Algebraic method for parameter identification of circuit models for batteries under non-zero initial condition

NASA Astrophysics Data System (ADS)

Devarakonda, Lalitha; Hu, Tingshu

2014-12-01

This paper presents an algebraic method for parameter identification of Thevenin's equivalent circuit models for batteries under non-zero initial condition. In traditional methods, it was assumed that all capacitor voltages have zero initial conditions at the beginning of each charging/discharging test. This would require a long rest time between two tests, leading to very lengthy tests for a charging/discharging cycle. In this paper, we propose an algebraic method which can extract the circuit parameters together with initial conditions. This would theoretically reduce the rest time to 0 and substantially accelerate the testing cycles.

Generalized derivation extensions of 3-Lie algebras and corresponding Nambu-Poisson structures

NASA Astrophysics Data System (ADS)

Song, Lina; Jiang, Jun

2018-01-01

In this paper, we introduce the notion of a generalized derivation on a 3-Lie algebra. We construct a new 3-Lie algebra using a generalized derivation and call it the generalized derivation extension. We show that the corresponding Leibniz algebra on the space of fundamental objects is the double of a matched pair of Leibniz algebras. We also determine the corresponding Nambu-Poisson structures under some conditions.

Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Morozov, Oleg I.

2018-06-01

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.

Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

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

Campoamor-Stursberg, R., E-mail: rutwig@mat.ucm.e

2008-05-15

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.

(Fuzzy) Ideals of BN-Algebras

PubMed Central

Walendziak, Andrzej

2015-01-01

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

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

Semiclassical states on Lie algebras

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

Tsobanjan, Artur, E-mail: artur.tsobanjan@gmail.com

2015-03-15

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

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.

Solving Absolute Value Equations Algebraically and Geometrically

ERIC Educational Resources Information Center

Shiyuan, Wei

2005-01-01

The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

Quantum Observables and Effect Algebras

NASA Astrophysics Data System (ADS)

Dvurečenskij, Anatolij

2018-03-01

We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a monotone σ-complete homogeneous effect algebra using its orthoalgebraic skeleton. In addition, we study compatibility in orthoalgebras and we show that every orthoalgebra satisfying RIP is an orthomodular poset.

An Analysis of the Algebraic Method for Balancing Chemical Reactions.

ERIC Educational Resources Information Center

Olson, John A.

1997-01-01

Analyzes the algebraic method for balancing chemical reactions. Introduces a third general condition that involves a balance between the total amount of oxidation and reduction. Requires the specification of oxidation states for all elements throughout the reaction. Describes the general conditions, the mathematical treatment, redox reactions, and…

Noncommutative Common Cause Principles in algebraic quantum field theory

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

Hofer-Szabo, Gabor; Vecsernyes, Peter

2013-04-15

States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{submore » B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.« less

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

On character amenability of Banach algebras

NASA Astrophysics Data System (ADS)

Kaniuth, E.; Lau, A. T.; Pym, J.

2008-08-01

We continue our work [E. Kaniuth, A.T. Lau, J. Pym, On [phi]-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008) 85-96] in the study of amenability of a Banach algebra A defined with respect to a character [phi] of A. Various necessary and sufficient conditions of a global and a pointwise nature are found for a Banach algebra to possess a [phi]-mean of norm 1. We also completely determine the size of the set of [phi]-means for a separable weakly sequentially complete Banach algebra A with no [phi]-mean in A itself. A number of illustrative examples are discussed.

Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

NASA Astrophysics Data System (ADS)

Abdelaziz, Y.; Maillard, J.-M.

2017-05-01

We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same {}_2F1 hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus {}_2F1 hypergeometric function example. We then focus on identities relating the same {}_2F1 hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to {}_3F2 , hypergeometric functions, and show that one just reduces to the previous {}_2F1 cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a _2F1 hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or {}_2F1 hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to develop more differentially algebraic symmetry analysis in physics.

Enhanced asymptotic BMS3 algebra of the flat spacetime solutions of generalized minimal massive gravity

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2018-01-01

We apply the new fall of conditions presented in the paper [1] on asymptotically flat spacetime solutions of Chern-Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the conserved charges of the asymptotically flat spacetimes in generalized minimal massive gravity, and by introducing Fourier modes we show that the asymptotic symmetry algebra is a semidirect product of a BMS3 algebra and two U (1) current algebras. Also we verify that the BMS3 algebra can be obtained by a contraction of the AdS3 asymptotic symmetry algebra when the AdS3 radius tends to infinity in the flat-space limit. Finally we find energy, angular momentum and entropy for a particular case and deduce that these quantities satisfy the first law of flat space cosmologies.

