matrix representations for the generators of the underlying algebra. The obtained simplifications and developments are applied to derive the characteristics of a deterministic port-based teleportation scheme written purely in terms of irreducible representations of the studied algebra. We solve an eigenproblem for the generators of the algebra, which is the first step towards a hybrid port-based teleportation scheme and gives us new proofs of the asymptotic behaviour of teleportation fidelity. We also show a connection between the density operator characterising port-based teleportation and a particular matrix composed of an irreducible representation of the symmetric group, which encodes properties of the investigated algebra.

An Algebraic Approach to Guarantee Harmonic Balance Method Using Gröbner Base

NASA Astrophysics Data System (ADS)

Yagi, Masakazu; Hisakado, Takashi; Okumura, Kohshi

Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Gröbner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.

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…

Algebraic features of some generalizations of the Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Bibik, Yu. V.; Sarancha, D. A.

2010-10-01

For generalizations of the Lotka-Volterra system, an integration method is proposed based on the nontrivial algebraic structure of these generalizations. The method makes use of an auxiliary first-order differential equation derived from the phase curve equation with the help of this algebraic structure. Based on this equation, a Hamiltonian approach can be developed and canonical variables (moreover, action-angle variables) can be constructed.

3D algebraic iterative reconstruction for cone-beam x-ray differential phase-contrast computed tomography.

PubMed

Fu, Jian; Hu, Xinhua; Velroyen, Astrid; Bech, Martin; Jiang, Ming; Pfeiffer, Franz

2015-01-01

Due to the potential of compact imaging systems with magnified spatial resolution and contrast, cone-beam x-ray differential phase-contrast computed tomography (DPC-CT) has attracted significant interest. The current proposed FDK reconstruction algorithm with the Hilbert imaginary filter will induce severe cone-beam artifacts when the cone-beam angle becomes large. In this paper, we propose an algebraic iterative reconstruction (AIR) method for cone-beam DPC-CT and report its experiment results. This approach considers the reconstruction process as the optimization of a discrete representation of the object function to satisfy a system of equations that describes the cone-beam DPC-CT imaging modality. Unlike the conventional iterative algorithms for absorption-based CT, it involves the derivative operation to the forward projections of the reconstructed intermediate image to take into account the differential nature of the DPC projections. This method is based on the algebraic reconstruction technique, reconstructs the image ray by ray, and is expected to provide better derivative estimates in iterations. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a mini-focus x-ray tube source. It is shown that the proposed method can reduce the cone-beam artifacts and performs better than FDK under large cone-beam angles. This algorithm is of interest for future cone-beam DPC-CT applications.

Characterizing the Nature of Students' Feature Noticing-and-Using with Respect to Mathematical Symbols across Different Levels of Algebra Exposure

ERIC Educational Resources Information Center

Sullivan, Patrick

2013-01-01

The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

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…

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…

Structuring students’ analogical reasoning in solving algebra problem

NASA Astrophysics Data System (ADS)

Lailiyah, S.; Nusantara, T.; Sa'dijah, C.; Irawan, E. B.; Kusaeri; Asyhar, A. H.

2018-01-01

The average achievement of Indonesian students’ mathematics skills according to Benchmark International Trends in Mathematics and Science Study (TIMSS) is ranked at the 38th out of 42 countries and according to the survey result in Program for International Student Assessment (PISA) is ranked at the 64th out of 65 countries. The low mathematics skill of Indonesian student has become an important reason to research more deeply about reasoning and algebra in mathematics. Analogical reasoning is a very important component in mathematics because it is the key to creativity and it can make the learning process in the classroom become effective. The major part of the analogical reasoning is about structuring including the processes of inferencing and decision-making happens. Those processes involve base domain and target domain. Methodologically, the subjects of this research were 42 students from class XII. The sources of data were derived from the results of thinks aloud, the transcribed interviews, and the videos taken while the subject working on the instruments and interviews. The collected data were analyzed using qualitative techniques. The result of this study described the structuring characteristics of students’ analogical reasoning in solving algebra problems from all the research subjects.

Rank-based decompositions of morphological templates.

PubMed

Sussner, P; Ritter, G X

2000-01-01

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. We derive a heuristic algorithm for the decomposition of matrices having arbitrary rank.

A new operational approach for solving fractional variational problems depending on indefinite integrals

NASA Astrophysics Data System (ADS)

Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

2018-04-01

In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

On the Performance of an Algebraic MultigridSolver on Multicore Clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, A H; Schulz, M; Yang, U M

2010-04-29

Algebraic multigrid (AMG) solvers have proven to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore cluster architectures, we face new challenges that can significantly harm AMG's performance. We discuss our experiences on such an architecture and present a set of techniques that help users to overcome the associated problems, including thread and process pinning and correct memory associations. We have implemented most of the techniques in a MultiCore SUPport library (MCSup), which helps to map OpenMP applications to multicore machines. We present results using both an MPI-only and a hybrid MPI/OpenMP model.

Analysis and synthesis of distributed-lumped-active networks by digital computer

NASA Technical Reports Server (NTRS)

1973-01-01

The use of digital computational techniques in the analysis and synthesis of DLA (distributed lumped active) networks is considered. This class of networks consists of three distinct types of elements, namely, distributed elements (modeled by partial differential equations), lumped elements (modeled by algebraic relations and ordinary differential equations), and active elements (modeled by algebraic relations). Such a characterization is applicable to a broad class of circuits, especially including those usually referred to as linear integrated circuits, since the fabrication techniques for such circuits readily produce elements which may be modeled as distributed, as well as the more conventional lumped and active ones.

Performance assessment in algebra learning process

NASA Astrophysics Data System (ADS)

Lestariani, Ida; Sujadi, Imam; Pramudya, Ikrar

2017-12-01

The purpose of research to describe the implementation of performance assessment on algebra learning process. The subject in this research is math educator of SMAN 1 Ngawi class X. This research includes descriptive qualitative research type. Techniques of data collecting are done by observation method, interview, and documentation. Data analysis technique is done by data reduction, data presentation, and conclusion. The results showed any indication that the steps taken by the educator in applying the performance assessment are 1) preparing individual worksheets and group worksheets, 2) preparing rubric assessments for independent worksheets and groups and 3) making performance assessments rubric to learners’ performance results with individual or groups task.

Improved cardiac motion detection from ultrasound images using TDIOF: a combined B-mode/ tissue Doppler approach

NASA Astrophysics Data System (ADS)

Tavakoli, Vahid; Stoddard, Marcus F.; Amini, Amir A.

2013-03-01

Quantitative motion analysis of echocardiographic images helps clinicians with the diagnosis and therapy of patients suffering from cardiac disease. Quantitative analysis is usually based on TDI (Tissue Doppler Imaging) or speckle tracking. These methods are based on two independent techniques - the Doppler Effect and image registration, respectively. In order to increase the accuracy of the speckle tracking technique and cope with the angle dependency of TDI, herein, a combined approach dubbed TDIOF (Tissue Doppler Imaging Optical Flow) is proposed. TDIOF is formulated based on the combination of B-mode and Doppler energy terms in an optical flow framework and minimized using algebraic equations. In this paper, we report on validations with simulated, physical cardiac phantom, and in-vivo patient data. It is shown that the additional Doppler term is able to increase the accuracy of speckle tracking, the basis for several commercially available echocardiography analysis techniques.

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

Multifunctional, three-dimensional tomography for analysis of eletrectrohydrodynamic jetting

NASA Astrophysics Data System (ADS)

Nguyen, Xuan Hung; Gim, Yeonghyeon; Ko, Han Seo

2015-05-01

A three-dimensional optical tomography technique was developed to reconstruct three-dimensional objects using a set of two-dimensional shadowgraphic images and normal gray images. From three high-speed cameras, which were positioned at an offset angle of 45° between each other, number, size, and location of electrohydrodynamic jets with respect to the nozzle position were analyzed using shadowgraphic tomography employing multiplicative algebraic reconstruction technique (MART). Additionally, a flow field inside a cone-shaped liquid (Taylor cone) induced under an electric field was observed using a simultaneous multiplicative algebraic reconstruction technique (SMART), a tomographic method for reconstructing light intensities of particles, combined with three-dimensional cross-correlation. Various velocity fields of circulating flows inside the cone-shaped liquid caused by various physico-chemical properties of liquid were also investigated.

Unsupervised color image segmentation using a lattice algebra clustering technique

NASA Astrophysics Data System (ADS)

Urcid, Gonzalo; Ritter, Gerhard X.

2011-08-01

In this paper we introduce a lattice algebra clustering technique for segmenting digital images in the Red-Green- Blue (RGB) color space. The proposed technique is a two step procedure. Given an input color image, the first step determines the finite set of its extreme pixel vectors within the color cube by means of the scaled min-W and max-M lattice auto-associative memory matrices, including the minimum and maximum vector bounds. In the second step, maximal rectangular boxes enclosing each extreme color pixel are found using the Chebychev distance between color pixels; afterwards, clustering is performed by assigning each image pixel to its corresponding maximal box. The two steps in our proposed method are completely unsupervised or autonomous. Illustrative examples are provided to demonstrate the color segmentation results including a brief numerical comparison with two other non-maximal variations of the same clustering technique.

Blur kernel estimation with algebraic tomography technique and intensity profiles of object boundaries

NASA Astrophysics Data System (ADS)

Ingacheva, Anastasia; Chukalina, Marina; Khanipov, Timur; Nikolaev, Dmitry

2018-04-01

Motion blur caused by camera vibration is a common source of degradation in photographs. In this paper we study the problem of finding the point spread function (PSF) of a blurred image using the tomography technique. The PSF reconstruction result strongly depends on the particular tomography technique used. We present a tomography algorithm with regularization adapted specifically for this task. We use the algebraic reconstruction technique (ART algorithm) as the starting algorithm and introduce regularization. We use the conjugate gradient method for numerical implementation of the proposed approach. The algorithm is tested using a dataset which contains 9 kernels extracted from real photographs by the Adobe corporation where the point spread function is known. We also investigate influence of noise on the quality of image reconstruction and investigate how the number of projections influence the magnitude change of the reconstruction error.

Complementary Reliability-Based Decodings of Binary Linear Block Codes

NASA Technical Reports Server (NTRS)

Fossorier, Marc P. C.; Lin, Shu

1997-01-01

This correspondence presents a hybrid reliability-based decoding algorithm which combines the reprocessing method based on the most reliable basis and a generalized Chase-type algebraic decoder based on the least reliable positions. It is shown that reprocessing with a simple additional algebraic decoding effort achieves significant coding gain. For long codes, the order of reprocessing required to achieve asymptotic optimum error performance is reduced by approximately 1/3. This significantly reduces the computational complexity, especially for long codes. Also, a more efficient criterion for stopping the decoding process is derived based on the knowledge of the algebraic decoding solution.

Utilization of variation theory in the classroom: Effect on students' algebraic achievement and motivation

NASA Astrophysics Data System (ADS)

Jing, Ting Jing; Tarmizi, Rohani Ahmad; Bakar, Kamariah Abu; Aralas, Dalia

2017-01-01

This study investigates the effect of utilizing Variation Theory Based Strategy on students' algebraic achievement and motivation in learning algebra. The study used quasi-experimental non-equivalent control group research design and involved 56 Form Two (Secondary Two) students in two classes (28 in experimental group, 28 in control group) in Malaysia The first class of students went through algebra class taught with Variation Theory Based Strategy (VTBS) while the second class of students experienced conventional teaching strategy. The instruments used for the study were a 24-item Algebra Test and 36-item Instructional Materials Motivation Survey. Result from analysis of Covariance indicated that experimental group students achieved significantly better test scores than control group. Result of Multivariate Analysis of Variance also shows evidences of significant effect of VTBS on experimental students' overall motivation in all the five subscales; attention, relevance, confidence, and satisfaction. These results suggested the utilization of VTBS would improve students' learning in algebra.

Three-dimensional nanostructure determination from a large diffraction data set recorded using scanning electron nanodiffraction.

PubMed

Meng, Yifei; Zuo, Jian-Min

2016-09-01

A diffraction-based technique is developed for the determination of three-dimensional nanostructures. The technique employs high-resolution and low-dose scanning electron nanodiffraction (SEND) to acquire three-dimensional diffraction patterns, with the help of a special sample holder for large-angle rotation. Grains are identified in three-dimensional space based on crystal orientation and on reconstructed dark-field images from the recorded diffraction patterns. Application to a nanocrystalline TiN thin film shows that the three-dimensional morphology of columnar TiN grains of tens of nanometres in diameter can be reconstructed using an algebraic iterative algorithm under specified prior conditions, together with their crystallographic orientations. The principles can be extended to multiphase nanocrystalline materials as well. Thus, the tomographic SEND technique provides an effective and adaptive way of determining three-dimensional nanostructures.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE PAGES

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-02-06

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

The Factorability of Quadratics: Motivation for More Techniques

ERIC Educational Resources Information Center

Bosse, Michael J.; Nandakumar, N. R.

2005-01-01

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

An effective automatic procedure for testing parameter identifiability of HIV/AIDS models.

PubMed

Saccomani, Maria Pia

2011-08-01

Realistic HIV models tend to be rather complex and many recent models proposed in the literature could not yet be analyzed by traditional identifiability testing techniques. In this paper, we check a priori global identifiability of some of these nonlinear HIV models taken from the recent literature, by using a differential algebra algorithm based on previous work of the author. The algorithm is implemented in a software tool, called DAISY (Differential Algebra for Identifiability of SYstems), which has been recently released (DAISY is freely available on the web site http://www.dei.unipd.it/~pia/ ). The software can be used to automatically check global identifiability of (linear and) nonlinear models described by polynomial or rational differential equations, thus providing a general and reliable tool to test global identifiability of several HIV models proposed in the literature. It can be used by researchers with a minimum of mathematical background.

Versatile and declarative dynamic programming using pair algebras.

PubMed

Steffen, Peter; Giegerich, Robert

2005-09-12

Dynamic programming is a widely used programming technique in bioinformatics. In sharp contrast to the simplicity of textbook examples, implementing a dynamic programming algorithm for a novel and non-trivial application is a tedious and error prone task. The algebraic dynamic programming approach seeks to alleviate this situation by clearly separating the dynamic programming recurrences and scoring schemes. Based on this programming style, we introduce a generic product operation of scoring schemes. This leads to a remarkable variety of applications, allowing us to achieve optimizations under multiple objective functions, alternative solutions and backtracing, holistic search space analysis, ambiguity checking, and more, without additional programming effort. We demonstrate the method on several applications for RNA secondary structure prediction. The product operation as introduced here adds a significant amount of flexibility to dynamic programming. It provides a versatile testbed for the development of new algorithmic ideas, which can immediately be put to practice.

Mixed-state fidelity susceptibility through iterated commutator series expansion

NASA Astrophysics Data System (ADS)

Tonchev, N. S.

2014-11-01

We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provide an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite-dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.

Color Algebras

NASA Technical Reports Server (NTRS)

Mulligan, Jeffrey B.

2017-01-01

A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.

Conical Lens for 5-Inch/54 Gun Launched Missile

DTIC Science & Technology

1981-06-01

Propagation, Interferenceand Diffraction of Light, 2nd ed. (revised), p. 121-124, Pergamon Press, 1964. 10. Anton , Howard, Elementary Linear Algebra , p. 1-21...equations is nonlinear in x, but is linear in the coefficients. Therefore, the techniques of linear algebra can be used on equation (F-13). The method...This thesis assumes the air to be homogenous, isotropic, linear , time indepen- dent (HILT) and free of shock waves in order to investigate the

Computational technique for stepwise quantitative assessment of equation correctness

NASA Astrophysics Data System (ADS)

Othman, Nuru'l Izzah; Bakar, Zainab Abu

2017-04-01

Many of the computer-aided mathematics assessment systems that are available today possess the capability to implement stepwise correctness checking of a working scheme for solving equations. The computational technique for assessing the correctness of each response in the scheme mainly involves checking the mathematical equivalence and providing qualitative feedback. This paper presents a technique, known as the Stepwise Correctness Checking and Scoring (SCCS) technique that checks the correctness of each equation in terms of structural equivalence and provides quantitative feedback. The technique, which is based on the Multiset framework, adapts certain techniques from textual information retrieval involving tokenization, document modelling and similarity evaluation. The performance of the SCCS technique was tested using worked solutions on solving linear algebraic equations in one variable. 350 working schemes comprising of 1385 responses were collected using a marking engine prototype, which has been developed based on the technique. The results show that both the automated analytical scores and the automated overall scores generated by the marking engine exhibit high percent agreement, high correlation and high degree of agreement with manual scores with small average absolute and mixed errors.

Algebridge. Concept Based Instructional Assessment.

ERIC Educational Resources Information Center

College Entrance Examination Board, Princeton, NJ.

Students who study algebra are more likely to attend college than those who don't. A major hurdle for students in studying algebra is the transition from arithmetic to algebra. In response to overcoming this hurdle, the College Board and Educational Testing Service has developed "Algebridge," a teaching supplement that integrates…

Promoting Quantitative Literacy in an Online College Algebra Course

ERIC Educational Resources Information Center

Tunstall, Luke; Bossé, Michael J.

2016-01-01

College algebra (a university freshman level algebra course) fulfills the quantitative literacy requirement of many college's general education programs and is a terminal course for most who take it. An online problem-based learning environment provides a unique means of engaging students in quantitative discussions and research. This article…

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

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

2014-12-05

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.

Two-dimensional ionospheric tomography over the low-latitude Indian region: An intercomparison of ART and MART algorithms

NASA Astrophysics Data System (ADS)

Das, Sukanta Kumar; Shukla, Ashish Kumar

2011-04-01

Single-frequency users of a satellite-based augmentation system (SBAS) rely on ionospheric models to mitigate the delay due to the ionosphere. The ionosphere is the major source of range and range rate errors for users of the Global Positioning System (GPS) who require high-accuracy positioning. The purpose of the present study is to develop a tomography model to reconstruct the total electron content (TEC) over the low-latitude Indian region which lies in the equatorial ionospheric anomaly belt. In the present study, the TEC data collected from the six TEC collection stations along a longitudinal belt of around 77 degrees are used. The main objective of the study is to find out optimum pixel size which supports a better reconstruction of the electron density and hence the TEC over the low-latitude Indian region. Performance of two reconstruction algorithms Algebraic Reconstruction Technique (ART) and Multiplicative Algebraic Reconstruction Technique (MART) is analyzed for different pixel sizes varying from 1 to 6 degrees in latitude. It is found from the analysis that the optimum pixel size is 5° × 50 km over the Indian region using both ART and MART algorithms.

Integrand Reduction Reloaded: Algebraic Geometry and Finite Fields

NASA Astrophysics Data System (ADS)

Sameshima, Ray D.; Ferroglia, Andrea; Ossola, Giovanni

2017-01-01

The evaluation of scattering amplitudes in quantum field theory allows us to compare the phenomenological prediction of particle theory with the measurement at collider experiments. The study of scattering amplitudes, in terms of their symmetries and analytic properties, provides a theoretical framework to develop techniques and efficient algorithms for the evaluation of physical cross sections and differential distributions. Tree-level calculations have been known for a long time. Loop amplitudes, which are needed to reduce the theoretical uncertainty, are more challenging since they involve a large number of Feynman diagrams, expressed as integrals of rational functions. At one-loop, the problem has been solved thanks to the combined effect of integrand reduction, such as the OPP method, and unitarity. However, plenty of work is still needed at higher orders, starting with the two-loop case. Recently, integrand reduction has been revisited using algebraic geometry. In this presentation, we review the salient features of integrand reduction for dimensionally regulated Feynman integrals, and describe an interesting technique for their reduction based on multivariate polynomial division. We also show a novel approach to improve its efficiency by introducing finite fields. Supported in part by the National Science Foundation under Grant PHY-1417354.