On the Primitive Ideal spaces of the C(*) -algebras of graphs

NASA Astrophysics Data System (ADS)

Bates, Teresa

2005-11-01

We characterise the topological spaces which arise as the primitive ideal spaces of the Cuntz-Krieger algebras of graphs satisfying condition (K): directed graphs in which every vertex lying on a loop lies on at least two loops. We deduce that the spaces which arise as Prim;C(*(E)) are precisely the spaces which arise as the primitive ideal spaces of AF-algebras. Finally, we construct a graph wt{E} from E such that C(*(wt{E})) is an AF-algebra and Prim;C(*(E)) and Prim;C(*(wt{E})) are homeomorphic.

Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür; Ertem, Ümit

2016-08-01

We consider geometric and supergravity Killing spinors and the spinor bilinears constructed out of them. The spinor bilinears of geometric Killing spinors correspond to the antisymmetric generalizations of Killing vector fields which are called Killing-Yano forms. They constitute a Lie superalgebra structure in constant curvature spacetimes. We show that the Dirac currents of geometric Killing spinors satisfy a Lie algebra structure up to a condition on 2-form spinor bilinears. We propose that the spinor bilinears of supergravity Killing spinors give way to different generalizations of Killing vector fields to higher degree forms. It is also shown that those supergravity Killing forms constitute a Lie algebra structure in six- and ten-dimensional cases. For five- and eleven-dimensional cases, the Lie algebra structure depends on an extra condition on supergravity Killing forms.

Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving later.

PubMed

Hoover, Jerome D; Healy, Alice F

2017-12-01

The classic bat-and-ball problem is used widely to measure biased and correct reasoning in decision-making. University students overwhelmingly tend to provide the biased answer to this problem. To what extent might reasoners be led to modify their judgement, and, more specifically, is it possible to facilitate problem solution by prompting participants to consider the problem from an algebraic perspective? One hundred ninety-seven participants were recruited to investigate the effect of algebraic cueing as a debiasing strategy on variants of the bat-and-ball problem. Participants who were cued to consider the problem algebraically were significantly more likely to answer correctly relative to control participants. Most of this cueing effect was confined to a condition that required participants to solve isomorphic algebra equations corresponding to the structure of bat-and-ball question types. On a subsequent critical question with differing item and dollar amounts presented without a cue, participants were able to generalize the learned information to significantly reduce overall bias. Math anxiety was also found to be significantly related to bat-and-ball problem accuracy. These results suggest that, under specific conditions, algebraic reasoning is an effective debiasing strategy on bat-and-ball problem variants, and provide the first documented evidence for the influence of math anxiety on Cognitive Reflection Test performance.

Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

NASA Astrophysics Data System (ADS)

Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János

2014-01-01

Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

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.

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

Guedes, Carlos; Oriti, Daniele; Raasakka, Matti

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-productmore » carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.« less

Image-algebraic design of multispectral target recognition algorithms

NASA Astrophysics Data System (ADS)

Schmalz, Mark S.; Ritter, Gerhard X.

1994-06-01

In this paper, we discuss methods for multispectral ATR (Automated Target Recognition) of small targets that are sensed under suboptimal conditions, such as haze, smoke, and low light levels. In particular, we discuss our ongoing development of algorithms and software that effect intelligent object recognition by selecting ATR filter parameters according to ambient conditions. Our algorithms are expressed in terms of IA (image algebra), a concise, rigorous notation that unifies linear and nonlinear mathematics in the image processing domain. IA has been implemented on a variety of parallel computers, with preprocessors available for the Ada and FORTRAN languages. An image algebra C++ class library has recently been made available. Thus, our algorithms are both feasible implementationally and portable to numerous machines. Analyses emphasize the aspects of image algebra that aid the design of multispectral vision algorithms, such as parameterized templates that facilitate the flexible specification of ATR filters.

The algebraic criteria for the stability of control systems

NASA Technical Reports Server (NTRS)

Cremer, H.; Effertz, F. H.

1986-01-01

This paper critically examines the standard algebraic criteria for the stability of linear control systems and their proofs, reveals important previously unnoticed connections, and presents new representations. Algebraic stability criteria have also acquired significance for stability studies of non-linear differential equation systems by the Krylov-Bogoljubov-Magnus Method, and allow realization conditions to be determined for classes of broken rational functions as frequency characteristics of electrical network.

A tensor Banach algebra approach to abstract kinetic equations

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

The study deals with a concrete algebraic construction providing the existence theory for abstract kinetic equation boundary-value problems, when the collision operator A is an accretive finite-rank perturbation of the identity operator in a Hilbert space H. An algebraic generalization of the Bochner-Phillips theorem is utilized to study solvability of the abstract boundary-value problem without any regulatory condition. A Banach algebra in which the convolution kernel acts is obtained explicitly, and this result is used to prove a perturbation theorem for bisemigroups, which then plays a vital role in solving the initial equations.

Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies

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

Li, Chuanzhong, E-mail: lichuanzhong@nbu.edu.cn; He, Jingsong, E-mail: hejingsong@nbu.edu.cn

We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified (or additional) terms because of a B type reduction condition of this integrable hierarchy. Further we show that the D type Drinfeld-Sokolov hierarchy, which is a reduction of the two-component BKP hierarchy, possess a complete Block type additional symmetry algebra. That D type Drinfeld-Sokolov hierarchy has a similar algebraic structure as the bigraded Toda hierarchy which is a differential-discrete integrable system.

On the homotopy equivalence of simple AI-algebras

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

Aristov, O Yu

1999-02-28

Let A and B be simple unital AI-algebras (an AI-algebra is an inductive limit of C*-algebras of the form BigOplus{sub i}{sup k}C([0,1],M{sub N{sub i}}). It is proved that two arbitrary unital homomorphisms from A into B such that the corresponding maps K{sub 0}A{yields}K{sub 0}B coincide are homotopic. Necessary and sufficient conditions on the Elliott invariant for A and B to be homotopy equivalent are indicated. Moreover, two algebras in the above class having the same K-theory but not homotopy equivalent are constructed. A theorem on the homotopy of approximately unitarily equivalent homomorphisms between AI-algebras is used in the proof, whichmore » is deduced in its turn from a generalization to the case of AI-algebras of a theorem of Manuilov stating that a unitary matrix almost commuting with a self-adjoint matrix h can be joined to 1 by a continuous path consisting of unitary matrices almost commuting with h.« less

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

Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

NASA Astrophysics Data System (ADS)

Demina, Maria V.

2018-05-01

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing-van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing-van der Pol system are constructed.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates.

PubMed

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Algebraic Riccati equations in zero-sum differential games

NASA Technical Reports Server (NTRS)

Johnson, T. L.; Chao, A.

1974-01-01

The procedure for finding the closed-loop Nash equilibrium solution of two-player zero-sum linear time-invariant differential games with quadratic performance criteria and classical information pattern may be reduced in most cases to the solution of an algebraic Riccati equation. Based on the results obtained by Willems, necessary and sufficient conditions for existence of solutions to these equations are derived, and explicit conditions for a scalar example are given.

Non-AdS holography in 3-dimensional higher spin gravity — General recipe and example

NASA Astrophysics Data System (ADS)

Afshar, H.; Gary, M.; Grumiller, D.; Rashkov, R.; Riegler, M.

2012-11-01

We present the general algorithm to establish the classical and quantum asymptotic symmetry algebra for non-AdS higher spin gravity and implement it for the specific example of spin-3 gravity in the non-principal embedding with Lobachevsky ( {{{{H}}^2}× {R}} ) boundary conditions. The asymptotic symmetry algebra for this example consists of a quantum W_3^{(2) } (Polyakov-Bershadsky) and an affine û(1) algebra. We show that unitary representations of the quantum W_3^{(2) } algebra exist only for two values of its central charge, the trivial c = 0 "theory" and the simple c = 1 theory.

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.

Computing algebraic transfer entropy and coupling directions via transcripts

NASA Astrophysics Data System (ADS)

Amigó, José M.; Monetti, Roberto; Graff, Beata; Graff, Grzegorz

2016-11-01

Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.

Hardware implementation of fuzzy Petri net as a controller.

PubMed

Gniewek, Lesław; Kluska, Jacek

2004-06-01

The paper presents a new approach to fuzzy Petri net (FPN) and its hardware implementation. The authors' motivation is as follows. Complex industrial processes can be often decomposed into many parallelly working subprocesses, which can, in turn, be modeled using Petri nets. If all the process variables (or events) are assumed to be two-valued signals, then it is possible to obtain a hardware or software control device, which works according to the algorithm described by conventional Petri net. However, the values of real signals are contained in some bounded interval and can be interpreted as events which are not only true or false, but rather true in some degree from the interval [0, 1]. Such a natural interpretation from multivalued logic (fuzzy logic) point of view, concerns sensor outputs, control signals, time expiration, etc. It leads to the idea of FPN as a controller, which one can rather simply obtain, and which would be able to process both analog, and binary signals. In the paper both graphical, and algebraic representations of the proposed FPN are given. The conditions under which transitions can be fired are described. The algebraic description of the net and a theorem which enables computation of new marking in the net, based on current marking, are formulated. Hardware implementation of the FPN, which uses fuzzy JK flip-flops and fuzzy gates, are proposed. An example illustrating usefulness of the proposed FPN for control algorithm description and its synthesis as a controller device for the concrete production process are presented.