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

2012-06-07

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.

Distortion theorems for polynomials on a circle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubinin, V N

2000-12-31

Inequalities for the derivatives with respect to {phi}=arg z the functions ReP(z), |P(z)|{sup 2} and arg P(z) are established for an algebraic polynomial P(z) at points on the circle |z|=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

The Care and Feeding of Pre-Meds

NASA Astrophysics Data System (ADS)

Magleby, Stephanie

2009-05-01

Most physics instructors will at some point in their teaching career face a room full of students bound for medical or dental school. This particular student clientele presents a host of distinctive challenges. My presentation will discuss insights gained while teaching premed sections of algebra-based College Physics over the last ten semesters. Topics will include syllabus structure, grading techniques, testing strategies, letters of recommendation and most importantly: how to get a good teaching evaluation from a Pre-Med.

The Care and Feeding of Pre-Meds

NASA Astrophysics Data System (ADS)

Magleby, Stephanie

2008-10-01

Most physics instructors will at some point in their teaching career face a room full of students bound for medical or dental school. This particular student clientele presents a host of distinctive challenges. My presentation will discuss insights gained while teaching premed sections of algebra-based College Physics over the last ten semesters. Topics will include syllabus structure, quiz techniques, testing strategies, letters of recommendation and how to get a good teaching evaluation from a pre-med.

Flight control application of new stability robustness bounds for linear uncertain systems

NASA Technical Reports Server (NTRS)

Yedavalli, Rama K.

1993-01-01

This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

NASA Technical Reports Server (NTRS)

Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

2013-01-01

Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

Climate and weather across scales: singularities and stochastic Levy-Clifford algebra

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2016-04-01

There have been several attempts to understand and simulate the fluctuations of weather and climate across scales. Beyond mono/uni-scaling approaches (e.g. using spectral analysis), this was done with the help of multifractal techniques that aim to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations of these equations (Royer et al., 2008, Lovejoy and Schertzer, 2013). However, these techniques were limited to deal with scalar fields, instead of dealing directly with a system of complex interactions and non trivial symmetries. The latter is unfortunately indispensable to answer to the challenging question of being able to assess the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013) or to fully address the question of the relevance of quasi-geostrophic turbulence and to define an effective, fractal dimension of the atmospheric motions (Schertzer et al., 2012). In this talk, we present a plausible candidate based on the combination of Lévy stable processes and Clifford algebra. Together they combine stochastic and structural properties that are strongly universal. They therefore define with the help of a few physically meaningful parameters a wide class of stochastic symmetries, as well as high dimensional vector- or manifold-valued fields respecting these symmetries (Schertzer and Tchiguirinskaia, 2015). Lovejoy, S. & Schertzer, D., 2013. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge U.K. Cambridge Univeristy Press. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.81-83. Royer, J.F. et al., 2008. Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario. C.R. Geoscience, 340(431-440). Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327-336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127.

The algebraic decoding of the (41, 21, 9) quadratic residue code

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Truong, T. K.; Chen, Xuemin; Yin, Xiaowei

1992-01-01

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spotz, William F.

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of themore » underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.« less

Carnegie Learning Curricula and Cognitive Tutor™. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2013

2013-01-01

"Carnegie Learning Curricula and Cognitive Tutor"®, published by Carnegie Learning, is a secondary math curricula that offers textbooks and interactive software to provide individualized, self-paced instruction based on student needs. The program includes pre-Algebra, Algebra I, Algebra II, and Geometry, as well as a three-course series…

An Emoji Is Worth a Thousand Variables

ERIC Educational Resources Information Center

McCaffrey, Tony; Matthews, Percival G.

2017-01-01

In this article, the authors discuss the potential of the icon-based mathematical games, emoji math and mobile math, to promote student engagement with and understanding of algebra. They describe how these games serve as accessible entry points for algebraic thinking and that, in contrast to traditional symbolic algebra, the use of these…

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

Optical Linear Algebra for Computational Light Transport

NASA Astrophysics Data System (ADS)

O'Toole, Matthew

Active illumination refers to optical techniques that use controllable lights and cameras to analyze the way light propagates through the world. These techniques confer many unique imaging capabilities (e.g. high-precision 3D scanning, image-based relighting, imaging through scattering media), but at a significant cost; they often require long acquisition and processing times, rely on predictive models for light transport, and cease to function when exposed to bright ambient sunlight. We develop a mathematical framework for describing and analyzing such imaging techniques. This framework is deeply rooted in numerical linear algebra, and models the transfer of radiant energy through an unknown environment with the so-called light transport matrix. Performing active illumination on a scene equates to applying a numerical operator on this unknown matrix. The brute-force approach to active illumination follows a two-step procedure: (1) optically measure the light transport matrix and (2) evaluate the matrix operator numerically. This approach is infeasible in general, because the light transport matrix is often much too large to measure, store, and analyze directly. Using principles from optical linear algebra, we evaluate these matrix operators in the optical domain, without ever measuring the light transport matrix in the first place. Specifically, we explore numerical algorithms that can be implemented partially or fully with programmable optics. These optical algorithms provide solutions to many longstanding problems in computer vision and graphics, including the ability to (1) photo-realistically change the illumination conditions of a given photo with only a handful of measurements, (2) accurately capture the 3D shape of objects in the presence of complex transport properties and strong ambient illumination, and (3) overcome the multipath interference problem associated with time-of-flight cameras. Most importantly, we introduce an all-new imaging regime---optical probing---that provides unprecedented control over which light paths contribute to a photo.

Selecting Students for Pre-Algebra: Examination of the Relative Utility of the Anchorage Pre-Algebra Screening Tests and the State of Alaska Standards Based Benchmark 2 Mathematics Study. An Examination of Consequential Validity and Recommendation.

ERIC Educational Resources Information Center

Fenton, Ray

This study examined the relative efficacy of the Anchorage (Alaska) Pre-Algebra Test and the State of Alaska Benchmark in 2 Math examination as tools used in the process of recommending grade 6 students for grade 7 Pre-Algebra placement. The consequential validity of the tests is explored in the context of class placements and grades earned. The…

A Quantum Groups Primer

NASA Astrophysics Data System (ADS)

Majid, Shahn

2002-05-01

Here is a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, the book is suitable as a primary text for graduate courses in quantum groups or supplementary reading for modern courses in advanced algebra. The material assumes knowledge of basic and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The volume is a primer for mathematicians but it will also be useful for mathematical physicists.

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

PubMed

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. Copyright © 2013 Elsevier Inc. All rights reserved.

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

NASA Astrophysics Data System (ADS)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-10-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

The role of difficulty and gender in numbers, algebra, geometry and mathematics achievement

NASA Astrophysics Data System (ADS)

Rabab'h, Belal Sadiq Hamed; Veloo, Arsaythamby; Perumal, Selvan

2015-05-01

This study aims to identify the role of difficulty and gender in numbers, algebra, geometry and mathematics achievement among secondary schools students in Jordan. The respondent of the study were 337 students from eight public secondary school in Alkoura district by using stratified random sampling. The study comprised of 179 (53%) males and 158 (47%) females students. The mathematics test comprises of 30 items which has eight items for numbers, 14 items for algebra and eight items for geometry. Based on difficulties among male and female students, the findings showed that item 4 (fractions - 0.34) was most difficult for male students and item 6 (square roots - 0.39) for females in numbers. For the algebra, item 11 (inequality - 0.23) was most difficult for male students and item 6 (algebraic expressions - 0.35) for female students. In geometry, item 3 (reflection - 0.34) was most difficult for male students and item 8 (volume - 0.33) for female students. Based on gender differences, female students showed higher achievement in numbers and algebra compare to male students. On the other hand, there was no differences between male and female students achievement in geometry test. This study suggest that teachers need to give more attention on numbers and algebra when teaching mathematics.

Three-dimensional nanostructure determination from a large diffraction data set recorded using scanning electron nanodiffraction

DOE PAGES

Meng, Yifei; Zuo, Jian -Min

2016-07-04

A diffraction-based technique is developed for the determination of three-dimensional nanostructures. The technique employs high-resolution and low-dose scanning electron nanodiffraction (SEND) to acquire three-dimensional diffraction patterns, with the help of a special sample holder for large-angle rotation. Grains are identified in three-dimensional space based on crystal orientation and on reconstructed dark-field images from the recorded diffraction patterns. Application to a nanocrystalline TiN thin film shows that the three-dimensional morphology of columnar TiN grains of tens of nanometres in diameter can be reconstructed using an algebraic iterative algorithm under specified prior conditions, together with their crystallographic orientations. The principles can bemore » extended to multiphase nanocrystalline materials as well. Furthermore, the tomographic SEND technique provides an effective and adaptive way of determining three-dimensional nanostructures.« less

Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems.

PubMed

Chang, Yeong-Chan

2005-12-01

This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.

Robust algebraic image enhancement for intelligent control systems

NASA Technical Reports Server (NTRS)

Lerner, Bao-Ting; Morrelli, Michael

1993-01-01

Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

Algebraic Thinking in Solving Linier Program at High School Level: Female Student’s Field Independent Cognitive Style

NASA Astrophysics Data System (ADS)

Hardiani, N.; Budayasa, I. K.; Juniati, D.

2018-01-01

The aim of this study was to describe algebraic thinking of high school female student’s field independent cognitive style in solving linier program problem by revealing deeply the female students’ responses. Subjects in this study were 7 female students having field independent cognitive style in class 11. The type of this research was descriptive qualitative. The method of data collection used was observation, documentation, and interview. Data analysis technique was by reduction, presentation, and conclusion. The results of this study showed that the female students with field independent cognitive style in solving the linier program problem had the ability to represent algebraic ideas from the narrative question that had been read by manipulating symbols and variables presented in tabular form, creating and building mathematical models in two variables linear inequality system which represented algebraic ideas, and interpreting the solutions as variables obtained from the point of intersection in the solution area to obtain maximum benefit.

Final Report: Subcontract B623868 Algebraic Multigrid solvers for coupled PDE systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brannick, J.

The Pennsylvania State University (“Subcontractor”) continued to work on the design of algebraic multigrid solvers for coupled systems of partial differential equations (PDEs) arising in numerical modeling of various applications, with a main focus on solving the Dirac equation arising in Quantum Chromodynamics (QCD). The goal of the proposed work was to develop combined geometric and algebraic multilevel solvers that are robust and lend themselves to efficient implementation on massively parallel heterogeneous computers for these QCD systems. The research in these areas built on previous works, focusing on the following three topics: (1) the development of parallel full-multigrid (PFMG) andmore » non-Galerkin coarsening techniques in this frame work for solving the Wilson Dirac system; (2) the use of these same Wilson MG solvers for preconditioning the Overlap and Domain Wall formulations of the Dirac equation; and (3) the design and analysis of algebraic coarsening algorithms for coupled PDE systems including Stokes equation, Maxwell equation and linear elasticity.« less

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…

Characterizing and Supporting Change in Algebra Students' Representational Fluency in a CAS/Paper-and-Pencil Environment

ERIC Educational Resources Information Center

Fonger, Nicole L.

2012-01-01

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

Interactions between Language and Mathematics with Deaf Students: Defining the "Language-Mathematics" Equation.

ERIC Educational Resources Information Center

Hillegeist, Eleanor; Epstein, Kenneth

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Introducing Algebra through the Graphical Representation of Functions: A Study among LD Students

ERIC Educational Resources Information Center

Sauriol, Jennifer

2013-01-01

This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

Proceedings of the International Conference on Algebraic Methodology and Software Technology (2nd) Held in Iowa City, Iowa on May 22-25, 1991.

DTIC Science & Technology

1992-05-25

d’Etat, University of Paris-Sud. [Boudol 84] G. Boudol, An asynchronous calculus MEIJE, in NATO summer school, La - Colle - sur - Loup , France (1984). [Da...on the propositional p-calculus. Theoretical Comput. Sci., 27:333-354, 1983. [12] M. Nivat. Sur la synchronisation des processus. Revue Technique...Meulen, E.A. Deriving In- Traynor, 0., de la Cruz, P., Uniform (Meta- ) De- cremental Implementations from Algebraic Specifica- velopment in the PROSPECTRA

An interactive grid generation procedure for axial and radial flow turbomachinery

NASA Technical Reports Server (NTRS)

Beach, Timothy A.

1989-01-01

A combination algebraic/elliptic technique is presented for the generation of three dimensional grids about turbo-machinery blade rows for both axial and radial flow machinery. The technique is built around use of an advanced engineering workstation to construct several two dimensional grids interactively on predetermined blade-to-blade surfaces. A three dimensional grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade-to-blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. This procedure lends itself well to zonal grid construction, an important example being the tip clearance region. Calculations done to date include a space shuttle main engine turbopump blade, a radial inflow turbine blade, and the first stator of the United Technologies Research Center large scale rotating rig. A finite Navier-Stokes solver was used in each case.

Formula recollection through a WORLDLY recognized mnemonic technique

NASA Astrophysics Data System (ADS)

Schunicht, Shannon

2009-10-01

Physics may be made fun, and encourage further learning through ease of recollection of complicated formulas; allthewhile increasing a student's confortability with their algebraic skills. Examples will be shown how ANY complicated formula will be made into a memorable acronym using this author's mnemonic technique, i.e. allowing each vowel to represent a mathematical operation: ``a'' multiplication implying ``@''; ``o''-division implying ``over''; ``i''-subtraction to imply ``minus''; ``u''-addition to imply ``plus''; and ``e'' implying ``equals''. Most constants and variables are indeed consonants; ``c'' = ``speed of light'' & ``z'' = ``altitude''. With this mnemonic technique ANY formula may be algebraically manipulated into a word, or series of words for ease of recollection. Additional letters may be added to enhance the intelligibility of such a letter combination, but these additional letters need be consonants ONLY. This mnemonic technique was developed as a compensatory memory method when taking physics at Texas A&M University following a severe head injury (19 days unconsciousness!) suffered by this author.

Algebraic grid generation with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, M.; Lombard, C. K.

1983-01-01

A simple noniterative algebraic procedure is presented for generating smooth computational meshes on a quadrilateral topology. Coordinate distribution and normal derivative are provided on all boundaries, one of which may include a slope discontinuity. The boundary conditions are sufficient to guarantee continuity of global meshes formed of joined patches generated by the procedure. The method extends to 3-D. The procedure involves a synthesis of prior techniques stretching functions, cubic blending functions, and transfinite interpolation - to which is added the functional form of the corner solution. The procedure introduces the concept of generalized blending, which is implemented as an automatic scaling of the boundary derivatives for effective interpolation. Some implications of the treatment at boundaries for techniques solving elliptic PDE's are discussed in an Appendix.

Asymptotics of bivariate generating functions with algebraic singularities

NASA Astrophysics Data System (ADS)

Greenwood, Torin

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

A Model-Based Diagnosis Framework for Distributed Systems

DTIC Science & Technology

2002-05-04

of centralized compilation techniques as applied to [6] Marco Cadoli and Francesco M . Donini . A survey several areas, of which diagnosis is one. Our...for doing so than the family for that (1) Vi 1 ... m . Xi E 2V; (2) V ui(Xi[Xi E 1). tree-structured systems. For simplicity of notation, we will that (i...our diagnosis synthesis diagnoses using a likelihood weight ri assigned to each as- algorithm. sumable Ai, i = I, ... m . Using the likelihood algebra

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Distortion theorems for polynomials on a circle

NASA Astrophysics Data System (ADS)

Dubinin, V. N.

2000-12-01

Inequalities for the derivatives with respect to \\varphi=\\arg z the functions \\operatorname{Re}P(z), \\vert P(z)\\vert^2 and \\arg P(z) are established for an algebraic polynomial P(z) at points on the circle \\vert z\\vert=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

An Analysis of Elliptic Grid Generation Techniques Using an Implicit Euler Solver.

DTIC Science & Technology

1986-06-09

automatic determination of the control fu.nction, . elements of covariant metric tensor in the elliptic grid generation system , from the Cm = 1,2,3...computational fluid d’nan1-cs code. Tne code Inclues a tnree-dimensional current research is aimed primaril: at algebraic generation system based on transfinite...start the iterative solution of the f. ow, nea, transfer, and combustion proble:s. elliptic generation system . Tn13 feature also .:ven-.ts :.t be made

Light-field camera-based 3D volumetric particle image velocimetry with dense ray tracing reconstruction technique

NASA Astrophysics Data System (ADS)

Shi, Shengxian; Ding, Junfei; New, T. H.; Soria, Julio

2017-07-01

This paper presents a dense ray tracing reconstruction technique for a single light-field camera-based particle image velocimetry. The new approach pre-determines the location of a particle through inverse dense ray tracing and reconstructs the voxel value using multiplicative algebraic reconstruction technique (MART). Simulation studies were undertaken to identify the effects of iteration number, relaxation factor, particle density, voxel-pixel ratio and the effect of the velocity gradient on the performance of the proposed dense ray tracing-based MART method (DRT-MART). The results demonstrate that the DRT-MART method achieves higher reconstruction resolution at significantly better computational efficiency than the MART method (4-50 times faster). Both DRT-MART and MART approaches were applied to measure the velocity field of a low speed jet flow which revealed that for the same computational cost, the DRT-MART method accurately resolves the jet velocity field with improved precision, especially for the velocity component along the depth direction.

Discrete Fourier Transform in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Smith, R. E.

1981-01-01

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

Superiorization-based multi-energy CT image reconstruction

PubMed Central

Yang, Q; Cong, W; Wang, G

2017-01-01

The recently-developed superiorization approach is efficient and robust for solving various constrained optimization problems. This methodology can be applied to multi-energy CT image reconstruction with the regularization in terms of the prior rank, intensity and sparsity model (PRISM). In this paper, we propose a superiorized version of the simultaneous algebraic reconstruction technique (SART) based on the PRISM model. Then, we compare the proposed superiorized algorithm with the Split-Bregman algorithm in numerical experiments. The results show that both the Superiorized-SART and the Split-Bregman algorithms generate good results with weak noise and reduced artefacts. PMID:28983142

Nonlinear secret image sharing scheme.

PubMed

Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young

2014-01-01

Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively.

Nonlinear Secret Image Sharing Scheme

PubMed Central

Shin, Sang-Ho; Yoo, Kee-Young

2014-01-01

Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2⁡m⌉ bit-per-pixel (bpp), respectively. PMID:25140334

A spatial operator algebra for manipulator modeling and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.; Jain, A.