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

New formulations for tsunami runup estimation

NASA Astrophysics Data System (ADS)

Kanoglu, U.; Aydin, B.; Ceylan, N.

2017-12-01

We evaluate shoreline motion and maximum runup in two folds: One, we use linear shallow water-wave equations over a sloping beach and solve as initial-boundary value problem similar to the nonlinear solution of Aydın and Kanoglu (2017, Pure Appl. Geophys., https://doi.org/10.1007/s00024-017-1508-z). Methodology we present here is simple; it involves eigenfunction expansion and, hence, avoids integral transform techniques. We then use several different types of initial wave profiles with and without initial velocity, estimate shoreline properties and confirm classical runup invariance between linear and nonlinear theories. Two, we use the nonlinear shallow water-wave solution of Kanoglu (2004, J. Fluid Mech. 513, 363-372) to estimate maximum runup. Kanoglu (2004) presented a simple integral solution for the nonlinear shallow water-wave equations using the classical Carrier and Greenspan transformation, and further extended shoreline position and velocity to a simpler integral formulation. In addition, Tinti and Tonini (2005, J. Fluid Mech. 535, 33-64) defined initial condition in a very convenient form for near-shore events. We use Tinti and Tonini (2005) type initial condition in Kanoglu's (2004) shoreline integral solution, which leads further simplified estimates for shoreline position and velocity, i.e. algebraic relation. We then use this algebraic runup estimate to investigate effect of earthquake source parameters on maximum runup and present results similar to Sepulveda and Liu (2016, Coast. Eng. 112, 57-68).

Topological defects in open string field theory

NASA Astrophysics Data System (ADS)

Kojita, Toshiko; Maccaferri, Carlo; Masuda, Toru; Schnabl, Martin

2018-04-01

We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.

An Algebraic Approach to the Study and Optimization of the Set of Rules of a Conditional Rewrite System

NASA Astrophysics Data System (ADS)

Makhortov, S. D.

2018-03-01

An algebraic system containing the semantics of a set of rules of the conditional equational theory (or the conditional term rewriting system) is introduced. The following basic questions are considered for the given model: existence of logical closure, structure of logical closure, possibility of equivalent transformations, and construction of logical reduction. The obtained results can be applied to the analysis and automatic optimization of the corresponding set of rules. The basis for the given research is the theory of lattices and binary relations.

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

Chung, Won Sang, E-mail: mimip4444@hanmail.net; Hounkonnou, Mahouton Norbert, E-mail: norbert.hounkonnou@cipma.uac.bj; Arjika, Sama, E-mail: rjksama2008@gmail.com

In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

[Biometric bases: basic concepts of probability calculation].

PubMed

Dinya, E

1998-04-26

The author gives or outline of the basic concepts of probability theory. The bases of the event algebra, definition of the probability, the classical probability model and the random variable are presented.

Soft hairy warped black hole entropy

NASA Astrophysics Data System (ADS)

Grumiller, Daniel; Hacker, Philip; Merbis, Wout

2018-02-01

We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u (1) current algebras and recover the surprisingly simple entropy formula S = 2 π( J 0 + + J 0 - ), where J 0 ± are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.

Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

NASA Technical Reports Server (NTRS)

Mook, D. J.; Lew, Jiann-Shiun

1991-01-01

Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

Effects of Computer Algebra System (CAS) with Metacognitive Training on Mathematical Reasoning.

ERIC Educational Resources Information Center

Kramarski, Bracha; Hirsch, Chaya

2003-01-01

Describes a study that investigated the differential effects of Computer Algebra Systems (CAS) and metacognitive training (META) on mathematical reasoning. Participants were 83 Israeli eighth-grade students. Results showed that CAS embedded within META significantly outperformed the META and CAS alone conditions, which in turn significantly…

Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays.

PubMed

Sun, Leping

2016-01-01

This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras

NASA Astrophysics Data System (ADS)

Fuksa, J.; Isaev, A. P.; Karakhanyan, D.; Kirschner, R.

2017-04-01

Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. On this basis we study the analogy of the Yang-Baxter operators considered earlier for the cases of orthogonal and symplectic symmetries: the vector (fundamental) R-matrix, the L-operator defining the Yangian algebra and its first and second order evaluations. We investigate the condition for L (u) in the case of the truncated expansion in inverse powers of u and give examples of Lie algebra representations obeying these conditions. We construct the R-operator intertwining two superspinor representations and study the fusion of L-operators involving the tensor product of such representations.

Effects of the Good Behavior Game on classwide off-task behavior in a high school basic algebra resource classroom.

PubMed

Flower, Andrea; McKenna, John; Muething, Colin S; Bryant, Diane Pedrotty; Bryant, Brian R

2014-01-01

This study investigated the effects of the Good Behavior Game (GBG) on classwide off-task behavior in two ninth-grade basic algebra resource classes. Ten students with a variety of disabilities, in two classrooms, and their special education resource teacher participated in this study. A reversal design was employed, in which the special education teacher implemented GBG compared to typical practice-algebra readiness instruction. Results showed that classwide off-task behavior decreased in the GBG conditions compared to the baseline and reversal conditions. Fidelity measures indicated that the teacher implemented GBG with fidelity. Students and the teacher rated GBG favorably. Overall findings support the use of GBG for reducing classwide off-task behavior. Implications for practice and future research directions are presented.

Metric 3-Leibniz algebras and M2-branes

NASA Astrophysics Data System (ADS)

Méndez-Escobar, Elena

2010-08-01

This thesis is concerned with superconformal Chern-Simons theories with matter in 3 dimensions. The interest in these theories is two-fold. On the one hand, it is a new family of theories in which to test the AdS/CFT correspondence and on the other, they are important to study one of the main objects of M-theory (M2-branes). All these theories have something in common: they can be written in terms of 3-Leibniz algebras. Here we study the structure theory of such algebras, paying special attention to a subclass of them that gives rise to maximal supersymmetry and that was the first to appear in this context: 3-Lie algebras. In chapter 2, we review the structure theory of metric Lie algebras and their unitary representations. In chapter 3, we study metric 3-Leibniz algebras and show, by specialising a construction originally due to Faulkner, that they are in one to one correspondence with pairs of real metric Lie algebras and unitary representations of them. We also show a third characterisation for six extreme cases of 3-Leibniz algebras as graded Lie (super)algebras. In chapter 4, we study metric 3-Lie algebras in detail. We prove a structural result and also classify those with a maximally isotropic centre, which is the requirement that ensures unitarity of the corresponding conformal field theory. Finally, in chapter 5, we study the universal structure of superpotentials in this class of superconformal Chern-Simons theories with matter in three dimensions. We provide a uniform formulation for all these theories and establish the connection between the amount of supersymmetry preserved and the gauge Lie algebra and the appropriate unitary representation to be used to write down the Lagrangian. The conditions for supersymmetry enhancement are then expressed equivalently in the language of representation theory of Lie algebras or the language of 3-Leibniz algebras.

Systems with outer constraints. Gupta-Bleuler electromagnetism as an algebraic field theory

NASA Astrophysics Data System (ADS)

Grundling, Hendrik

1988-03-01

Since there are some important systems which have constraints not contained in their field algebras, we develop here in a C*-context the algebraic structures of these. The constraints are defined as a group G acting as outer automorphisms on the field algebra ℱ, α: G ↦ Aut ℱ, α G ⊄ Inn ℱ, and we find that the selection of G-invariant states on ℱ is the same as the selection of states ω on M( G M(Gmathop × limits_α F) ℱ) by ω( U g)=1∨ g∈ G, where U g ∈ M ( G M(Gmathop × limits_α F) ℱ)/ℱ are the canonical elements implementing α g . These states are taken as the physical states, and this specifies the resulting algebraic structure of the physics in M( G M(Gmathop × limits_α F) ℱ), and in particular the maximal constraint free physical algebra ℛ. A nontriviality condition is given for ℛ to exist, and we extend the notion of a crossed product to deal with a situation where G is not locally compact. This is necessary to deal with the field theoretical aspect of the constraints. Next the C*-algebra of the CCR is employed to define the abstract algebraic structure of Gupta-Bleuler electromagnetism in the present framework. The indefinite inner product representation structure is obtained, and this puts Gupta-Bleuler electromagnetism on a rigorous footing. Finally, as a bonus, we find that the algebraic structures just set up, provide a blueprint for constructive quadratic algebraic field theory.

The Hom-Yang-Baxter equation and Hom-Lie algebras

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

Yau, Donald

2011-05-15

Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In this paper, several more classes of solutions of the HYBE are constructed. Some of the solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drinfel'd modules. Under some invertibility conditions, we construct a new infinite sequence of solutions of the HYBE from a given one.