1989-01-01

A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

PubMed Central

Mishra, Bud

2009-01-01

Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher's somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations. PMID:19364723

Enhancing Engagement in Algebra: Didactical Strategies Implemented and Discussed by Teachers

ERIC Educational Resources Information Center

Nyman, Rimma; Kilhamn, Cecilia

2015-01-01

The aim of this study is to investigate student engagement from the point of view of the teacher, by focusing on teacher's didactical strategies used to engage students during algebra introduction. Eight teachers in grade 6 and 7 participated in a focus-group interview study. The findings are based on episodes of student engagement in algebra and…

Making Sense of Abstract Algebra: Exploring Secondary Teachers' Understandings of Inverse Functions in Relation to Its Group Structure

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2017-01-01

This article draws on semi-structured, task-based interviews to explore secondary teachers' (N = 7) understandings of inverse functions in relation to abstract algebra. In particular, a concept map task is used to understand the degree to which participants, having recently taken an abstract algebra course, situated inverse functions within its…

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…

Algebraic special functions and SO(3,2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

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 inmore » 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.« less

The effects of an integrated Algebra 1/physical science curriculum on student achievement in Algebra 1, proportional reasoning and graphing abilities

NASA Astrophysics Data System (ADS)

Lawrence, Lettie Carol

1997-08-01

The purpose of this investigation was to determine if an integrated curriculum in algebra 1/physical science facilitates acquisition of proportional reasoning and graphing abilities better than a non-integrated, traditional, algebra 1 curriculum. Also, this study was to ascertain if the integrated algebra 1/physical science curriculum resulted in greater student achievement in algebra 1. The curriculum used in the experimental class was SAM 9 (Science and Mathematics 9), an investigation-based curriculum that was written to integrate physical science and basic algebra content. The experiment was conducted over one school year. The subjects in the study were 61 ninth grade students. The experimental group consisted of one class taught concurrently by a mathematics teacher and a physical science teacher. The control group consisted of three classes of algebra 1 students taught by one mathematics teacher and taking physical science with other teachers in the school who were not participating in the SAM 9 program. This study utilized a quasi-experimental non-randomized control group pretest-posttest design. The investigator obtained end-of-algebra 1 scores from student records. The written open-ended graphing instruments and the proportional reasoning instrument were administered to both groups as pretests and posttests. The graphing instruments were also administered as a midtest. A two sample t-test for independent means was used to determine significant differences in achievement on the end-of-course algebra 1 test. Quantitative data from the proportional reasoning and graphing instruments were analyzed using a repeated measures analysis of variance to determine differences in scores over time for the experimental and control groups. The findings indicate no significant difference between the experimental and control groups on the end-of-course algebra 1 test. Results also indicate no significant differences in proportional reasoning and graphing abilities between the two groups over time. However, all subjects (experimental and control groups) made significant improvement in graphing abilities over one school year. In this study, students participating in an investigation-based curriculum integrating algebra 1 and physical science performed as well on the instruments as the students in the traditional curriculum. Therefore, an argument can be made that instruction using an integrated curriculum (algebra l/physical science) is a viable alternative to instruction using a more traditional algebra 1 curriculum. Finally, the integrated curriculum adheres to the constructivist theoretical perspective (Krupnik-Gotlieb, 1995) and is more consistent with recommendations in the NCTM Standards (1992) than the traditional curriculum.

TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION

NASA Technical Reports Server (NTRS)

Smith, R. E.

1994-01-01

TBGG, Two-Boundary Grid Generation, applies an interactive algebraic grid generation technique in two dimensions. The program incorporates mathematical equations that relate the computational domain to the physical domain. TBGG has application to a variety of problems using finite difference techniques, such as computational fluid dynamics. Examples include the creation of a C-type grid about an airfoil and a nozzle configuration in which no left or right boundaries are specified. The underlying two-boundary technique of grid generation is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are defined by two ordered sets of points, referred to as the top and bottom. Left and right side boundaries may also be specified, and call upon linear blending functions to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly spaced computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth cubic spline functions is also presented. The TBGG program is written in FORTRAN 77. It works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. The program has been implemented on a CDC Cyber 170 series computer using NOS 2.4 operating system, with a central memory requirement of 151,700 (octal) 60 bit words. TBGG requires a Tektronix 4015 terminal and the DI-3000 Graphics Library of Precision Visuals, Inc. TBGG was developed in 1986.

A three-dimensional wide-angle BPM for optical waveguide structures.

PubMed

Ma, Changbao; Van Keuren, Edward

2007-01-22

Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra's scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

An Algebra-Based Introductory Computational Neuroscience Course with Lab.

PubMed

Fink, Christian G

2017-01-01

A course in computational neuroscience has been developed at Ohio Wesleyan University which requires no previous experience with calculus or computer programming, and which exposes students to theoretical models of neural information processing and techniques for analyzing neural data. The exploration of theoretical models of neural processes is conducted in the classroom portion of the course, while data analysis techniques are covered in lab. Students learn to program in MATLAB and are offered the opportunity to conclude the course with a final project in which they explore a topic of their choice within computational neuroscience. Results from a questionnaire administered at the beginning and end of the course indicate significant gains in student facility with core concepts in computational neuroscience, as well as with analysis techniques applied to neural data.

A three-dimensional wide-angle BPM for optical waveguide structures

NASA Astrophysics Data System (ADS)

Ma, Changbao; van Keuren, Edward

2007-01-01

Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra’s scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

Helical Axis Data Visualization and Analysis of the Knee Joint Articulation.

PubMed

Millán Vaquero, Ricardo Manuel; Vais, Alexander; Dean Lynch, Sean; Rzepecki, Jan; Friese, Karl-Ingo; Hurschler, Christof; Wolter, Franz-Erich

2016-09-01

We present processing methods and visualization techniques for accurately characterizing and interpreting kinematical data of flexion-extension motion of the knee joint based on helical axes. We make use of the Lie group of rigid body motions and particularly its Lie algebra for a natural representation of motion sequences. This allows to analyze and compute the finite helical axis (FHA) and instantaneous helical axis (IHA) in a unified way without redundant degrees of freedom or singularities. A polynomial fitting based on Legendre polynomials within the Lie algebra is applied to provide a smooth description of a given discrete knee motion sequence which is essential for obtaining stable instantaneous helical axes for further analysis. Moreover, this allows for an efficient overall similarity comparison across several motion sequences in order to differentiate among several cases. Our approach combines a specifically designed patient-specific three-dimensional visualization basing on the processed helical axes information and incorporating computed tomography (CT) scans for an intuitive interpretation of the axes and their geometrical relation with respect to the knee joint anatomy. In addition, in the context of the study of diseases affecting the musculoskeletal articulation, we propose to integrate the above tools into a multiscale framework for exploring related data sets distributed across multiple spatial scales. We demonstrate the utility of our methods, exemplarily processing a collection of motion sequences acquired from experimental data involving several surgery techniques. Our approach enables an accurate analysis, visualization and comparison of knee joint articulation, contributing to the evaluation and diagnosis in medical applications.

Developing CORE model-based worksheet with recitation task to facilitate students’ mathematical communication skills in linear algebra course

NASA Astrophysics Data System (ADS)

Risnawati; Khairinnisa, S.; Darwis, A. H.

2018-01-01

The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.

Computerized Proof Techniques for Undergraduates

ERIC Educational Resources Information Center

Smith, Christopher J.; Tefera, Akalu; Zeleke, Aklilu

2012-01-01

The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf-Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete…

Dynamic Programming: An Introduction by Example

ERIC Educational Resources Information Center

Zietz, Joachim

2007-01-01

The author introduces some basic dynamic programming techniques, using examples, with the help of the computer algebra system "Maple". The emphasis is on building confidence and intuition for the solution of dynamic problems in economics. To integrate the material better, the same examples are used to introduce different techniques. One covers the…

Quantum deformations of conformal algebras with mass-like deformation parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frydryszak, Andrzej; Lukierski, Jerzy; Mozrzymas, Marek

1998-12-15

We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2)more » reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.« less

Quantum teleportation and Birman-Murakami-Wenzl algebra

NASA Astrophysics Data System (ADS)

Zhang, Kun; Zhang, Yong

2017-02-01

In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman-Murakami-Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley-Lieb projector and the Yang-Baxter gate. We describe quantum teleportation using the Temperley-Lieb projector and the Yang-Baxter gate, respectively, and study teleportation-based quantum computation using the Yang-Baxter gate. On the other hand, we exploit the extended Temperley-Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore, our research sheds a light on a link between quantum information science and low-dimensional topology.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

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.

The Effect of a Math Emporium Course Redesign in Developmental and Introductory Mathematics Courses on Student Achievement and Students' Attitudes toward Mathematics at a Two-Year College

ERIC Educational Resources Information Center

Bishop, Amy Renee

2010-01-01

The purpose of this research was to determine the effect of computer-based instruction on student mathematics achievement and students' attitudes toward mathematics in developmental and introductory mathematics courses, namely Elementary Algebra, Intermediate Algebra, and College Algebra, at a community college. The researcher also examined the…

Using the Interactive Learning Environment Aplusix for Teaching and Learning School Algebra: A Research Experiment in a Middle School

ERIC Educational Resources Information Center

Hadjerrouit, Said

2011-01-01

Most software tools that have been developed with the aim of helping students to learn school algebra have not yet achieved successful results in classroom. Almost all of them are menu-based systems that provide transformation rules in menus and buttons. Aplusix is a new interactive software tool for learning school algebra. In contrast to…

Teaching Algebra to Ninth and Tenth Grade Pupils with the Use of Programmed Materials and Teaching Machines.

ERIC Educational Resources Information Center

Raymond, Roger A.

In the second year of a study to compare and evaluate programed and conventional instruction in algebra for the ninth and tenth grades, comparisons of the control and experimental groups in each grade were again based on scores from the Lankton First-Year Algebra Test and the California Study Methods Survey (CSMS). Although there was a…

Gauge backgrounds and zero-mode counting in F-theory

NASA Astrophysics Data System (ADS)

Bies, Martin; Mayrhofer, Christoph; Weigand, Timo

2017-11-01

Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.

A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots

NASA Technical Reports Server (NTRS)

Yang, S. L.; Cline, M. C.; Chen, R.; Chang, Y. L.

1993-01-01

A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots.

The Bethe ansatz

NASA Astrophysics Data System (ADS)

Levkovich-Maslyuk, Fedor

2016-08-01

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

A Comparison of Solver Performance for Complex Gastric Electrophysiology Models

PubMed Central

Sathar, Shameer; Cheng, Leo K.; Trew, Mark L.

2016-01-01

Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems. PMID:26736543

Applications of computer algebra to distributed parameter systems

NASA Technical Reports Server (NTRS)

Storch, Joel A.

1993-01-01

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

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…

Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

ERIC Educational Resources Information Center

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-01-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

Students’ Algebraic Thinking Process in Context of Point and Line Properties

NASA Astrophysics Data System (ADS)

Nurrahmi, H.; Suryadi, D.; Fatimah, S.

2017-09-01

Learning of schools algebra is limited to symbols and operating procedures, so students are able to work on problems that only require the ability to operate symbols but unable to generalize a pattern as one of part of algebraic thinking. The purpose of this study is to create a didactic design that facilitates students to do algebraic thinking process through the generalization of patterns, especially in the context of the property of point and line. This study used qualitative method and includes Didactical Design Research (DDR). The result is students are able to make factual, contextual, and symbolic generalization. This happen because the generalization arises based on facts on local terms, then the generalization produced an algebraic formula that was described in the context and perspective of each student. After that, the formula uses the algebraic letter symbol from the symbol t hat uses the students’ language. It can be concluded that the design has facilitated students to do algebraic thinking process through the generalization of patterns, especially in the context of property of the point and line. The impact of this study is this design can use as one of material teaching alternative in learning of school algebra.

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

NASA Astrophysics Data System (ADS)

Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

2016-03-01

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

Direct methods in protein crystallography.

PubMed

Karle, J

1989-11-01

It is pointed out that the 'direct methods' of phase determination for small-structure crystallography do not have immediate applicability to macromolecular structures. The term 'direct methods in macromolecular crystallography' is suggested to categorize a spectrum of approaches to macromolecular structure determination in which the analyses are characterized by the use of two-phase and higher-order-phase invariants. The evaluation of the invariants is generally obtained by the use of heavy-atom techniques. The results of a number of the more recent algebraic and probabilistic studies involving isomorphous replacement and anomalous dispersion thus become valid subjects for discussion here. These studies are described and suggestions are also presented concerning future applicability. Additional discussion concerns the special techniques of filtering, the use of non-crystallographic symmetry, some features of maximum entropy and attempts to apply phase-determining formulas to the refinement of macromolecular structure. It is noted that, in addition to the continuing remarkable progress in macromolecular crystallography based on the traditional applications of isomorphous replacement and anomalous dispersion, recent valuable advances have been made in the application of non-crystallographic symmetry, in particular, to virus structures and in applications of filtering. Good progress has also been reported in the application of exact linear algebra to multiple-wavelength anomalous-dispersion investigations of structures containing anomalous scatterers of only moderate scattering power.

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

NASA Astrophysics Data System (ADS)

Nazarov, Anton

2012-11-01

In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent algorithm based on generalization of Weyl character formula. We also offer alternative implementation based on the Freudenthal multiplicity formula which can be faster in some cases. Restrictions: Computational complexity grows fast with the rank of an algebra, so computations for algebras of ranks greater than 8 are not practical. Unusual features: We offer the possibility of using a traditional mathematical notation for the objects in representation theory of Lie algebras in computations if Affine.m is used in the Mathematica notebook interface. Running time: From seconds to days depending on the rank of the algebra and the complexity of the representation.

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

NASA Technical Reports Server (NTRS)

Moitra, Anutosh

1989-01-01

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation

NASA Technical Reports Server (NTRS)

Mcreynolds, S. R.

1975-01-01

A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heroux, Michael Allen; Marker, Bryan

This report summarizes the progress made as part of a one year lab-directed research and development (LDRD) project to fund the research efforts of Bryan Marker at the University of Texas at Austin. The goal of the project was to develop new techniques for automatically tuning the performance of dense linear algebra kernels. These kernels often represent the majority of computational time in an application. The primary outcome from this work is a demonstration of the value of model driven engineering as an approach to accurately predict and study performance trade-offs for dense linear algebra computations.

The Development and Validation of the Algebra Curriculum Based Measure: A Measure of Preschool Children's Sorting and Classifying Skills

ERIC Educational Resources Information Center

Maherally, Mohammad Iqbal

2014-01-01

The purpose of this study was to develop and validate an assessment tool entitled the Algebra Curriculum Based Measure (ACBM) with the intent of measuring preschool children's sorting and classifying skills based on one attribute (color, shape, and size) and two attributes (color and shape) simultaneously; and their ability to explain their…

Application of Quaternions for Mesh Deformation

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2002-01-01

A new three-dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.

Application of Quaternions for Mesh

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2002-01-01

A new three dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.

Yang-Baxter algebras, integrable theories and Bethe Ansatz

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Vega, H.J.

1990-03-10

This paper presents the Yang-Baxter algebras (YBA) in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Behe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitly. The generalization of YB algebras to face language is considered. The algebraic BA for the SOS model of Andrews, Baxter and Forrester is described using these face YB algebras. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approachmore » permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underlay the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

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 deformedmore » 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.« less

Algebraic Systems and Pushdown Automata

NASA Astrophysics Data System (ADS)

Petre, Ion; Salomaa, Arto

We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

A Novel Approach to Realize of All Optical Frequency Encoded Dibit Based XOR and XNOR Logic Gates Using Optical Switches with Simulated Verification

NASA Astrophysics Data System (ADS)

Ghosh, B.; Hazra, S.; Haldar, N.; Roy, D.; Patra, S. N.; Swarnakar, J.; Sarkar, P. P.; Mukhopadhyay, S.

2018-03-01

Since last few decades optics has already proved its strong potentiality for conducting parallel logic, arithmetic and algebraic operations due to its super-fast speed in communication and computation. So many different logical and sequential operations using all optical frequency encoding technique have been proposed by several authors. Here, we have keened out all optical dibit representation technique, which has the advantages of high speed operation as well as reducing the bit error problem. Exploiting this phenomenon, we have proposed all optical frequency encoded dibit based XOR and XNOR logic gates using the optical switches like add/drop multiplexer (ADM) and reflected semiconductor optical amplifier (RSOA). Also the operations of these gates have been verified through proper simulation using MATLAB (R2008a).

Dolan Grady relations and noncommutative quasi-exactly solvable systems

NASA Astrophysics Data System (ADS)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds

NASA Astrophysics Data System (ADS)

Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung

2016-06-01

We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

Two dissimilar approaches to dynamical systems on hyper MV -algebras and their information entropy

NASA Astrophysics Data System (ADS)

Mehrpooya, Adel; Ebrahimi, Mohammad; Davvaz, Bijan

2017-09-01

Measuring the flow of information that is related to the evolution of a system which is modeled by applying a mathematical structure is of capital significance for science and usually for mathematics itself. Regarding this fact, a major issue in concern with hyperstructures is their dynamics and the complexity of the varied possible dynamics that exist over them. Notably, the dynamics and uncertainty of hyper MV -algebras which are hyperstructures and extensions of a central tool in infinite-valued Lukasiewicz propositional calculus that models many valued logics are of primary concern. Tackling this problem, in this paper we focus on the subject of dynamical systems on hyper MV -algebras and their entropy. In this respect, we adopt two varied approaches. One is the set-based approach in which hyper MV -algebra dynamical systems are developed by employing set functions and set partitions. By the other method that is based on points and point partitions, we establish the concept of hyper injective dynamical systems on hyper MV -algebras. Next, we study the notion of entropy for both kinds of systems. Furthermore, we consider essential ergodic characteristics of those systems and their entropy. In particular, we introduce the concept of isomorphic hyper injective and hyper MV -algebra dynamical systems, and we demonstrate that isomorphic systems have the same entropy. We present a couple of theorems in order to help calculate entropy. In particular, we prove a contemporary version of addition and Kolmogorov-Sinai Theorems. Furthermore, we provide a comparison between the indispensable properties of hyper injective and semi-independent dynamical systems. Specifically, we present and prove theorems that draw comparisons between the entropies of such systems. Lastly, we discuss some possible relationships between the theories of hyper MV -algebra and MV -algebra dynamical systems.