Characterizations of Some Fuzzy Prefilters (Filters) in EQ-Algebras

PubMed Central

Xin, Xiao Long; Yang, Yong Wei

2014-01-01

We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some conditions under which a fuzzy implicative prefilter (filter) is equivalent to a fuzzy positive implicative prefilter (filter). As applications, we obtain some new results about classical filters in EQ-algebras and some related results about fuzzy filters in residuated lattices. PMID:24892096

Super-BMS3 algebras from {N}=2 flat supergravities

NASA Astrophysics Data System (ADS)

Lodato, Ivano; Merbis, Wout

2016-11-01

We consider two possible flat space limits of three dimensional {N}=(1, 1) AdS supergravity. They differ by how the supercharges are scaled with the AdS radius ℓ: the first limit (democratic) leads to the usual super-Poincaré theory, while a novel `twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non- and ultra-relativistic limits of the {N}=(1, 1) Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.

Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays.

PubMed

Popa, Călin-Adrian

2018-06-08

This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the states, weights, and activation functions belong to the normed division algebra of octonions. The octonion algebra is a nonassociative and noncommutative generalization of the complex and quaternion algebras, but does not belong to the category of Clifford algebras, which are associative. In order to avoid the nonassociativity of the octonion algebra and also the noncommutativity of the quaternion algebra, the Cayley-Dickson construction is used to decompose the OVNNs into 4 complex-valued systems. By using appropriate Lyapunov-Krasovskii functionals, with double and triple integral terms, the free weighting matrix method, and simple and double integral Jensen inequalities, delay-dependent criteria are established for the exponential stability of the considered OVNNs. The criteria are given in terms of complex-valued linear matrix inequalities, for two types of Lipschitz conditions which are assumed to be satisfied by the octonion-valued activation functions. Finally, two numerical examples illustrate the feasibility, effectiveness, and correctness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Quantization and Superselection Sectors I:. Transformation Group C*-ALGEBRAS

NASA Astrophysics Data System (ADS)

Landsman, N. P.

Quantization is defined as the act of assigning an appropriate C*-algebra { A} to a given configuration space Q, along with a prescription mapping self-adjoint elements of { A} into physically interpretable observables. This procedure is adopted to solve the problem of quantizing a particle moving on a homogeneous locally compact configuration space Q=G/H. Here { A} is chosen to be the transformation group C*-algebra corresponding to the canonical action of G on Q. The structure of these algebras and their representations are examined in some detail. Inequivalent quantizations are identified with inequivalent irreducible representations of the C*-algebra corresponding to the system, hence with its superselection sectors. Introducing the concept of a pre-Hamiltonian, we construct a large class of G-invariant time-evolutions on these algebras, and find the Hamiltonians implementing these time-evolutions in each irreducible representation of { A}. “Topological” terms in the Hamiltonian (or the corresponding action) turn out to be representation-dependent, and are automatically induced by the quantization procedure. Known “topological” charge quantization or periodicity conditions are then identically satisfied as a consequence of the representation theory of { A}.

Graphs in kinematics—a need for adherence to principles of algebraic functions

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej

2017-11-01

Graphs in physics are central to the analysis of phenomena and to learning about a system’s behavior. The ways students handle graphs are frequently researched. Students’ misconceptions are highlighted, and methods of improvement suggested. While kinematics graphs are to represent a real motion, they are also algebraic entities that must satisfy conditions for being algebraic functions. To be algebraic functions, they must pass certain tests before they can be used to infer more about motion. A preliminary survey of some physics resources has revealed that little attention is paid to verifying if the position, velocity and acceleration versus time graphs, that are to depict real motion, satisfy the most critical condition for being an algebraic function; the vertical line test. The lack of attention to this adherence shows as vertical segments in piecewise graphs. Such graphs generate unrealistic interpretations and may confuse students. A group of 25 college physics students was provided with such a graph and asked to analyse its adherence to reality. The majority of the students (N  =  16, 64%) questioned the graph’s validity. It is inferred that such graphs might not only jeopardize the function principles studied in mathematics but also undermine the purpose of studying these principles. The aim of this study was to bring this idea forth and suggest a better alignment of physics and mathematics methods.

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…

Asymptotic symmetries of colored gravity in three dimensions

NASA Astrophysics Data System (ADS)

Joung, Euihun; Kim, Jaewon; Kim, Jihun; Rey, Soo-Jong

2018-03-01

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the SU( N)-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with SU( N, N) × SU( N, N) gauge group, the theory contains graviton, SU( N) Chern-Simons gauge fields and massless spin-two multiplets in the SU( N) adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of \\widehat{su(N)} Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.

Noncommuting local common causes for correlations violating the Clauser-Horne inequality

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

Hofer-Szabo, Gabor; Vecsernyes, Peter

2012-12-15

In the paper, the EPR-Bohm scenario will be reproduced in an algebraic quantum field theoretical setting with locally finite degrees of freedom. It will be shown that for a set of spatially separated correlating events (projections) maximally violating the Clauser-Horne inequality there can be given a common causal explanation if commutativity is abandoned between the common cause and the correlating events. Moreover, the noncommuting common cause will be local and supported in the common past of the correlating events.

The smooth entropy formalism for von Neumann algebras

NASA Astrophysics Data System (ADS)

Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

2016-01-01

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

The smooth entropy formalism for von Neumann algebras

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

Berta, Mario, E-mail: berta@caltech.edu; Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp; Scholz, Volkher B., E-mail: scholz@phys.ethz.ch

2016-01-15

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

Flatspace chiral supergravity

NASA Astrophysics Data System (ADS)

Bagchi, Arjun; Basu, Rudranil; Detournary, Stéphane; Parekh, Pulastya

2018-05-01

We propose a holographic duality between a 2 dimensional (2d) chiral superconformal field theory and a certain theory of supergravity in 3d with flatspace boundary conditions that is obtained as a double scaling limit of a parity breaking theory of supergravity. We show how the asymptotic symmetries of the bulk theory reduce from the "despotic" super Bondi-Metzner-Sachs algebra (or equivalently the inhomogeneous super Galilean conformal algebra) to a single copy of the super-Virasoro algebra in this limit and also reproduce the same reduction from a study of null vectors in the putative 2d dual field theory.

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Spike detection, characterization, and discrimination using feature analysis software written in LabVIEW.

PubMed

Stewart, C M; Newlands, S D; Perachio, A A

2004-12-01

Rapid and accurate discrimination of single units from extracellular recordings is a fundamental process for the analysis and interpretation of electrophysiological recordings. We present an algorithm that performs detection, characterization, discrimination, and analysis of action potentials from extracellular recording sessions. The program was entirely written in LabVIEW (National Instruments), and requires no external hardware devices or a priori information about action potential shapes. Waveform events are detected by scanning the digital record for voltages that exceed a user-adjustable trigger. Detected events are characterized to determine nine different time and voltage levels for each event. Various algebraic combinations of these waveform features are used as axis choices for 2-D Cartesian plots of events. The user selects axis choices that generate distinct clusters. Multiple clusters may be defined as action potentials by manually generating boundaries of arbitrary shape. Events defined as action potentials are validated by visual inspection of overlain waveforms. Stimulus-response relationships may be identified by selecting any recorded channel for comparison to continuous and average cycle histograms of binned unit data. The algorithm includes novel aspects of feature analysis and acquisition, including higher acquisition rates for electrophysiological data compared to other channels. The program confirms that electrophysiological data may be discriminated with high-speed and efficiency using algebraic combinations of waveform features derived from high-speed digital records.

CENTER CONDITIONS AND CYCLICITY FOR A FAMILY OF CUBIC SYSTEMS: COMPUTER ALGEBRA APPROACH.

PubMed

Ferčec, Brigita; Mahdi, Adam

2013-01-01

Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety.

Higher spin black holes with soft hair

NASA Astrophysics Data System (ADS)

Grumiller, Daniel; Pérez, Alfredo; Prohazka, Stefan; Tempo, David; Troncoso, Ricardo

2016-10-01

We construct a new set of boundary conditions for higher spin gravity, inspired by a recent "soft Heisenberg hair"-proposal for General Relativity on three-dimensional Anti-de Sitter space. The asymptotic symmetry algebra consists of a set of affine û(1) current algebras. Its associated canonical charges generate higher spin soft hair. We focus first on the spin-3 case and then extend some of our main results to spin- N , many of which resemble the spin-2 results: the generators of the asymptotic W 3 algebra naturally emerge from composite operators of the û(1) charges through a twisted Sugawara construction; our boundary conditions ensure regularity of the Euclidean solutions space independently of the values of the charges; solutions, which we call "higher spin black flowers", are stationary but not necessarily spherically symmetric. Finally, we derive the entropy of higher spin black flowers, and find that for the branch that is continuously connected to the BTZ black hole, it depends only on the affine purely gravitational zero modes. Using our map to W -algebra currents we recover well-known expressions for higher spin entropy. We also address higher spin black flowers in the metric formalism and achieve full consistency with previous results.