Analysis of Costs in an Algebra I Curriculum Effectiveness Study. Technical Report

ERIC Educational Resources Information Center

Daugherty, Lindsay; Phillips, Andrea; Pane, John F.; Karam, Rita

2012-01-01

In an ongoing study, RAND researchers are evaluating the effectiveness of Carnegie Learning's Cognitive Tutor Algebra I (CTAI) curriculum, a technology-based curriculum that combines classroom instruction with individualized instruction by a computer-based tutor. While the effectiveness of the curriculum in raising student achievement is the main…

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…

Blob-enhanced reconstruction technique

NASA Astrophysics Data System (ADS)

Castrillo, Giusy; Cafiero, Gioacchino; Discetti, Stefano; Astarita, Tommaso

2016-09-01

A method to enhance the quality of the tomographic reconstruction and, consequently, the 3D velocity measurement accuracy, is presented. The technique is based on integrating information on the objects to be reconstructed within the algebraic reconstruction process. A first guess intensity distribution is produced with a standard algebraic method, then the distribution is rebuilt as a sum of Gaussian blobs, based on location, intensity and size of agglomerates of light intensity surrounding local maxima. The blobs substitution regularizes the particle shape allowing a reduction of the particles discretization errors and of their elongation in the depth direction. The performances of the blob-enhanced reconstruction technique (BERT) are assessed with a 3D synthetic experiment. The results have been compared with those obtained by applying the standard camera simultaneous multiplicative reconstruction technique (CSMART) to the same volume. Several blob-enhanced reconstruction processes, both substituting the blobs at the end of the CSMART algorithm and during the iterations (i.e. using the blob-enhanced reconstruction as predictor for the following iterations), have been tested. The results confirm the enhancement in the velocity measurements accuracy, demonstrating a reduction of the bias error due to the ghost particles. The improvement is more remarkable at the largest tested seeding densities. Additionally, using the blobs distributions as a predictor enables further improvement of the convergence of the reconstruction algorithm, with the improvement being more considerable when substituting the blobs more than once during the process. The BERT process is also applied to multi resolution (MR) CSMART reconstructions, permitting simultaneously to achieve remarkable improvements in the flow field measurements and to benefit from the reduction in computational time due to the MR approach. Finally, BERT is also tested on experimental data, obtaining an increase of the signal-to-noise ratio in the reconstructed flow field and a higher value of the correlation factor in the velocity measurements with respect to the volume to which the particles are not replaced.

Statistical mechanics of broadcast channels using low-density parity-check codes.

PubMed

Nakamura, Kazutaka; Kabashima, Yoshiyuki; Morelos-Zaragoza, Robert; Saad, David

2003-03-01

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

Invariant resolutions for several Fueter operators

NASA Astrophysics Data System (ADS)

Colombo, Fabrizio; Souček, Vladimir; Struppa, Daniele C.

2006-07-01

A proper generalization of complex function theory to higher dimension is Clifford analysis and an analogue of holomorphic functions of several complex variables were recently described as the space of solutions of several Dirac equations. The four-dimensional case has special features and is closely connected to functions of quaternionic variables. In this paper we present an approach to the Dolbeault sequence for several quaternionic variables based on symmetries and representation theory. In particular we prove that the resolution of the Cauchy-Fueter system obtained algebraically, via Gröbner bases techniques, is equivalent to the one obtained by R.J. Baston (J. Geom. Phys. 1992).

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Analysis of eletrectrohydrodynamic jetting using multifunctional and three-dimensional tomography

NASA Astrophysics Data System (ADS)

Ko, Han Seo; Nguyen, Xuan Hung; Lee, Soo-Hong; Kim, Young Hyun

2013-11-01

Three-dimensional optical tomography technique was developed to reconstruct three-dimensional flow fields using a set of two-dimensional shadowgraphic images and normal gray images. From three high speed cameras, which were positioned at an offset angle of 45° relative to one another, number, size and location of electrohydrodynamic jets with respect to the nozzle position were analyzed using shadowgraphic tomography employing a multiplicative algebraic reconstruction technique (MART). Additionally, a flow field inside cone-shaped liquid (Taylor cone) which was induced under electric field was also observed using a simultaneous multiplicative algebraic reconstruction technique (SMART) for reconstructing intensities of particle light and combining with a three-dimensional cross correlation. Various velocity fields of a circulating flow inside the cone-shaped liquid due to different physico-chemical properties of liquid and applied voltages were also investigated. This work supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean government (MEST) (No. S-2011-0023457).

Assessing the Effectiveness of Studio Physics in Introductory-Level Courses at Georgia State University

NASA Astrophysics Data System (ADS)

Upton, Brianna; Evans, John; Morrow, Cherilynn; Thoms, Brian

2009-11-01

Previous studies have shown that many students have misconceptions about basic concepts in physics. Moreover, it has been concluded that one of the challenges lies in the teaching methodology. To address this, Georgia State University has begun teaching studio algebra-based physics. Although many institutions have implemented studio physics, most have done so in calculus-based sequences. The effectiveness of the studio approach in an algebra-based introductory physics course needs further investigation. A 3-semester study assessing the effectiveness of studio physics in an algebra-based physics sequence has been performed. This study compares the results of student pre- and post-tests using the Force Concept Inventory. Using the results from this assessment tool, we will discuss the effectiveness of the studio approach to teaching physics at GSU.

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

A tensor approach to modeling of nonhomogeneous nonlinear systems

NASA Technical Reports Server (NTRS)

Yurkovich, S.; Sain, M.

1980-01-01

Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.

Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1997-01-01

An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.

Exceptional quantum geometry and particle physics

NASA Astrophysics Data System (ADS)

Dubois-Violette, Michel

2016-11-01

Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group SU (3) and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to the exceptional real Jordan algebra of dimension 27 (the Euclidean Albert algebra) is relevant for the description of internal spaces in the theory of particles. In particular, the triality which corresponds to the 3 off-diagonal octonionic elements of the exceptional algebra is associated to the 3 generations of the Standard Model while the representation of the octonions as a complex 4-dimensional space C ⊕C3 is associated to the quark-lepton symmetry (one complex for the lepton and 3 for the corresponding quark). More generally it is suggested that the replacement of the algebra of real functions on spacetime by the algebra of functions on spacetime with values in a finite-dimensional Euclidean Jordan algebra which plays the role of "the algebra of real functions" on the corresponding almost classical quantum spacetime is relevant in particle physics. This leads us to study the theory of Jordan modules and to develop the differential calculus over Jordan algebras (i.e. to introduce the appropriate notion of differential forms). We formulate the corresponding definition of connections on Jordan modules.

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.

Classical Affine W-Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2018-06-01

We prove that any classical affine W-algebra W (g, f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.

Mapping chemicals in air using an environmental CAT scanning system: evaluation of algorithms

NASA Astrophysics Data System (ADS)

Samanta, A.; Todd, L. A.

A new technique is being developed which creates near real-time maps of chemical concentrations in air for environmental and occupational environmental applications. This technique, we call Environmental CAT Scanning, combines the real-time measuring technique of open-path Fourier transform infrared spectroscopy with the mapping capabilitites of computed tomography to produce two-dimensional concentration maps. With this system, a network of open-path measurements is obtained over an area; measurements are then processed using a tomographic algorithm to reconstruct the concentrations. This research focussed on the process of evaluating and selecting appropriate reconstruction algorithms, for use in the field, by using test concentration data from both computer simultation and laboratory chamber studies. Four algorithms were tested using three types of data: (1) experimental open-path data from studies that used a prototype opne-path Fourier transform/computed tomography system in an exposure chamber; (2) synthetic open-path data generated from maps created by kriging point samples taken in the chamber studies (in 1), and; (3) synthetic open-path data generated using a chemical dispersion model to create time seires maps. The iterative algorithms used to reconstruct the concentration data were: Algebraic Reconstruction Technique without Weights (ART1), Algebraic Reconstruction Technique with Weights (ARTW), Maximum Likelihood with Expectation Maximization (MLEM) and Multiplicative Algebraic Reconstruction Technique (MART). Maps were evaluated quantitatively and qualitatively. In general, MART and MLEM performed best, followed by ARTW and ART1. However, algorithm performance varied under different contaminant scenarios. This study showed the importance of using a variety of maps, particulary those generated using dispersion models. The time series maps provided a more rigorous test of the algorithms and allowed distinctions to be made among the algorithms. A comprehensive evaluation of algorithms, for the environmental application of tomography, requires the use of a battery of test concentration data before field implementation, which models reality and tests the limits of the algorithms.

Brain activity associated with translation from a visual to a symbolic representation in algebra and geometry.

PubMed

Leikin, Mark; Waisman, Ilana; Shaul, Shelley; Leikin, Roza

2014-03-01

This paper presents a small part of a larger interdisciplinary study that investigates brain activity (using event related potential methodology) of male adolescents when solving mathematical problems of different types. The study design links mathematics education research with neurocognitive studies. In this paper we performed a comparative analysis of brain activity associated with the translation from visual to symbolic representations of mathematical objects in algebra and geometry. Algebraic tasks require translation from graphical to symbolic representation of a function, whereas tasks in geometry require translation from a drawing of a geometric figure to a symbolic representation of its property. The findings demonstrate that electrical activity associated with the performance of geometrical tasks is stronger than that associated with solving algebraic tasks. Additionally, we found different scalp topography of the brain activity associated with algebraic and geometric tasks. Based on these results, we argue that problem solving in algebra and geometry is associated with different patterns of brain activity.

A tire contact solution technique

NASA Technical Reports Server (NTRS)

Tielking, J. T.

1983-01-01

An efficient method for calculating the contact boundary and interfacial pressure distribution was developed. This solution technique utilizes the discrete Fourier transform to establish an influence coefficient matrix for the portion of the pressurized tire surface that may be in the contact region. This matrix is used in a linear algebra algorithm to determine the contact boundary and the array of forces within the boundary that are necessary to hold the tire in equilibrium against a specified contact surface. The algorithm also determines the normal and tangential displacements of those points on the tire surface that are included in the influence coefficient matrix. Displacements within and outside the contact region are calculated. The solution technique is implemented with a finite-element tire model that is based on orthotropic, nonlinear shell of revolution elements which can respond to nonaxisymmetric loads. A sample contact solution is presented.

Decomposition Theory in the Teaching of Elementary Linear Algebra.

ERIC Educational Resources Information Center

London, R. R.; Rogosinski, H. P.

1990-01-01

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Lumped Model Generation and Evaluation: Sensitivity and Lie Algebraic Techniques with Applications to Combustion

DTIC Science & Technology

1989-03-03

address global parameter space mapping issues for first order differential equations. The rigorous criteria for the existence of exact lumping by linear projective transformations was also established.

Application of Canonical Effective Methods to Background-Independent Theories

NASA Astrophysics Data System (ADS)

Buyukcam, Umut

Effective formalisms play an important role in analyzing phenomena above some given length scale when complete theories are not accessible. In diverse exotic but physically important cases, the usual path-integral techniques used in a standard Quantum Field Theory approach seldom serve as adequate tools. This thesis exposes a new effective method for quantum systems, called the Canonical Effective Method, which owns particularly wide applicability in backgroundindependent theories as in the case of gravitational phenomena. The central purpose of this work is to employ these techniques to obtain semi-classical dynamics from canonical quantum gravity theories. Application to non-associative quantum mechanics is developed and testable results are obtained. Types of non-associative algebras relevant for magnetic-monopole systems are discussed. Possible modifications of hypersurface deformation algebra and the emergence of effective space-times are presented. iii.

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters.

PubMed

Manjappa, Rakesh; Makki S, Sharath; Kumar, Rajesh; Kanhirodan, Rajan

2015-02-01

Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending. The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at the inhomogeneities. Jacob's ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented. The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented. The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results.

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manjappa, Rakesh; Makki S, Sharath; Kanhirodan, Rajan, E-mail: rajan@physics.iisc.ernet.in

2015-02-15

Purpose: Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending. Methods: The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at themore » inhomogeneities. Jacob’s ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented. Results: The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented. Conclusions: The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results.« less

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%…

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…

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.

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.

Algorithms for Hyperspectral Endmember Extraction and Signature Classification with Morphological Dendritic Networks

NASA Astrophysics Data System (ADS)

Schmalz, M.; Ritter, G.

Accurate multispectral or hyperspectral signature classification is key to the nonimaging detection and recognition of space objects. Additionally, signature classification accuracy depends on accurate spectral endmember determination [1]. Previous approaches to endmember computation and signature classification were based on linear operators or neural networks (NNs) expressed in terms of the algebra (R, +, x) [1,2]. Unfortunately, class separation in these methods tends to be suboptimal, and the number of signatures that can be accurately classified often depends linearly on the number of NN inputs. This can lead to poor endmember distinction, as well as potentially significant classification errors in the presence of noise or densely interleaved signatures. In contrast to traditional CNNs, autoassociative morphological memories (AMM) are a construct similar to Hopfield autoassociatived memories defined on the (R, +, ?,?) lattice algebra [3]. Unlimited storage and perfect recall of noiseless real valued patterns has been proven for AMMs [4]. However, AMMs suffer from sensitivity to specific noise models, that can be characterized as erosive and dilative noise. On the other hand, the prior definition of a set of endmembers corresponds to material spectra lying on vertices of the minimum convex region covering the image data. These vertices can be characterized as morphologically independent patterns. It has further been shown that AMMs can be based on dendritic computation [3,6]. These techniques yield improved accuracy and class segmentation/separation ability in the presence of highly interleaved signature data. In this paper, we present a procedure for endmember determination based on AMM noise sensitivity, which employs morphological dendritic computation. We show that detected endmembers can be exploited by AMM based classification techniques, to achieve accurate signature classification in the presence of noise, closely spaced or interleaved signatures, and simulated camera optical distortions. In particular, we examine two critical cases: (1) classification of multiple closely spaced signatures that are difficult to separate using distance measures, and (2) classification of materials in simulated hyperspectral images of spaceborne satellites. In each case, test data are derived from a NASA database of space material signatures. Additional analysis pertains to computational complexity and noise sensitivity, which are superior to classical NN based techniques.

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.

An efficient solution technique for shockwave-boundary layer interactions with flow separation and slot suction effects

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. Scott

1991-01-01

An efficient method for computing two-dimensional compressible Navier-Stokes flow fields is presented. The solution algorithm is a fully-implicit approximate factorization technique based on an unsymmetric line Gauss-Seidel splitting of the equation system Jacobian matrix. Convergence characteristics are improved by the addition of acceleration techniques based on Shamanskii's method for nonlinear equations and Broyden's quasi-Newton update. Characteristic-based differencing of the equations is provided by means of Van Leer's flux vector splitting. In this investigation, emphasis is placed on the fast and accurate computation of shock-wave-boundary layer interactions with and without slot suction effects. In the latter context, a set of numerical boundary conditions for simulating the transpiration flow in an open slot is devised. Both laminar and turbulent cases are considered, with turbulent closure provided by a modified Cebeci-Smith algebraic model. Comparisons with computational and experimental data sets are presented for a variety of interactions, and a fully-coupled simulation of a plenum chamber/inlet flowfield with shock interaction and suction is also shown and discussed.

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

Atomic temporal interval relations in branching time: calculation and application

NASA Astrophysics Data System (ADS)

Anger, Frank D.; Ladkin, Peter B.; Rodriguez, Rita V.

1991-03-01

A practical method of reasoning about intervals in a branching-time model which is dense, unbounded, future-branching, without rejoining branches is presented. The discussion is based on heuristic constraint- propagation techniques using the relation algebra of binary temporal relations among the intervals over the branching-time model. This technique has been applied with success to models of intervals over linear time by Allen and others, and is of cubic-time complexity. To extend it to branding-time models, it is necessary to calculate compositions of the relations; thus, the table of compositions for the 'atomic' relations is computed, enabling the rapid determination of the composition of arbitrary relations, expressed as disjunctions or unions of the atomic relations.

Does Early Algebraic Reasoning Differ as a Function of Students’ Difficulty with Calculations versus Word Problems?

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.

2014-01-01

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044

Analysis of algebraic reasoning ability of cognitive style perspectives on field dependent field independent and gender

NASA Astrophysics Data System (ADS)

Rosita, N. T.

2018-03-01

The purpose of this study is to analyse algebraic reasoning ability using the SOLO model as a theoretical framework to assess students’ algebraic reasoning abilities of Field Dependent cognitive (FD), Field Independent (FI) and Gender perspectives. The method of this study is a qualitative research. The instrument of this study is the researcher himself assisted with algebraic reasoning tests, the problems have been designed based on NCTM indicators and algebraic reasoning according to SOLO model. While the cognitive style of students is determined using Group Embedded Figure Test (GEFT), as well as interviews on the subject as triangulation. The subjects are 15 female and 15 males of the sixth semester students of mathematics education, STKIP Sebelas April. The results of the qualitative data analysis is that most subjects are at the level of unistructural and multi-structural, subjects at the relational level have difficulty in forming a new linear pattern. While the subjects at the extended abstract level are able to meet all the indicators of algebraic reasoning ability even though some of the answers are not perfect yet. Subjects of FI tend to have higher algebraic reasoning abilities than of the subject of FD.

Using Psychometric Technology in Educational Assessment: The Case of a Schema-Based Isomorphic Approach to the Automatic Generation of Quantitative Reasoning Items

ERIC Educational Resources Information Center

Arendasy, Martin; Sommer, Markus

2007-01-01

This article deals with the investigation of the psychometric quality and constructs validity of algebra word problems generated by means of a schema-based version of the automatic min-max approach. Based on review of the research literature in algebra word problem solving and automatic item generation this new approach is introduced as a…

Relational Algebra in Spatial Decision Support Systems Ontologies.

PubMed

Diomidous, Marianna; Chardalias, Kostis; Koutonias, Panagiotis; Magnita, Adrianna; Andrianopoulos, Charalampos; Zimeras, Stelios; Mechili, Enkeleint Aggelos

2017-01-01

Decision Support Systems (DSS) is a powerful tool, for facilitates researchers to choose the correct decision based on their final results. Especially in medical cases where doctors could use these systems, to overcome the problem with the clinical misunderstanding. Based on these systems, queries must be constructed based on the particular questions that doctors must answer. In this work, combination between questions and queries would be presented via relational algebra.

C-arm technique using distance driven method for nephrolithiasis and kidney stones detection

NASA Astrophysics Data System (ADS)

Malalla, Nuhad; Sun, Pengfei; Chen, Ying; Lipkin, Michael E.; Preminger, Glenn M.; Qin, Jun

2016-04-01

Distance driven represents a state of art method that used for reconstruction for x-ray techniques. C-arm tomography is an x-ray imaging technique that provides three dimensional information of the object by moving the C-shaped gantry around the patient. With limited view angle, C-arm system was investigated to generate volumetric data of the object with low radiation dosage and examination time. This paper is a new simulation study with two reconstruction methods based on distance driven including: simultaneous algebraic reconstruction technique (SART) and Maximum Likelihood expectation maximization (MLEM). Distance driven is an efficient method that has low computation cost and free artifacts compared with other methods such as ray driven and pixel driven methods. Projection images of spherical objects were simulated with a virtual C-arm system with a total view angle of 40 degrees. Results show the ability of limited angle C-arm technique to generate three dimensional images with distance driven reconstruction.

Birman—Wenzl—Murakami Algebra and Topological Basis

NASA Astrophysics Data System (ADS)

Zhou, Cheng-Cheng; Xue, Kang; Wang, Gang-Cheng; Sun, Chun-Fang; Du, Gui-Jiao

2012-02-01

In this paper, we use entangled states to construct 9 × 9-matrix representations of Temperley—Lieb algebra (TLA), then a family of 9 × 9-matrix representations of Birman—Wenzl—Murakami algebra (BWMA) have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast nine-dimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special case.

Multiple Alternatives for Educational Evaluation and Decision-Making. Interim Draft. Paper and Report Series No. 72.

ERIC Educational Resources Information Center

Wholeben, Brent E.

This volume is an exposition of a mathematical modeling technique for use in the evaluation and solution of complex educational problems at all levels. It explores in detail the application of simple algebraic techniques to such issues as program reduction, fiscal rollbacks, and computer curriculum planning. Part I ("Introduction to the…

A Jigsaw Lesson for Operations of Complex Numbers.

ERIC Educational Resources Information Center

Lucas, Carol A.

2000-01-01

Explains the cooperative learning technique of jigsaw. Details the use of a jigsaw lesson for explaining complex numbers to intermediate algebra students. Includes copies of the handouts given to the expert groups. (Author/ASK)

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Combined geometric and algebraic solutions for removal of bSSFP banding artifacts with performance comparisons.

PubMed

Hoff, Michael N; Andre, Jalal B; Xiang, Qing-San

2017-02-01

Balanced steady state free precession (bSSFP) imaging suffers from off-resonance artifacts such as signal modulation and banding. Solutions for removal of bSSFP off-resonance dependence are described and compared, and an optimal solution is proposed. An Algebraic Solution (AS) that complements a previously described Geometric Solution (GS) is derived from four phase-cycled bSSFP datasets. A composite Geometric-Algebraic Solution (GAS) is formed from a noise-variance-weighted average of the AS and GS images. Two simulations test the solutions over a range of parameters, and phantom and in vivo experiments are implemented. Image quality and performance of the GS, AS, and GAS are compared with the complex sum and a numerical parameter estimation algorithm. The parameter estimation algorithm, GS, AS, and GAS remove most banding and signal modulation in bSSFP imaging. The variable performance of the GS and AS on noisy data justifies generation of the GAS, which consistently provides the highest performance. The GAS is a robust technique for bSSFP signal demodulation that balances the regional efficacy of the GS and AS to remove banding, a feat not possible with prevalent techniques. Magn Reson Med 77:644-654, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

[From Algebra as art to School Algebra : The textbooks written by Pierre de La Ramée, Bernard Salignac and Lazare Schöner].

PubMed

Loget, François

2011-01-01

Bernard Salignac and Lazare Schöner both published a treatise based on La Ramée's Algebra. Why did they endeavour to republish a book that their master had abandoned ? What changes did they make in the original ? They turned algebra into apedagogical discipline at a time when Ramism was making its presence felt in some Northern European educational establishments. Salignac took La Ramée's thoughts concerning the language of mathematics further and offered an original and precocious contribution to what I call the "scriptural turn" of mathematics at the end of the 16(th) century.

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.

Comparing Cognitive Models of Domain Mastery and Task Performance in Algebra: Validity Evidence for a State Assessment

ERIC Educational Resources Information Center

Warner, Zachary B.

2013-01-01

This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

Investigating the Use of Mastery-Style Online Homework Exercises in Introductory Algebra-Based Mechanics in a Controlled Clinical Study

ERIC Educational Resources Information Center

Evans, William R.; Selen, Mats A.

2017-01-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs. traditional-style homework with students in both algebra-based and…

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…

Microscopic approach based on a multiscale algebraic version of the resonating group model for radiative capture reactions

NASA Astrophysics Data System (ADS)

Solovyev, Alexander S.; Igashov, Sergey Yu.

2017-12-01

A microscopic approach to description of radiative capture reactions based on a multiscale algebraic version of the resonating group model is developed. The main idea of the approach is to expand wave functions of discrete spectrum and continuum for a nuclear system over different bases of the algebraic version of the resonating group model. These bases differ from each other by values of oscillator radius playing a role of scale parameter. This allows us in a unified way to calculate total and partial cross sections (astrophysical S factors) as well as branching ratio for the radiative capture reaction, to describe phase shifts for the colliding nuclei in the initial channel of the reaction, and at the same time to reproduce breakup thresholds of the final nucleus. The approach is applied to the theoretical study of the mirror 3H(α ,γ )7Li and 3He(α ,γ )7Be reactions, which are of great interest to nuclear astrophysics. The calculated results are compared with existing experimental data and with our previous calculations in the framework of the single-scale algebraic version of the resonating group model.

BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1994-01-01

The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

NASA Astrophysics Data System (ADS)

Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

2018-05-01

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

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.

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

Control and stabilization of decentralized systems

NASA Technical Reports Server (NTRS)

Byrnes, Christopher I.; Gilliam, David; Martin, Clyde F.

1989-01-01

Proceeding from the problem posed by the need to stabilize the motion of two helicopters maneuvering a single load, a methodology is developed for the stabilization of classes of decentralized systems based on a more algebraic approach, which involves the external symmetries of decentralized systems. Stabilizing local-feedback laws are derived for any class of decentralized systems having a semisimple algebra of symmetries; the helicopter twin-lift problem, as well as certain problems involving the stabilization of discretizations of distributed parameter problems, have just such algebras of symmetries.

Lunar terrain mapping and relative-roughness analysis

USGS Publications Warehouse

Rowan, Lawrence C.; McCauley, John F.; Holm, Esther A.

1971-01-01

Terrain maps of the equatorial zone (long 70° E.-70° W. and lat 10° N-10° S.) were prepared at scales of 1:2,000,000 and 1:1,000,000 to classify lunar terrain with respect to roughness and to provide a basis for selecting sites for Surveyor and Apollo landings as well as for Ranger and Lunar Orbiter photographs. The techniques that were developed as a result of this effort can be applied to future planetary exploration. By using the best available earth-based observational data and photographs 1:1,000,000-scale and U.S. Geological Survey lunar geologic maps and U.S. Air Force Aeronautical Chart and Information Center LAC charts, lunar terrain was described by qualitative and quantitative methods and divided into four fundamental classes: maria, terrae, craters, and linear features. Some 35 subdivisions were defined and mapped throughout the equatorial zone, and, in addition, most of the map units were illustrated by photographs. The terrain types were analyzed quantitatively to characterize and order their relative-roughness characteristics. Approximately 150,000 east-west slope measurements made by a photometric technique (photoclinometry) in 51 sample areas indicate that algebraic slope-frequency distributions are Gaussian, and so arithmetic means and standard deviations accurately describe the distribution functions. The algebraic slope-component frequency distributions are particularly useful for rapidly determining relative roughness of terrain. The statistical parameters that best describe relative roughness are the absolute arithmetic mean, the algebraic standard deviation, and the percentage of slope reversal. Statistically derived relative-relief parameters are desirable supplementary measures of relative roughness in the terrae. Extrapolation of relative roughness for the maria was demonstrated using Ranger VII slope-component data and regional maria slope data, as well as the data reported here. It appears that, for some morphologically homogeneous mare areas, relative roughness can be extrapolated to the large scales from measurements at small scales.

[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.

Resolution Study of a Hyperspectral Sensor using Computed Tomography in the Presence of Noise

DTIC Science & Technology

2012-06-14

diffraction efficiency is dependent on wavelength. Compared to techniques developed by later work, simple algebraic reconstruction techniques were used...spectral di- mension, using computed tomography (CT) techniques with only a finite number of diverse images. CTHIS require a reconstruction algorithm in...many frames are needed to reconstruct the spectral cube of a simple object using a theoretical lower bound. In this research a new algorithm is derived

Linearized gravity in terms of differential forms

NASA Astrophysics Data System (ADS)

Baykal, Ahmet; Dereli, Tekin

2017-01-01

A technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior algebra of differential forms.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Matthew Reynolds | NREL

Science.gov Websites

food science. Matthew's research at NREL is focused on applying uncertainty quantification techniques . Research Interests Uncertainty quantification Computational multilinear algebra Approximation theory of and the Canonical Tensor Decomposition, Journal of Computational Physics (2017) Randomized Alternating

Robust image retrieval from noisy inputs using lattice associative memories

NASA Astrophysics Data System (ADS)

Urcid, Gonzalo; Nieves-V., José Angel; García-A., Anmi; Valdiviezo-N., Juan Carlos

2009-02-01

Lattice associative memories also known as morphological associative memories are fully connected feedforward neural networks with no hidden layers, whose computation at each node is carried out with lattice algebra operations. These networks are a relatively recent development in the field of associative memories that has proven to be an alternative way to work with sets of pattern pairs for which the storage and retrieval stages use minimax algebra. Different associative memory models have been proposed to cope with the problem of pattern recall under input degradations, such as occlusions or random noise, where input patterns can be composed of binary or real valued entries. In comparison to these and other artificial neural network memories, lattice algebra based memories display better performance for storage and recall capability; however, the computational techniques devised to achieve that purpose require additional processing or provide partial success when inputs are presented with undetermined noise levels. Robust retrieval capability of an associative memory model is usually expressed by a high percentage of perfect recalls from non-perfect input. The procedure described here uses noise masking defined by simple lattice operations together with appropriate metrics, such as the normalized mean squared error or signal to noise ratio, to boost the recall performance of either the min or max lattice auto-associative memories. Using a single lattice associative memory, illustrative examples are given that demonstrate the enhanced retrieval of correct gray-scale image associations from inputs corrupted with random noise.

Graphical construction of a local perspective on differentiation and integration

NASA Astrophysics Data System (ADS)

Hong, Ye Yoon; Thomas, Michael O. J.

2015-06-01

Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually established through the school curriculum to a view of function that includes a local, or interval, perspective. This is necessary for study of concepts such as continuity and limit that underpin calculus and analysis at university. In this study, a first-year university calculus course in Korea was constructed that integrated use of digital technology and considered the epistemic value of the associated techniques. The aim was to encourage versatile thinking about functions, especially in relation to properties arising from a graphical investigation of differentiation and integration. In this paper, the results of this approach for the learning of derivative and antiderivative, based on integrated technology use, are presented. They show the persistence of what Tall ( Mathematics Education Research Journal, 20(2), 5-24, 2008) describes as symbolic world algebraic thinking on the part of a significant minority of students, who feel the need to introduce algebraic methods, in spite of its disadvantages, even when no explicit algebra is provided. However, the results also demonstrate the ability of many of the students to use technology mediation to build local or interval conceptual thinking about derivative and antiderivative functions.

The analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference

NASA Astrophysics Data System (ADS)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

The aim of this study was to describe the analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference. The purpose of this study is to describe the analysis of mathematics teacher's learning on limit algebraic functions in terms of the differences of teaching experience. Learning analysis focused on Pedagogical Content Knowledge (PCK) of teachers in mathematics on limit algebraic functions related to the knowledge of pedagogy. PCK of teachers on limit algebraic function is a type of specialized knowledge for teachers on how to teach limit algebraic function that can be understood by students. Subjects are two high school mathematics teacher who has difference of teaching experience they are one Novice Teacher (NP) and one Experienced Teacher (ET). Data are collected through observation of learning in the class, videos of learning, and then analyzed using qualitative analysis. Teacher's knowledge of Pedagogic defined as a knowledge and understanding of teacher about planning and organizing of learning, and application of learning strategy. The research results showed that the Knowledge of Pedagogy on subject NT in mathematics learning on the material of limit function algebra showed that the subject NT tended to describe procedurally, without explaining the reasons why such steps were used, asking questions which tended to be monotonous not be guiding and digging deeper, and less varied in the use of learning strategies while subject ET gave limited guidance and opportunities to the students to find their own answers, exploit the potential of students to answer questions, provide an opportunity for students to interact and work in groups, and subject ET tended to combine conceptual and procedural explanation.

Automatic Blocking Of QR and LU Factorizations for Locality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yi, Q; Kennedy, K; You, H

2004-03-26

QR and LU factorizations for dense matrices are important linear algebra computations that are widely used in scientific applications. To efficiently perform these computations on modern computers, the factorization algorithms need to be blocked when operating on large matrices to effectively exploit the deep cache hierarchy prevalent in today's computer memory systems. Because both QR (based on Householder transformations) and LU factorization algorithms contain complex loop structures, few compilers can fully automate the blocking of these algorithms. Though linear algebra libraries such as LAPACK provides manually blocked implementations of these algorithms, by automatically generating blocked versions of the computations, moremore » benefit can be gained such as automatic adaptation of different blocking strategies. This paper demonstrates how to apply an aggressive loop transformation technique, dependence hoisting, to produce efficient blockings for both QR and LU with partial pivoting. We present different blocking strategies that can be generated by our optimizer and compare the performance of auto-blocked versions with manually tuned versions in LAPACK, both using reference BLAS, ATLAS BLAS and native BLAS specially tuned for the underlying machine architectures.« less

A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.

PubMed

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-06-21

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate [Formula: see text]. In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques.

GRID3D-v2: An updated version of the GRID2D/3D computer program for generating grid systems in complex-shaped three-dimensional spatial domains

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Shih, T. I-P.; Roelke, R. J.

1991-01-01

In order to generate good quality systems for complicated three-dimensional spatial domains, the grid-generation method used must be able to exert rather precise controls over grid-point distributions. Several techniques are presented that enhance control of grid-point distribution for a class of algebraic grid-generation methods known as the two-, four-, and six-boundary methods. These techniques include variable stretching functions from bilinear interpolation, interpolating functions based on tension splines, and normalized K-factors. The techniques developed in this study were incorporated into a new version of GRID3D called GRID3D-v2. The usefulness of GRID3D-v2 was demonstrated by using it to generate a three-dimensional grid system in the coolent passage of a radial turbine blade with serpentine channels and pin fins.

Four-dimensional modeling of recent vertical movements in the area of the southern California uplift

USGS Publications Warehouse

Vanicek, Petr; Elliot, Michael R.; Castle, Robert O.

1979-01-01

This paper describes an analytical technique that utilizes scattered geodetic relevelings and tide-gauge records to portray Recent vertical crustal movements that may have been characterized by spasmodic changes in velocity. The technique is based on the fitting of a time-varying algebraic surface of prescribed degree to the geodetic data treated as tilt elements and to tide-gauge readings treated as point movements. Desired variations in time can be selected as any combination of powers of vertical movement velocity and episodic events. The state of the modeled vertical displacement can be shown for any number of dates for visual display. Statistical confidence limits of the modeled displacements, derived from the density of measurements in both space and time, line length, and accuracy of input data, are also provided. The capabilities of the technique are demonstrated on selected data from the region of the southern California uplift. 

Effects of Modified Schema-Based Instruction on Real-World Algebra Problem Solving of Students with Autism Spectrum Disorder and Moderate Intellectual Disability

ERIC Educational Resources Information Center

Root, Jenny Rose

2016-01-01

The current study evaluated the effects of modified schema-based instruction (SBI) on the algebra problem solving skills of three middle school students with autism spectrum disorder and moderate intellectual disability (ASD/ID). Participants learned to solve two types of group word problems: missing-whole and missing-part. The themes of the word…

A pseudo-discrete algebraic reconstruction technique (PDART) prior image-based suppression of high density artifacts in computed tomography

NASA Astrophysics Data System (ADS)

Pua, Rizza; Park, Miran; Wi, Sunhee; Cho, Seungryong

2016-12-01

We propose a hybrid metal artifact reduction (MAR) approach for computed tomography (CT) that is computationally more efficient than a fully iterative reconstruction method, but at the same time achieves superior image quality to the interpolation-based in-painting techniques. Our proposed MAR method, an image-based artifact subtraction approach, utilizes an intermediate prior image reconstructed via PDART to recover the background information underlying the high density objects. For comparison, prior images generated by total-variation minimization (TVM) algorithm, as a realization of fully iterative approach, were also utilized as intermediate images. From the simulation and real experimental results, it has been shown that PDART drastically accelerates the reconstruction to an acceptable quality of prior images. Incorporating PDART-reconstructed prior images in the proposed MAR scheme achieved higher quality images than those by a conventional in-painting method. Furthermore, the results were comparable to the fully iterative MAR that uses high-quality TVM prior images.

A simple method for processing data with least square method

NASA Astrophysics Data System (ADS)

Wang, Chunyan; Qi, Liqun; Chen, Yongxiang; Pang, Guangning

2017-08-01

The least square method is widely used in data processing and error estimation. The mathematical method has become an essential technique for parameter estimation, data processing, regression analysis and experimental data fitting, and has become a criterion tool for statistical inference. In measurement data analysis, the distribution of complex rules is usually based on the least square principle, i.e., the use of matrix to solve the final estimate and to improve its accuracy. In this paper, a new method is presented for the solution of the method which is based on algebraic computation and is relatively straightforward and easy to understand. The practicability of this method is described by a concrete example.

The Orbital precession around oblate spheroids

NASA Astrophysics Data System (ADS)

Montanus, J. M. C.

2006-07-01

An exact series will be given for the gravitational potential generated by an oblate gravitating source. To this end the corresponding Epstein-Hubbell type elliptic integral is evaluated. The procedure is based on the Legendre polynomial expansion method and on combinatorial techniques. The result is of interest for gravitational models based on the linearity of the gravitational potential. The series approximation for such potentials is of use for the analysis of orbital motions around a nonspherical source. It can be considered advantageous that the analysis is purely algebraic. Numerical approximations are not required. As an important example, the expression for the orbital precession will be derived for an object orbiting around an oblate homogeneous spheroid.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liakh, Dmitry I

While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locallymore » supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).« less

A mechanized process algebra for verification of device synchronization protocols

NASA Technical Reports Server (NTRS)

Schubert, E. Thomas

1992-01-01

We describe the formalization of a process algebra based on CCS within the Higher Order Logic (HOL) theorem-proving system. The representation of four types of device interactions and a correctness proof of the communication between a microprocessor and MMU is presented.

Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners.

PubMed

Hendler, R W; Shrager, R I

1994-01-01

Singular value decomposition (SVD) is deeply rooted in the theory of linear algebra, and because of this is not readily understood by a large group of researchers who could profit from its application. In this paper, we discuss the subject on a level that should be understandable to scientists who are not well versed in linear algebra. However, because it is necessary that certain key concepts in linear algebra be appreciated in order to comprehend what is accomplished by SVD, we present the section, 'Bare basics of linear algebra'. This is followed by a discussion of the theory of SVD. Next we present step-by-step examples to illustrate how SVD is applied to deconvolute a titration involving a mixture of three pH indicators. One noiseless case is presented as well as two cases where either a fixed or varying noise level is present. Finally, we discuss additional deconvolutions of mixed spectra based on the use of the pseudoinverse.

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 support projection in the center. All together, we see that there are many advantages when we develop the theory of locally compact quantum groups in the von Neumann algebra framework, rather than in the C^*-algebra framework. It is not only simpler, the theory of weights on von Neumann algebras is better known and one needs very little to go from the C^*-algebras to the von Neumann algebras. Moreover, in many cases when constructing examples, the von Neumann algebra with the coproduct is constructed from the very beginning and the Haar weights are constructed as weights on this von Neumann algebra (using left Hilbert algebra theory). This paper is written in a concise way. In many cases, only indications for the proofs of the results are given. This information should be enough to see that these results are correct. We will give more details in forthcoming paper, which will be expository, aimed at non-specialists. See also [Bull. Kerala Math. Assoc. (2005), 153-177] for an 'expanded' version of the appendix.

Many-core graph analytics using accelerated sparse linear algebra routines

NASA Astrophysics Data System (ADS)

Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

2016-05-01

Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

Effective Lagrangians and Current Algebra in Three Dimensions

NASA Astrophysics Data System (ADS)

Ferretti, Gabriele

In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.

Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

NASA Astrophysics Data System (ADS)

Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong

2018-04-01

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

The Resolvent Algebra of Non-relativistic Bose Fields: Observables, Dynamics and States

NASA Astrophysics Data System (ADS)

Buchholz, Detlev

2018-05-01

The structure of the gauge invariant (particle number preserving) C*-algebra generated by the resolvents of a non-relativistic Bose field is analyzed. It is shown to form a dense subalgebra of the bounded inverse limit of a directed system of approximately finite dimensional C*-algebras. Based on this observation, it is proven that the closure of the gauge invariant algebra is stable under the dynamics induced by Hamiltonians involving pair potentials. These facts allow to proceed to a description of interacting Bosons in terms of C*-dynamical systems. It is outlined how the present approach leads to simplifications in the construction of infinite bosonic states and sheds new light on topics in many body theory.

Three-dimensional polarization algebra for all polarization sensitive optical systems.

PubMed

Li, Yahong; Fu, Yuegang; Liu, Zhiying; Zhou, Jianhong; Bryanston-Cross, P J; Li, Yan; He, Wenjun

2018-05-28

Using three-dimensional (3D) coherency vector (9 × 1), we develop a new 3D polarization algebra to calculate the polarization properties of all polarization sensitive optical systems, especially when the incident optical field is partially polarized or un-polarized. The polarization properties of a high numerical aperture (NA) microscope objective (NA = 1.25 immersed in oil) are analyzed based on the proposed 3D polarization algebra. Correspondingly, the polarization simulation of this high NA optical system is performed by the commercial software VirtualLAB Fusion. By comparing the theoretical calculations with polarization simulations, a perfect matching relation is obtained, which demonstrates that this 3D polarization algebra is valid to quantify the 3D polarization properties for all polarization sensitive optical systems.

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.

Accounting for estimated IQ in neuropsychological test performance with regression-based techniques.

PubMed

Testa, S Marc; Winicki, Jessica M; Pearlson, Godfrey D; Gordon, Barry; Schretlen, David J

2009-11-01

Regression-based normative techniques account for variability in test performance associated with multiple predictor variables and generate expected scores based on algebraic equations. Using this approach, we show that estimated IQ, based on oral word reading, accounts for 1-9% of the variability beyond that explained by individual differences in age, sex, race, and years of education for most cognitive measures. These results confirm that adding estimated "premorbid" IQ to demographic predictors in multiple regression models can incrementally improve the accuracy with which regression-based norms (RBNs) benchmark expected neuropsychological test performance in healthy adults. It remains to be seen whether the incremental variance in test performance explained by estimated "premorbid" IQ translates to improved diagnostic accuracy in patient samples. We describe these methods, and illustrate the step-by-step application of RBNs with two cases. We also discuss the rationale, assumptions, and caveats of this approach. More broadly, we note that adjusting test scores for age and other characteristics might actually decrease the accuracy with which test performance predicts absolute criteria, such as the ability to drive or live independently.

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.

1986-01-01

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study.

PubMed

MacLean, Adam L; Harrington, Heather A; Stumpf, Michael P H; Byrne, Helen M

2016-01-01

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Calculation of the change in corneal astigmatism following cataract extraction.

PubMed

Cravy, T V

1979-01-01

Obtaining a minimal amount of postoperative astigmatism following cataract surgery is becoming increasingly important. One aspect of the patient's surgery which should not be overlooked is the preoperative keratometry which provides a basis for preoperative planning of surgical technique to be used and a point of reference for determining the amount of change in astigmatism produced by the surgery. Analysis of the surgically induced change in astigmatism using the calculations described in this paper will allow the surgeon to evaluate his own techniques and to maximize his potential for obtaining consistently good postoperative astigmatic results without the need for suture removal. The method presented is based upon concepts in common use in surgical ophthalmology and requires only simple mathematical procedures, familiar to all with a background in algebra and trigonometry.

Implementation of control point form of algebraic grid-generation technique

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Miller, David P.; Reno, Charles J.

1991-01-01

The control point form (CPF) provides explicit control of physical grid shape and grid spacing through the movement of the control points. The control point array, called a control net, is a space grid type arrangement of locations in physical space with an index for each direction. As an algebraic method CPF is efficient and works well with interactive computer graphics. A family of menu-driven, interactive grid-generation computer codes (TURBO) is being developed by using CPF. Key features of TurboI (a TURBO member) are discussed and typical results are presented. TurboI runs on any IRIS 4D series workstation.

Computerized proof techniques for undergraduates

NASA Astrophysics Data System (ADS)

Smith, Christopher J.; Tefera, Akalu; Zeleke, Aklilu

2012-12-01

The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf-Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete mathematics. We demonstrate by examples how one can use these computerized proof techniques to raise students' interests in the discovery and proof of mathematical identities and enhance their problem-solving skills.

Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style

NASA Astrophysics Data System (ADS)

Indraswari, N. F.; Budayasa, I. K.; Ekawati, R.

2018-01-01

This study aimed to describe algebraic reasoning of secondary school’s pupils with different learning styles in solving mathematical problem. This study begins by giving the questionnaire to find out the learning styles and followed by mathematical ability test to get three subjects of 8th-grade whereas the learning styles of each pupil is visual, auditory, kinesthetic and had similar mathematical abilities. Then it continued with given algebraic problems and interviews. The data is validated using triangulation of time. The result showed that in the pattern of seeking indicator, subjects identified the things that were known and asked based on them observations. The visual and kinesthetic learners represented the known information in a chart, whereas the auditory learner in a table. In addition, they found the elements which makes the pattern and made a relationship between two quantities. In the pattern recognition indicator, they created conjectures on the relationship between two quantities and proved it. In the generalization indicator, they were determining the general rule of pattern found on each element of pattern using algebraic symbols and created a mathematical model. Visual and kinesthetic learners determined the general rule of equations which was used to solve problems using algebraic symbols, but auditory learner in a sentence.

Deriving the Work Done by an Inverse Square Force in Non-Calculus-Based Introductory Physics Courses

ERIC Educational Resources Information Center

Hu, Ben Yu-Kuang

2012-01-01

I describe a method of evaluating the integral of 1/r[superscript 2] with respect to r that uses only algebra and the concept of area underneath a curve, and which does not formally employ any calculus. This is useful for algebra-based introductory physics classes (where the use of calculus is forbidden) to derive the work done by the force of one…

Prime factorization using quantum annealing and computational algebraic geometry

NASA Astrophysics Data System (ADS)

Dridi, Raouf; Alghassi, Hedayat

2017-02-01

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians.

LETTER TO THE EDITOR: Landau levels on the hyperbolic plane

NASA Astrophysics Data System (ADS)

Fakhri, H.; Shariati, M.

2004-11-01

The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength.

Math remediation intervention for student success in the algebra-based introductory physics course

NASA Astrophysics Data System (ADS)

Forrest, Rebecca L.; Stokes, Donna W.; Burridge, Andrea B.; Voight, Carol D.

2017-12-01

Pretesting and early intervention measures to identify and remediate at-risk students were implemented in algebra-based introductory physics to help improve student success rates. Pretesting via a math and problem-solving diagnostic exam administered at the beginning of the course was employed to identify at-risk students based on their scores. At-risk students were encouraged to utilize an online math tutorial to increase their chances of passing the course. The tutorial covers the same math topics covered by the diagnostic exam. Results from 643 students enrolled in the course showed that the 61 at-risk students who successfully completed the math tutorial increased their odds of passing the course by roughly 4 times those of the at-risk students who did not. This intervention is easily implemented, short term, and can be administered concurrently with the course. Based on these results, the Department of Physics has implemented the math tutorials in all sections of the introductory algebra as well as the calculus-based physics courses.

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…

A Linear Algebra Measure of Cluster Quality.

ERIC Educational Resources Information Center

Mather, Laura A.

2000-01-01

Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)

Developing Students' Functional Thinking in Algebra through Different Visualisations of a Growing Pattern's Structure

ERIC Educational Resources Information Center

Wilkie, Karina J.; Clarke, Doug M.

2016-01-01

Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buchstaber, V M; Ustinov, A V

We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients. Bibliography: 37 titles.

Using an Online Tool for Learning about and Implementing Algebra Progress Monitoring

ERIC Educational Resources Information Center

Foegen, Anne; Stecker, Pamela M.; Genareo, Vincent R.; Lyons, Renée; Olson, Jeannette R.; Simpson, Amber; Romig, John Elwood; Jones, Rachel

2016-01-01

Research supports special educators' use of progress-monitoring data for instructional decision-making purposes as an evidence-based practice for improving student achievement. This article describes the Professional Development for Algebra Progress Monitoring (PD-APM) system. PD-APM, is an online system that includes two "hubs" that…

Generalized EMV-Effect Algebras

NASA Astrophysics Data System (ADS)

Borzooei, R. A.; Dvurečenskij, A.; Sharafi, A. H.

2018-04-01

Recently in Dvurečenskij and Zahiri (2017), new algebraic structures, called EMV-algebras which generalize both MV-algebras and generalized Boolean algebras, were introduced. We present equivalent conditions for EMV-algebras. In addition, we define a partial algebraic structure, called a generalized EMV-effect algebra, which is close to generalized MV-effect algebras. Finally, we show that every generalized EMV-effect algebra is either an MV-effect algebra or can be embedded into an MV-effect algebra as a maximal ideal.

Does Calculation or Word-Problem Instruction Provide A Stronger Route to Pre-Algebraic Knowledge?

PubMed Central

Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

2014-01-01

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and pre-algebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to pre-algebraic knowledge. Participants were 1102 children in 127 2nd-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) to pre-algebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to pre-algebraic knowledge. PMID:25541565

Properties of coupled-cluster equations originating in excitation sub-algebras

NASA Astrophysics Data System (ADS)

Kowalski, Karol

2018-03-01

In this paper, we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving the corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending active-space and seniority number concepts to provide an accurate description of electron correlation effects. Moreover, a new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for tough cases defined by the presence of strong static and dynamical correlation effects. We will also explore invariance properties associated with excitation sub-algebras to define a new class of CC approximations referred to in this paper as the sub-algebra-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.

Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities

NASA Astrophysics Data System (ADS)

Adamović, Dražen; Lin, Xianzu; Milas, Antun

2015-03-01

We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c=1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p)^{A_m}) and A(W(p)^{D_m}), where A_m and D_m are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p)^Γ-modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun. Contemp. Math. 15 (2013), 1350028, 30 pages; Internat. J. Math. 25 (2014), 1450001, 34 pages] provide a complete list of irreducible W(p)^{A_m} and W(p)^{D_m}-modules. This paper is a continuation of our previous work on the ADE subalgebras of the triplet vertex algebra W(p).

In Praise of Numerical Computation

NASA Astrophysics Data System (ADS)

Yap, Chee K.

Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms’ design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name “numerical computational geometry” for such activities.

On the stabilizability of multivariable systems by minimum order compensation

NASA Technical Reports Server (NTRS)

Byrnes, C. I.; Anderson, B. D. O.

1983-01-01

In this paper, a derivation is provided of the necessary condition, mp equal to or greater than n, for stabilizability by constant gain feedback of the generic degree n, p x m system. This follows from another of the main results, which asserts that generic stabilizability is equivalent to generic solvability of a deadbeat control problem, provided mp equal to or less than n. Taken together, these conclusions make it possible to make some sharp statements concerning minimum order stabilization. The techniques are primarily drawn from decision algebra and classical algebraic geometry and have additional consequences for problems of stabilizability and pole-assignability. Among these are the decidability (by a Sturm test) of the equivalence of generic pole-assignability and generic stabilizability, the semi-algebraic nature of the minimum order, q, of a stabilizing compensator, and the nonexistence of formulae involving rational operations and extraction of square roots for pole-assigning gains when they exist, answering in the negative a question raised by Anderson, Bose, and Jury (1975).

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Navigating around the algebraic jungle of QCD: efficient evaluation of loop helicity amplitudes

NASA Astrophysics Data System (ADS)

Lam, C. S.

1993-05-01

A method is developed whereby spinor helicity techniques can be used to simlify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear. Other shortcuts motivated by the Bern-Kosower one-loop string calculations can be incorporated into the formalism. This includes color reorganization into Chan-Paton factors and the use of background Feynman gauge. This method is applicable to any Feynman diagram with any number of loops as long as the external masses can be ignored. In order to minimize the very considerable algebra encountered in non-abelian gauge theories, graphical methods are developed for most of the calculations. This enables the large number of terms encountered to be organized implicitly in the Feynman diagram without the necessity of writing down any of them algebraically. A one-loop four-gluon amplitude in a particular helicity configuration is computed explicitly to illustrate the method.

Mathematics and Information Retrieval.

ERIC Educational Resources Information Center

Salton, Gerald

1979-01-01

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

Effective gene prediction by high resolution frequency estimator based on least-norm solution technique

PubMed Central

2014-01-01

Linear algebraic concept of subspace plays a significant role in the recent techniques of spectrum estimation. In this article, the authors have utilized the noise subspace concept for finding hidden periodicities in DNA sequence. With the vast growth of genomic sequences, the demand to identify accurately the protein-coding regions in DNA is increasingly rising. Several techniques of DNA feature extraction which involves various cross fields have come up in the recent past, among which application of digital signal processing tools is of prime importance. It is known that coding segments have a 3-base periodicity, while non-coding regions do not have this unique feature. One of the most important spectrum analysis techniques based on the concept of subspace is the least-norm method. The least-norm estimator developed in this paper shows sharp period-3 peaks in coding regions completely eliminating background noise. Comparison of proposed method with existing sliding discrete Fourier transform (SDFT) method popularly known as modified periodogram method has been drawn on several genes from various organisms and the results show that the proposed method has better as well as an effective approach towards gene prediction. Resolution, quality factor, sensitivity, specificity, miss rate, and wrong rate are used to establish superiority of least-norm gene prediction method over existing method. PMID:24386895

Continuum analogues of contragredient Lie algebras (Lie algebras with a Cartan operator and nonlinear dynamical systems)

NASA Astrophysics Data System (ADS)

Saveliev, M. V.; Vershik, A. M.

1989-12-01

We present an axiomatic formulation of a new class of infinitedimensional Lie algebras-the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras “continuum Lie algebras.” The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered.

Prime factorization using quantum annealing and computational algebraic geometry

PubMed Central

Dridi, Raouf; Alghassi, Hedayat

2017-01-01

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians. PMID:28220854

Spacetime from locality of interactions in deformations of special relativity: The example of κ -Poincaré Hopf algebra

NASA Astrophysics Data System (ADS)

Carmona, J. M.; Cortés, J. L.; Relancio, J. J.

2018-03-01

A new proposal for the notion of spacetime in a relativistic generalization of special relativity based on a modification of the composition law of momenta is presented. Locality of interactions is the principle which defines the spacetime structure for a system of particles. The formulation based on κ -Poincaré Hopf algebra is shown to be contained in this framework as a particular example.

Image Algebra Matlab language version 2.3 for image processing and compression research

NASA Astrophysics Data System (ADS)

Schmalz, Mark S.; Ritter, Gerhard X.; Hayden, Eric

2010-08-01

Image algebra is a rigorous, concise notation that unifies linear and nonlinear mathematics in the image domain. Image algebra was developed under DARPA and US Air Force sponsorship at University of Florida for over 15 years beginning in 1984. Image algebra has been implemented in a variety of programming languages designed specifically to support the development of image processing and computer vision algorithms and software. The University of Florida has been associated with development of the languages FORTRAN, Ada, Lisp, and C++. The latter implementation involved a class library, iac++, that supported image algebra programming in C++. Since image processing and computer vision are generally performed with operands that are array-based, the Matlab™ programming language is ideal for implementing the common subset of image algebra. Objects include sets and set operations, images and operations on images, as well as templates and image-template convolution operations. This implementation, called Image Algebra Matlab (IAM), has been found to be useful for research in data, image, and video compression, as described herein. Due to the widespread acceptance of the Matlab programming language in the computing community, IAM offers exciting possibilities for supporting a large group of users. The control over an object's computational resources provided to the algorithm designer by Matlab means that IAM programs can employ versatile representations for the operands and operations of the algebra, which are supported by the underlying libraries written in Matlab. In a previous publication, we showed how the functionality of IAC++ could be carried forth into a Matlab implementation, and provided practical details of a prototype implementation called IAM Version 1. In this paper, we further elaborate the purpose and structure of image algebra, then present a maturing implementation of Image Algebra Matlab called IAM Version 2.3, which extends the previous implementation of IAM to include polymorphic operations over different point sets, as well as recursive convolution operations and functional composition. We also show how image algebra and IAM can be employed in image processing and compression research, as well as algorithm development and analysis.

Chemical Equation Balancing.

ERIC Educational Resources Information Center

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

"Playing the Game" of Story Problems: Coordinating Situation-Based Reasoning with Algebraic Representation

ERIC Educational Resources Information Center

Walkington, Candace; Sherman, Milan; Petrosino, Anthony

2012-01-01

This study critically examines a key justification used by educational stakeholders for placing mathematics in context--the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were…

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…

Modelling of nanoscale quantum tunnelling structures using algebraic topology method

NASA Astrophysics Data System (ADS)

Sankaran, Krishnaswamy; Sairam, B.

2018-05-01

We have modelled nanoscale quantum tunnelling structures using Algebraic Topology Method (ATM). The accuracy of ATM is compared to the analytical solution derived based on the wave nature of tunnelling electrons. ATM provides a versatile, fast, and simple model to simulate complex structures. We are currently expanding the method for modelling electrodynamic systems.

Avoiding Communication in Dense Linear Algebra

DTIC Science & Technology

2013-08-16

Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Asymptotic Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6...and parallelizing Strassen’s matrix multiplication algorithm (Chapter 11). 6 Chapter 2 Preliminaries 2.1 Notation and Definitions In this section we...between computations and algo- rithms). The following definition is based on [56]: Definition 2.1. A classical algorithm in linear algebra is one that

Analysis of Computer Algebra System Tutorials Using Cognitive Load Theory

ERIC Educational Resources Information Center

May, Patricia

2004-01-01

Most research in the area of Computer Algebra Systems (CAS) has been designed to compare the effectiveness of instructional technology to traditional lecture-based formats. While results are promising, research also indicates evidence of the steep learning curve imposed by the technology. Yet no studies have been conducted to investigate this…

Examining the Implementation of Technology-Based Blended Algebra I Curriculum at Scale

ERIC Educational Resources Information Center

Karam, Rita; Pane, John F.; Griffin, Beth Ann; Robyn, Abby; Phillips, Andrea; Daugherty, Lindsay

2017-01-01

Studies on blended education pay little attention to implementation, thus limiting the understanding of how such programs contribute to student math learning. This article examines the implementation of a widely used blended algebra curriculum and the relationship between implementation and student outcomes. The study was conducted in 74 middle…

Enhancing Mathematical Communication for Virtual Math Teams

ERIC Educational Resources Information Center

Stahl, Gerry; Çakir, Murat Perit; Weimar, Stephen; Weusijana, Baba Kofi; Ou, Jimmy Xiantong

2010-01-01

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies…

Knowledge of Algebra for Teaching: A Framework of Knowledge and Practices

ERIC Educational Resources Information Center

McCrory, Raven; Floden, Robert; Ferrini-Mundy, Joan; Reckase, Mark D.; Senk, Sharon L.

2012-01-01

Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, analysis of video, interviews with teachers, and analysis of textbooks, we define categories of knowledge and practices of teaching for understanding and assessing teachers'…

Superitem Test: An Alternative Assessment Tool to Assess Students' Algebraic Solving Ability

ERIC Educational Resources Information Center

Lian, Lim Hooi; Yew, Wun Thiam; Idris, Noraini

2010-01-01

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

Student Reactions to Learning Theory Based Curriculum Materials in Linear Algebra--A Survey Analysis

ERIC Educational Resources Information Center

Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff

2016-01-01

In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…

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.…

Proposing and Testing a Model to Explain Traits of Algebra Preparedness

ERIC Educational Resources Information Center

Venenciano, Linda; Heck, Ronald

2016-01-01

Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…

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…

High level language-based robotic control system

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo (Inventor); Kruetz, Kenneth K. (Inventor); Jain, Abhinandan (Inventor)

1994-01-01

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robot's environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages.

High level language-based robotic control system

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo (Inventor); Kreutz, Kenneth K. (Inventor); Jain, Abhinandan (Inventor)

1996-01-01

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robot's environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages.

Observables and microscopic entropy of higher spin black holes

NASA Astrophysics Data System (ADS)

Compère, Geoffrey; Jottar, Juan I.; Song, Wei

2013-11-01

In the context of recently proposed holographic dualities between higher spin theories in AdS3 and (1 + 1)-dimensional CFTs with symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[ λ] algebra, and on the sl( N,[InlineMediaObject not available: see fulltext.]) algebra for any choice of sl(2 ,[InlineMediaObject not available: see fulltext.]) embedding.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Analysis of Newton's Third Law Questions on the Force Concepts Inventory at Georgia State University

NASA Astrophysics Data System (ADS)

Oakley, Christopher; Thoms, Brian

2012-03-01

A major emphasis of the Physics Education Research program at Georgia State University is an effort to assess and improve students' understanding of Newton's Laws concepts. As part of these efforts the Force Concepts Inventory (FCI) has been given to students in both the algebra-based and calculus-based introductory physics sequences. In addition, the algebra-based introductory physics sequence is taught in both a SCALE-UP and a traditional lecture format. The results of the FCI have been analyzed by individual question and also as categorized by content. The analysis indicates that students in both algebra and calculus-based courses are successful at overcoming Aristotelian misconceptions regarding Newton's Third Law (N3) in the context of a stationary system. However, students are less successful on N3 questions involving objects in constant motion or accelerating. Interference between understanding of Newton's Second and Third Laws as well as other possible explanations for lower student performance on N3 questions involving non-stationary objects will be discussed.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

Performance of Renormalization Group Algebraic Turbulence Model on Boundary Layer Transition Simulation

NASA Technical Reports Server (NTRS)

Ahn, Kyung H.

1994-01-01

The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.

Two and three dimensional grid generation by an algebraic homotopy procedure

NASA Technical Reports Server (NTRS)

Moitra, Anutosh

1990-01-01

An algebraic method for generating two- and three-dimensional grid systems for aerospace vehicles is presented. The method is based on algebraic procedures derived from homotopic relations for blending between inner and outer boundaries of any given configuration. Stable properties of homotopic maps have been exploited to provide near-orthogonality and specified constant spacing at the inner boundary. The method has been successfully applied to analytically generated blended wing-body configurations as well as discretely defined geometries such as the High-Speed Civil Transport Aircraft. Grid examples representative of the capabilities of the method are presented.

Coherent orthogonal polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-08-15

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relatemore » these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the corresponding OP family. •Generalized coherent polynomials are obtained from OP.« less

A graph algebra for scalable visual analytics.

PubMed

Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V

2012-01-01

Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data.

Architecture studies and system demonstrations for optical parallel processor for AI and NI

NASA Astrophysics Data System (ADS)

Lee, Sing H.

1988-03-01

In solving deterministic AI problems the data search for matching the arguments of a PROLOG expression causes serious bottleneck when implemented sequentially by electronic systems. To overcome this bottleneck we have developed the concepts for an optical expert system based on matrix-algebraic formulation, which will be suitable for parallel optical implementation. The optical AI system based on matrix-algebraic formation will offer distinct advantages for parallel search, adult learning, etc.

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.

Subalgebras of BCK/BCI-Algebras Based on Cubic Soft Sets

PubMed Central

Muhiuddin, G.; Jun, Young Bae

2014-01-01

Operations of cubic soft sets including “AND” operation and “OR” operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, some properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter are discussed. PMID:24895652

Mitigating randomness of consumer preferences under certain conditional choices

NASA Astrophysics Data System (ADS)

Bothos, John M. A.; Thanos, Konstantinos-Georgios; Papadopoulou, Eirini; Daveas, Stelios; Thomopoulos, Stelios C. A.

2017-05-01

Agent-based crowd behaviour consists a significant field of research that has drawn a lot of attention in recent years. Agent-based crowd simulation techniques have been used excessively to forecast the behaviour of larger or smaller crowds in terms of certain given conditions influenced by specific cognition models and behavioural rules and norms, imposed from the beginning. Our research employs conditional event algebra, statistical methodology and agent-based crowd simulation techniques in developing a behavioural econometric model about the selection of certain economic behaviour by a consumer that faces a spectre of potential choices when moving and acting in a multiplex mall. More specifically we try to analyse the influence of demographic, economic, social and cultural factors on the economic behaviour of a certain individual and then we try to link its behaviour with the general behaviour of the crowds of consumers in multiplex malls using agent-based crowd simulation techniques. We then run our model using Generalized Least Squares and Maximum Likelihood methods to come up with the most probable forecast estimations, regarding the agent's behaviour. Our model is indicative about the formation of consumers' spectre of choices in multiplex malls under the condition of predefined preferences and can be used as a guide for further research in this area.

IGB grid: User's manual (A turbomachinery grid generation code)

NASA Technical Reports Server (NTRS)

Beach, T. A.; Hoffman, G.

1992-01-01

A grid generation code called IGB is presented for use in computational investigations of turbomachinery flowfields. It contains a combination of algebraic and elliptic techniques coded for use on an interactive graphics workstation. The instructions for use and a test case are included.

The International Mathematical Olympiad Training Session.

ERIC Educational Resources Information Center

Rousseau, Cecil; Patruno, Gregg

1985-01-01

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

Analysis of Information Content in High-Spectral Resolution Sounders using Subset Selection Analysis

NASA Technical Reports Server (NTRS)

Velez-Reyes, Miguel; Joiner, Joanna

1998-01-01

In this paper, we summarize the results of the sensitivity analysis and data reduction carried out to determine the information content of AIRS and IASI channels. The analysis and data reduction was based on the use of subset selection techniques developed in the linear algebra and statistical community to study linear dependencies in high dimensional data sets. We applied the subset selection method to study dependency among channels by studying the dependency among their weighting functions. Also, we applied the technique to study the information provided by the different levels in which the atmosphere is discretized for retrievals and analysis. Results from the method correlate well with intuition in many respects and point out to possible modifications for band selection in sensor design and number and location of levels in the analysis process.

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. Copyright © 2010 Elsevier Inc. All rights reserved.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fahimian, Benjamin P.; Zhao Yunzhe; Huang Zhifeng

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). Inmore » each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.« less

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

PubMed

Fahimian, Benjamin P; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J; Osher, Stanley J; McNitt-Gray, Michael F; Miao, Jianwei

2013-03-01

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

PubMed Central

Fahimian, Benjamin P.; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J.; Osher, Stanley J.; McNitt-Gray, Michael F.; Miao, Jianwei

2013-01-01

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method. PMID:23464329

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

DOE PAGES

Bank, R.; Falgout, R. D.; Jones, T.; ...

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

Mathematical biodescriptors of proteomics maps: background and applications.

PubMed

Basak, Subhash C; Gute, Brian D

2008-05-01

This article reviews recent developments in the formulation and application of biodescriptors to characterize proteomics maps. Such biodescriptors can be derived by applying techniques from discrete mathematics (graph theory, linear algebra and information theory). This review focuses on the development of biodescriptors for proteomics maps derived from 2D gel electrophoresis. Preliminary results demonstrated that such descriptors have a reasonable ability to differentiate between proteomics patterns that result from exposure to closely related individual chemicals and complex mixtures, such as the jet fuel JP-8. Further research is required to evaluate the utility of these proteomics-based biodescriptors for drug discovery and predictive toxicology.

Entanglement classification with matrix product states

NASA Astrophysics Data System (ADS)

Sanz, M.; Egusquiza, I. L.; di Candia, R.; Saberi, H.; Lamata, L.; Solano, E.

2016-07-01

We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .

Upper Primary School Teachers' Mathematical Knowledge for Teaching Functional Thinking in Algebra

ERIC Educational Resources Information Center

Wilkie, Karina J.

2014-01-01

This article is based on a project that investigated teachers' knowledge in teaching an important aspect of algebra in the middle years of schooling--functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research…

Teaching Mathematics in the PC Lab--The Students' Viewpoints

ERIC Educational Resources Information Center

Schmidt, Karsten; Kohler, Anke

2013-01-01

The Matrix Algebra portion of the intermediate mathematics course at the Schmalkalden University Faculty of Business and Economics has been moved from a traditional classroom setting to a technology-based setting in the PC lab. A Computer Algebra System license was acquired that also allows its use on the students' own PCs. A survey was carried…

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…

The Impact of Teachers' Characteristics and Self-Reported Practices on Students' Algebra Achievement

ERIC Educational Resources Information Center

Cope, Liza M.

2013-01-01

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…

Algebra I Achievement of Eighth Grade Mexican American Students Using Cooperative Learning versus Traditional Instruction

ERIC Educational Resources Information Center

Bunrasi, John Bosco Tuptip

2012-01-01

The purpose of this study was to examine constructivist-based algebra lessons and a cooperative construct to address the achievement gap between White (non-Hispanic) and Mexican American 8th grade students at a southern California middle school. The lessons were designed to facilitate social interdependence which promoted peer-to-peer interaction…

Exploring How Understandings from Abstract Algebra Can Influence the Teaching of Structure in Early Algebra

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2017-01-01

Empirical work that connects content knowledge to teaching practice has become increasingly important in discussions around a professional knowledge base for teaching. This paper aims to continue that work, reporting a single exploratory case study of one elementary mathematics teacher. The purpose of the study was to investigate how introducing…

Developing Students' Functional Thinking in Algebra through Different Visualisations of a Growing Pattern's Structure

ERIC Educational Resources Information Center

Wilkie, Karina J,; Clarke, Doug

2014-01-01

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one…

Students' Use of Variables and Multiple Representations in Generalizing Functional Relationships Prior to Secondary School

ERIC Educational Resources Information Center

Wilkie, Karina J.

2016-01-01

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

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,…

Examining the Use of Computer Algebra Systems in University-Level Mathematics Teaching

ERIC Educational Resources Information Center

Lavicza, Zsolt

2009-01-01

The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…

Experiences in Evaluating Outcomes in Tool-Based, Competence Building Education in Dynamical Systems Using Symbolic Computer Algebra

ERIC Educational Resources Information Center

Perram, John W.; Andersen, Morten; Ellekilde, Lars-Peter; Hjorth, Poul G.

2004-01-01

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç

2017-01-01

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Michael

2016-01-01

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

Linear Algebra and the Experiences of a "Flipper"

ERIC Educational Resources Information Center

Wright, Sarah E.

2015-01-01

This paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own…

An Introduction to the Profound Potential of Connected Algebra Activities: Issues of Representation, Engagement and Pedagogy

ERIC Educational Resources Information Center

Hegedus, Stephen J.; Kaput, James J.

2004-01-01

We present two vignettes of classroom episodes that exemplify new activity structures for introducing core algebra ideas such as linear functions, slope as rate and parametric variation within a new educational technology environment that combines two kinds of classroom technology affordances, one based in dynamic representation and the other…

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…

Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays.

PubMed

Li, Hongfei; Jiang, Haijun; Hu, Cheng

2016-03-01

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modifying ``Six Ideas that Shaped Physics'' for a Life-Science major audience at Hope College

NASA Astrophysics Data System (ADS)

Mader, Catherine

2005-04-01

The ``Six Ideas That Shaped Physics'' textbook has been adapted and used for use in the algebra-based introductory physics course for non-physics science majors at Hope College. The results of the first use will be presented. Comparison of FCI for pre and post test scores will be compared with results from 8 years of results from both the algebra-based course and the calculus-based course (when we first adopted ``Six Ideas that Shaped Physcs" for the Calculus-based course). In addition, comparison on quantitative tests and homework problems with prior student groups will also be made. Because a large fraction of the audience in the algebra-based course is life-science majors, a goal of this project is to make the material relevant for these students. Supplemental materials that emphasize the connection between the life sciences and the fundamental physics concepts are being be developed to accompany the new textbook. Samples of these materials and how they were used (and received) during class testing will be presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slattery, Stuart R.

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

Precise calculation of quasienergies of a driven two-level atom based on the Guo-Wu-Van Woerkom solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Yi; Zhang Jingtao; Xu Zhizhan

2010-07-15

The exact algebraic solution recently obtained by Guo, Wu, and Van Woerkom (Phys. Rev. A 73 (2006) 023419) made possible accurate calculations of quasienergies of a driven two-level atom with an arbitrary original energy spacing and laser intensity. Due to the complication of the analytic solutions that involves an infinite number of infinite determinants, many mathematical difficulties must be overcome to obtain precise values of quasienergies. In this paper, with a further developed algebraic method, we show how to solve the computational problem completely and results are presented in a data table. With this table, one can easily obtain allmore » quasienergies of a driven two-level atom with an arbitrary original energy spacing and arbitrary intensity and frequency of the driving laser. The numerical solution technique developed here can be applied to the calculation of Freeman resonances in photoelectron energy spectra. As an example for applications, we show how to use the data table to calculate the peak laser intensity at which a Freeman resonance occurs in the transition between the ground Xe 5p P{sub 3/2} state and the Rydberg state Xe 8p P{sub 3/2}.« less

The Elements of Teaching Nonscientists: Make it Conceptual, Social, Modern, and Interactive

NASA Astrophysics Data System (ADS)

Hobson, Art

2001-03-01

Physics literacy for all students should be a top priority for every physics department. Reasons include each department's self-interest, and the health of our profession. But most importantly, as the American Association for the Adancement of Science puts it, "Without a scientifically literate population, the outlook for a better world is not promising." Because nonscientists have little need and less desire for algebra-based physics problems, these courses should be conceptual (non-algebraic) although they should certainly be numerate. Since 1976, I have developed and taught a course of this type that includes most of the major principles of physics. Its success has stemmed from (1) a conceptual approach, (2) inclusion of relevant societal topics such as energy resources, scientific methodology, pseudoscience, global warming, and technological risk, (3) modern physics topics that occupy 50instruction techniques even in (especially in!) classes of over 200. I will describe this course and present interactive teaching ideas for one socially relevant topic: transportation and energy efficiency. A textbook is available: Physics: Concepts and Connections, by Art Hobson (Prentice Hall, 2nd Edition 1999). Further info: http://www.uark.edu/depts/physics/about/hobson.html

The Elements of Teaching Nonscientists: Make it Conceptual, Social, Modern, and Interactive

NASA Astrophysics Data System (ADS)

Hobson, Art

2000-04-01

Physics literacy for all students should be a top priority for every physics department. Reasons include each department's self-interest, and the health of our profession. But most importantly, as the American Association for the Adancement of Science puts it, "Without a scientifically literate population, the outlook for a better world is not promising." Because nonscientists have little need and less desire for algebra-based physics problems, these courses should be conceptual (non-algebraic) although they should certainly be numerate. Since 1976, I have developed and taught a course of this type that includes most of the major principles of physics. Its success has stemmed from (1) a conceptual approach, (2) inclusion of relevant societal topics such as energy resources, scientific methodology, pseudoscience, global warming, and technological risk, (3) modern physics topics that occupy 50instruction techniques even in (especially in!) classes of over 200. I will describe this course and conduct an "active learning" demonstration of ideas for teaching one socially relevant topic: transportation and energy efficiency. A textbook is available: Physics: Concepts and Connections, by Art Hobson (Prentice Hall, 2nd Edition 1999). Further info: http://www.uark.edu/depts/physics/about/hobson.html

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique.

PubMed

Meyer, Frans J C; Davidson, David B; Jakobus, Ulrich; Stuchly, Maria A

2003-02-01

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.

Algebraic model checking for Boolean gene regulatory networks.

PubMed

Tran, Quoc-Nam

2011-01-01

We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.

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.

Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE

NASA Astrophysics Data System (ADS)

Jiang, Yunfeng; Zhang, Yang

2018-03-01

In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar N=4 super-Yang-Mills theory.

Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes

DOE PAGES

Parker, Daniel E.; Scherlis, Adam; Spradlin, Marcus; ...

2015-11-20

Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the A n cluster algebra. As a result, using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.

Multigrid techniques for unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1995-01-01

An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

Nifty Nines and Repeating Decimals

ERIC Educational Resources Information Center

Brown, Scott A.

2016-01-01

The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…

Mathematical Modeling of Chemical Stoichiometry

ERIC Educational Resources Information Center

Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

2007-01-01

In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

Integrating Map Algebra and Statistical Modeling for Spatio- Temporal Analysis of Monthly Mean Daily Incident Photosynthetically Active Radiation (PAR) over a Complex Terrain.

PubMed

Evrendilek, Fatih

2007-12-12

This study aims at quantifying spatio-temporal dynamics of monthly mean dailyincident photosynthetically active radiation (PAR) over a vast and complex terrain such asTurkey. The spatial interpolation method of universal kriging, and the combination ofmultiple linear regression (MLR) models and map algebra techniques were implemented togenerate surface maps of PAR with a grid resolution of 500 x 500 m as a function of fivegeographical and 14 climatic variables. Performance of the geostatistical and MLR modelswas compared using mean prediction error (MPE), root-mean-square prediction error(RMSPE), average standard prediction error (ASE), mean standardized prediction error(MSPE), root-mean-square standardized prediction error (RMSSPE), and adjustedcoefficient of determination (R² adj. ). The best-fit MLR- and universal kriging-generatedmodels of monthly mean daily PAR were validated against an independent 37-year observeddataset of 35 climate stations derived from 160 stations across Turkey by the Jackknifingmethod. The spatial variability patterns of monthly mean daily incident PAR were moreaccurately reflected in the surface maps created by the MLR-based models than in thosecreated by the universal kriging method, in particular, for spring (May) and autumn(November). The MLR-based spatial interpolation algorithms of PAR described in thisstudy indicated the significance of the multifactor approach to understanding and mappingspatio-temporal dynamics of PAR for a complex terrain over meso-scales.

Using postural synergies to animate a low-dimensional hand avatar in haptic simulation.

PubMed

Mulatto, Sara; Formaglio, Alessandro; Malvezzi, Monica; Prattichizzo, Domenico

2013-01-01

A technique to animate a realistic hand avatar with 20 DoFs based on the biomechanics of the human hand is presented. The animation does not use any sensor glove or advanced tracker with markers. The proposed approach is based on the knowledge of a set of kinematic constraints on the model of the hand, referred to as postural synergies, which allows to represent the hand posture using a number of variables lower than the number of joints of the hand model. This low-dimensional set of parameters is estimated from direct measurement of the motion of thumb and index finger tracked using two haptic devices. A kinematic inversion algorithm has been developed, which takes synergies into account and estimates the kinematic configuration of the whole hand, i.e., also of the fingers whose end tips are not directly tracked by the two haptic devices. The hand skin is deformable and its deformation is computed using a linear vertex blending technique. The proposed synergy-based animation of the hand avatar involves only algebraic computations and is suitable for real-time implementation as required in haptics.

Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Graphical tensor product reduction scheme for the Lie algebras so(5) = sp(2) , su(3) , and g(2)

NASA Astrophysics Data System (ADS)

Vlasii, N. D.; von Rütte, F.; Wiese, U.-J.

2016-08-01

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2) , su(3) , and g(2) . This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a ;landscape; of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic ;girdle; method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.

Mathematical Modeling for Inherited Diseases.

PubMed

Anis, Saima; Khan, Madad; Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

Relations between elliptic multiple zeta values and a special derivation algebra

NASA Astrophysics Data System (ADS)

Broedel, Johannes; Matthes, Nils; Schlotterer, Oliver

2016-04-01

We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing eMZVs as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for eMZVs and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for eMZVs over a wide range of weights and lengths.

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

NASA Astrophysics Data System (ADS)

Ashwinkumar, Meer; Cao, Jingnan; Luo, Yuan; Tan, Meng-Chwan; Zhao, Qin

2018-03-01

We study the ground states and left-excited states of the Ak-1 N = (2 , 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU (k). The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.

Mathematical Modeling for Inherited Diseases

PubMed Central

Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra. PMID:28781606

Material decomposition in an arbitrary number of dimensions using noise compensating projection

NASA Astrophysics Data System (ADS)

O'Donnell, Thomas; Halaweish, Ahmed; Cormode, David; Cheheltani, Rabee; Fayad, Zahi A.; Mani, Venkatesh

2017-03-01

Purpose: Multi-energy CT (e.g., dual energy or photon counting) facilitates the identification of certain compounds via data decomposition. However, the standard approach to decomposition (i.e., solving a system of linear equations) fails if - due to noise - a pixel's vector of HU values falls outside the boundary of values describing possible pure or mixed basis materials. Typically, this is addressed by either throwing away those pixels or projecting them onto the closest point on this boundary. However, when acquiring four (or more) energy volumes, the space bounded by three (or more) materials that may be found in the human body (either naturally or through injection) can be quite small. Noise may significantly limit the number of those pixels to be included within. Therefore, projection onto the boundary becomes an important option. But, projection in higher than 3 dimensional space is not possible with standard vector algebra: the cross-product is not defined. Methods: We describe a technique which employs Clifford Algebra to perform projection in an arbitrary number of dimensions. Clifford Algebra describes a manipulation of vectors that incorporates the concepts of addition, subtraction, multiplication, and division. Thereby, vectors may be operated on like scalars forming a true algebra. Results: We tested our approach on a phantom containing inserts of calcium, gadolinium, iodine, gold nanoparticles and mixtures of pairs thereof. Images were acquired on a prototype photon counting CT scanner under a range of threshold combinations. Comparison of the accuracy of different threshold combinations versus ground truth are presented. Conclusions: Material decomposition is possible with three or more materials and four or more energy thresholds using Clifford Algebra projection to mitigate noise.

Intelligent Machines in the 21st Century: Automating the Processes of Inference and Inquiry

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2003-01-01

The last century saw the application of Boolean algebra toward the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines. in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. However, modern intelligent machines work by inferring knowledge using only their pre-programmed prior knowledge and the data provided. They lack the ability to ask questions, or request data that would aid their inferences. Recent advances in understanding the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we identified the algebra of questions as the free distributive algebra, which now allows us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper we describe this logic of inference and inquiry using the mathematics of partially ordered sets and the scaffolding of lattice theory, discuss the far-reaching implications of the methodology, and demonstrate its application with current examples in machine learning. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them to not only make inferences from data, but also decide which question to ask, experiment to perform, or measurement to take given what they have learned and what they are designed to understand.

Deriving Laws from Ordering Relations

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2004-01-01

The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.

A Practical Approach to Implementing Real-Time Semantics

NASA Technical Reports Server (NTRS)

Luettgen, Gerald; Bhat, Girish; Cleaveland, Rance

1999-01-01

This paper investigates implementations of process algebras which are suitable for modeling concurrent real-time systems. It suggests an approach for efficiently implementing real-time semantics using dynamic priorities. For this purpose a proces algebra with dynamic priority is defined, whose semantics corresponds one-to-one to traditional real-time semantics. The advantage of the dynamic-priority approach is that it drastically reduces the state-space sizes of the systems in question while preserving all properties of their functional and real-time behavior. The utility of the technique is demonstrated by a case study which deals with the formal modeling and verification of the SCSI-2 bus-protocol. The case study is carried out in the Concurrency Workbench of North Carolina, an automated verification tool in which the process algebra with dynamic priority is implemented. It turns out that the state space of the bus-protocol model is about an order of magnitude smaller than the one resulting from real-time semantics. The accuracy of the model is proved by applying model checking for verifying several mandatory properties of the bus protocol.

Baby de Sitter black holes and dS3/CFT2

NASA Astrophysics Data System (ADS)

de Buyl, Sophie; Detournay, Stéphane; Giribet, Gaston; Ng, Gim Seng

2014-02-01

Unlike three-dimensional Einstein gravity, three-dimensional massive gravity admits asymptotically de Sitter space (dS) black hole solutions. These black holes present interesting features and provide us with toy models to study the dS/CFT correspondence. A remarkable property of these black holes is that they are always in thermal equilibrium with the cosmological horizon of the space that hosts them. This invites us to study the thermodynamics of these solutions within the context of dS/CFT. We study the asymptotic symmetry group of the theory and find that it indeed coincides with the local two-dimensional conformal algebra. The charge algebra associated to the asymptotic Killing vectors consists of two copies of the Virasoro algebra with non-vanishing central extension. We compute the mass and angular momentum of the dS black holes and verify that a naive application of Cardy's formula exactly reproduces the entropy of both the black hole and the cosmological horizon. By adapting the holographic renormalization techniques to the case of dS space, we define the boundary stress tensor of the dual Euclidean conformal field theory.

Explicit Filtering Based Low-Dose Differential Phase Reconstruction Algorithm with the Grating Interferometry.

PubMed

Jiang, Xiaolei; Zhang, Li; Zhang, Ran; Yin, Hongxia; Wang, Zhenchang

2015-01-01

X-ray grating interferometry offers a novel framework for the study of weakly absorbing samples. Three kinds of information, that is, the attenuation, differential phase contrast (DPC), and dark-field images, can be obtained after a single scanning, providing additional and complementary information to the conventional attenuation image. Phase shifts of X-rays are measured by the DPC method; hence, DPC-CT reconstructs refraction indexes rather than attenuation coefficients. In this work, we propose an explicit filtering based low-dose differential phase reconstruction algorithm, which enables reconstruction from reduced scanning without artifacts. The algorithm adopts a differential algebraic reconstruction technique (DART) with the explicit filtering based sparse regularization rather than the commonly used total variation (TV) method. Both the numerical simulation and the biological sample experiment demonstrate the feasibility of the proposed algorithm.

Explicit Filtering Based Low-Dose Differential Phase Reconstruction Algorithm with the Grating Interferometry

PubMed Central

Zhang, Li; Zhang, Ran; Yin, Hongxia; Wang, Zhenchang

2015-01-01

X-ray grating interferometry offers a novel framework for the study of weakly absorbing samples. Three kinds of information, that is, the attenuation, differential phase contrast (DPC), and dark-field images, can be obtained after a single scanning, providing additional and complementary information to the conventional attenuation image. Phase shifts of X-rays are measured by the DPC method; hence, DPC-CT reconstructs refraction indexes rather than attenuation coefficients. In this work, we propose an explicit filtering based low-dose differential phase reconstruction algorithm, which enables reconstruction from reduced scanning without artifacts. The algorithm adopts a differential algebraic reconstruction technique (DART) with the explicit filtering based sparse regularization rather than the commonly used total variation (TV) method. Both the numerical simulation and the biological sample experiment demonstrate the feasibility of the proposed algorithm. PMID:26089971

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Classification of real Lie superalgebras based on a simple Lie algebra, giving rise to interesting examples involving {mathfrak {su}}(2,2)

NASA Astrophysics Data System (ADS)

Guzzo, H.; Hernández, I.; Sánchez-Valenzuela, O. A.

2014-09-01

Finite dimensional semisimple real Lie superalgebras are described via finite dimensional semisimple complex Lie superalgebras. As an application of these results, finite dimensional real Lie superalgebras mathfrak {m}=mathfrak {m}_0 oplus mathfrak {m}_1 for which mathfrak {m}_0 is a simple Lie algebra are classified up to isomorphism.

Evaluation of Madison Park PLATO Training on August 2000 BPS City Algebra Test Achievement.

ERIC Educational Resources Information Center

Baum, Christopher F.

This report presents empirical findings from the analysis of the performance of 85 students from Madison Park High School, Boston, Massachusetts, on the Boston Public Schools City Algebra Test (BPSCAT) in June and August 2000, and how their participation in Jobs for Youths Boston PLATO computer-based instruction in the intervening months may have…

Competence with Fractions in Fifth or Sixth Grade as a Unique Predictor of Algebraic Thinking?

ERIC Educational Resources Information Center

Pearn, Catherine; Stephens, Max

2016-01-01

Researchers have argued that there are strong links between primary school students' competence with fraction concepts and operations and their algebraic readiness. This study involving 162 Years 5/6 students in three primary schools examined the strength of that relationship using a test based on familiar fraction tasks and a test of algebraic…

Sources of Student Errors and Misconceptions in Algebra and Effectiveness of Classroom Practice Remediation in Machakos County--Kenya

ERIC Educational Resources Information Center

Mulungye, Mary M.; O'Connor, Miheso; Ndethiu, S.

2016-01-01

This paper is based on a study which sought to examine the various errors and misconceptions committed by students in algebra with the view to exposing the nature and origin of the errors and misconceptions in secondary schools in Machakos district. Teachers' knowledge on students' errors was investigated together with strategies for remedial…

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…

Comparative Effectiveness of Carnegie Learning's "Cognitive Tutor"[R] Algebra I Curriculum: A Report of a Randomized Experiment in the Maui School District. Research Summary

ERIC Educational Resources Information Center

Empirical Education Inc., 2007

2007-01-01

The Maui Hawaii Educational consortium (the Maui School District and Maui Community College) sought scientifically based evidence for the effectiveness of the "Cognitive Tutor" ("CT") Algebra I Curriculum to inform adoption decisions. Decision makers were particularly interested in whether the use of the "CT" program…

Comparative Effectiveness of Carnegie Learning's "Cognitive Tutor" Algebra I Curriculum: A Report of a Randomized Experiment in the Maui School District. Research Report

ERIC Educational Resources Information Center

Cabalo, Jessica Villaruz; Vu, Minh-Thien

2007-01-01

The Maui Hawaii Educational consortium (the Maui School District and Maui Community College) sought scientifically based evidence for the effectiveness of the "Cognitive Tutor (CT) Algebra I Curriculum" to inform adoption decisions. Decision makers were particularly interested in whether the use of the "CT" program affects…

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…

On the Integration of Computer Algebra Systems (CAS) by Canadian Mathematicians: Results of a National Survey

ERIC Educational Resources Information Center

Buteau, Chantal; Jarvis, Daniel H.; Lavicza, Zsolt

2014-01-01

In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the…

High-School Students' Approaches to Solving Algebra Problems that Are Posed Symbolically: Results from an Interview Study

ERIC Educational Resources Information Center

Huntley, Mary Ann; Davis, Jon D.

2008-01-01

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are…

Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

NASA Astrophysics Data System (ADS)

Wilkie, Karina J.

2016-06-01

A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

A New Technique for Personality Scale Construction. Preliminary Findings.

ERIC Educational Resources Information Center

Schaffner, Paul E.; Darlington, Richard B.

Most methods of personality scale construction have clear statistical disadvantages. A hybrid method (Darlington and Bishop, 1966) was found to increase scale validity more than any other method, with large item pools. A simple modification of the Darlington-Bishop method (algebraically and conceptually similar to ridge regression, but…

Application of Vectors to Relative Velocity

ERIC Educational Resources Information Center

Tin-Lam, Toh

2004-01-01

The topic 'relative velocity' has recently been introduced into the Cambridge Ordinary Level Additional Mathematics syllabus under the application of Vectors. In this note, the results of relative velocity and the 'reduction to rest' technique of teaching relative velocity are derived mathematically from vector algebra, in the hope of providing…

The Vigenere Cipher with the TI-83

ERIC Educational Resources Information Center

Hamilton, Michael; Yankosky, Bill

2004-01-01

Cryptology, the science of secret writing, is a great way to introduce students to different areas of mathematics such as number theory, linear algebra, probability and statistics. Cryptology consists of two branches: cryptography and cryptanalysis. Cryptography is the science of designing techniques for encrypting and decrypting a message.…

Discovering Authorities and Hubs in Different Topological Web Graph Structures.

ERIC Educational Resources Information Center

Meghabghab, George

2002-01-01

Discussion of citation analysis on the Web considers Web hyperlinks as a source to analyze citations. Topics include basic graph theory applied to Web pages, including matrices, linear algebra, and Web topology; and hubs and authorities, including a search technique called HITS (Hyperlink Induced Topic Search). (Author/LRW)

Fundamentals of Digital Logic.

ERIC Educational Resources Information Center

Noell, Monica L.

This course is designed to prepare electronics personnel for further training in digital techniques, presenting need to know information that is basic to any maintenance course on digital equipment. It consists of seven study units: (1) binary arithmetic; (2) boolean algebra; (3) logic gates; (4) logic flip-flops; (5) nonlogic circuits; (6)…

A Unified Introduction to Ordinary Differential Equations

ERIC Educational Resources Information Center

Lutzer, Carl V.

2006-01-01

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua

Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.

A short note on calculating the adjusted SAR index

USDA-ARS?s Scientific Manuscript database

A simple algebraic technique is presented for computing the adjusted SAR Index proposed by Suarez (1981). The statistical formula presented in this note facilitates the computation of the adjusted SAR without the use of either a look-up table, custom computer software or the need to compute exact a...

Investigating the use of mastery-style online homework exercises in introductory algebra-based mechanics in a controlled clinical study

NASA Astrophysics Data System (ADS)

Evans, William R.; Selen, Mats A.

2017-12-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs traditional-style homework with students in both algebra-based and calculus-based introductory mechanics. Results indicate a benefit from mastery-style over traditional-style homework, principally for weaker students who are less familiar with the material being covered and on questions that are nearer transfer to the study materials.

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)

Highly efficient full-wave electromagnetic analysis of 3-D arbitrarily shaped waveguide microwave devices using an integral equation technique

NASA Astrophysics Data System (ADS)

Vidal, A.; San-Blas, A. A.; Quesada-Pereira, F. D.; Pérez-Soler, J.; Gil, J.; Vicente, C.; Gimeno, B.; Boria, V. E.

2015-07-01

A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RME technique. The developed tool also provides an accurate computation of the electromagnetic fields at an arbitrary observation point of the considered device, so it can be used for predicting high-power breakdown phenomena. In order to validate the accuracy and efficiency of this novel approach, several new designs of band-pass waveguides filters are presented. The obtained results (S-parameters and electromagnetic fields) are successfully compared both to experimental data and to numerical simulations provided by a commercial software based on the finite element technique. The results obtained show that the new technique is specially suitable for the efficient full-wave analysis of complex waveguide devices considering an integrated coaxial excitation, where the coaxial probes may be in contact with the metallic insets of the component.

Algebras Generated by Geometric Scalar Forms and their Applications in Physics and Social Sciences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Jaime

2008-09-17

The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the K{sup th} power of the linear form, requiring {l_brace}e{sub i};i = 1,...,N;(e{sub i}){sup K} = 1{r_brace} and d-vector {sigma}{sub i}x{sub i}e{sub i}. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K-order scalarmore » forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered.For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006)« less

Dictionary-learning-based reconstruction method for electron tomography.

PubMed

Liu, Baodong; Yu, Hengyong; Verbridge, Scott S; Sun, Lizhi; Wang, Ge

2014-01-01

Electron tomography usually suffers from so-called “missing wedge” artifacts caused by limited tilt angle range. An equally sloped tomography (EST) acquisition scheme (which should be called the linogram sampling scheme) was recently applied to achieve 2.4-angstrom resolution. On the other hand, a compressive sensing inspired reconstruction algorithm, known as adaptive dictionary based statistical iterative reconstruction (ADSIR), has been reported for X-ray computed tomography. In this paper, we evaluate the EST, ADSIR, and an ordered-subset simultaneous algebraic reconstruction technique (OS-SART), and compare the ES and equally angled (EA) data acquisition modes. Our results show that OS-SART is comparable to EST, and the ADSIR outperforms EST and OS-SART. Furthermore, the equally sloped projection data acquisition mode has no advantage over the conventional equally angled mode in this context.

Non-naturally reductive Einstein metrics on exceptional Lie groups

NASA Astrophysics Data System (ADS)

Chrysikos, Ioannis; Sakane, Yusuke

2017-06-01

Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Gröbner bases and classify the real solutions of the associated algebraic systems. For the Lie group G2 we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E7 and E8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K) -invariant by different Lie subgroups K.

Simplifications for hydronic system models in modelica

DOE PAGES

Jorissen, F.; Wetter, M.; Helsen, L.

2018-01-12

Building systems and their heating, ventilation and air conditioning flow networks, are becoming increasingly complex. Some building energy simulation tools simulate these flow networks using pressure drop equations. These flow network models typically generate coupled algebraic nonlinear systems of equations, which become increasingly more difficult to solve as their sizes increase. This leads to longer computation times and can cause the solver to fail. These problems also arise when using the equation-based modelling language Modelica and Annex 60-based libraries. This may limit the applicability of the library to relatively small problems unless problems are restructured. This paper discusses two algebraicmore » loop types and presents an approach that decouples algebraic loops into smaller parts, or removes them completely. The approach is applied to a case study model where an algebraic loop of 86 iteration variables is decoupled into smaller parts with a maximum of five iteration variables.« less

A note on derivations of Murray-von Neumann algebras.

PubMed

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Banach Synaptic Algebras

NASA Astrophysics Data System (ADS)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

Uncertainties in Atomic Data and Their Propagation Through Spectral Models. I.

NASA Technical Reports Server (NTRS)

Bautista, M. A.; Fivet, V.; Quinet, P.; Dunn, J.; Gull, T. R.; Kallman, T. R.; Mendoza, C.

2013-01-01

We present a method for computing uncertainties in spectral models, i.e., level populations, line emissivities, and emission line ratios, based upon the propagation of uncertainties originating from atomic data.We provide analytic expressions, in the form of linear sets of algebraic equations, for the coupled uncertainties among all levels. These equations can be solved efficiently for any set of physical conditions and uncertainties in the atomic data. We illustrate our method applied to spectral models of Oiii and Fe ii and discuss the impact of the uncertainties on atomic systems under different physical conditions. As to intrinsic uncertainties in theoretical atomic data, we propose that these uncertainties can be estimated from the dispersion in the results from various independent calculations. This technique provides excellent results for the uncertainties in A-values of forbidden transitions in [Fe ii]. Key words: atomic data - atomic processes - line: formation - methods: data analysis - molecular data - molecular processes - techniques: spectroscopic