Compressive Information Extraction: A Dynamical Systems Approach

DTIC Science & Technology

2016-01-24

sparsely encoded in very large data streams. (a) Target tracking in an urban canyon; (b) and (c) sample frames showing contextually abnormal events: onset...extraction to identify contextually abnormal se- quences (see section 2.2.3). Formally, the problem of interest can be stated as establishing whether a noisy...relaxations with optimality guarantees can be obtained using tools from semi-algebraic geometry. 2.2 Application: Detecting Contextually Abnormal Events

Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces

NASA Astrophysics Data System (ADS)

Choi, Yun Sung; Han, Kwang Hee

2006-11-01

Let be the Banach algebra of all complex-valued bounded continuous functions on the closed unit ball BE of a complex Banach space E and holomorphic in the interior of BE and let be the closed subalgebra of those functions which are uniformly continuous on BE. For the case whose bidual is a Marcinkiewicz sequence space Mw, we describe some sufficient conditions for a set to be a boundary of either or . Moreover, we consider some analogous problems on to those which were studied on the Gowers space Gp of characteristic p by Grados and Moraes [L.R. Grados, L.A. Moraes, Boundaries for algebras of holomorphic functions, J. Math. Anal. Appl. 281 (2003) 575-586; L.R. Grados, L.A. Moraes, Boundaries for an algebra of bounded holomorphic functions, J. Korean Math. Soc. 41 (1) (2004) 231-242].

An extension of the OpenModelica compiler for using Modelica models in a discrete event simulation

DOE PAGES

Nutaro, James

2014-11-03

In this article, a new back-end and run-time system is described for the OpenModelica compiler. This new back-end transforms a Modelica model into a module for the adevs discrete event simulation package, thereby extending adevs to encompass complex, hybrid dynamical systems. The new run-time system that has been built within the adevs simulation package supports models with state-events and time-events and that comprise differential-algebraic systems with high index. Finally, although the procedure for effecting this transformation is based on adevs and the Discrete Event System Specification, it can be adapted to any discrete event simulation package.

Representations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices

PubMed Central

Liu, Xiaoji; Qin, Xiaolan

2015-01-01

We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix. PMID:25729767

Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices.

PubMed

Liu, Xiaoji; Qin, Xiaolan

2015-01-01

We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.

The Existence of the Solution to One Kind of Algebraic Riccati Equation

NASA Astrophysics Data System (ADS)

Liu, Jianming

2018-03-01

The matrix equation ATX + XA + XRX + Q = O is called algebraic Riccati equation, which is very important in the fields of automatic control and other engineering applications. Many researchers have studied the solutions to various algebraic Riccati equations and most of them mainly applied the matrix methods, while few used the functional analysis theories. This paper mainly studies the existence of the solution to the following kind of algebraic Riccati equation from the functional view point: ATX + XA + XRX ‑λX + Q = O Here, X, A, R, Q ∈ n×n , Q is a symmetric matrix, and R is a positive or negative semi-definite matrix, λ is arbitrary constants. This paper uses functional approach such as fixed point theorem and contraction mapping thinking so as to provide two sufficient conditions for the solvability about this kind of Riccati equation and to arrive at some relevant conclusions.

Short Round Sub-Linear Zero-Knowledge Argument for Linear Algebraic Relations

NASA Astrophysics Data System (ADS)

Seo, Jae Hong

Zero-knowledge arguments allows one party to prove that a statement is true, without leaking any other information than the truth of the statement. In many applications such as verifiable shuffle (as a practical application) and circuit satisfiability (as a theoretical application), zero-knowledge arguments for mathematical statements related to linear algebra are essentially used. Groth proposed (at CRYPTO 2009) an elegant methodology for zero-knowledge arguments for linear algebraic relations over finite fields. He obtained zero-knowledge arguments of the sub-linear size for linear algebra using reductions from linear algebraic relations to equations of the form z = x *' y, where x, y ∈ Fnp are committed vectors, z ∈ Fp is a committed element, and *' : Fnp × Fnp → Fp is a bilinear map. These reductions impose additional rounds on zero-knowledge arguments of the sub-linear size. The round complexity of interactive zero-knowledge arguments is an important measure along with communication and computational complexities. We focus on minimizing the round complexity of sub-linear zero-knowledge arguments for linear algebra. To reduce round complexity, we propose a general transformation from a t-round zero-knowledge argument, satisfying mild conditions, to a (t - 2)-round zero-knowledge argument; this transformation is of independent interest.

Enlarged symmetry algebras of spin chains, loop models, and S-matrices

NASA Astrophysics Data System (ADS)

Read, N.; Saleur, H.

2007-08-01

The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site ( m⩾2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform alternately along the chain in the fundamental m and its conjugate representation m¯. We find that these spin chains, even with arbitrary coefficients of these interactions, have a symmetry algebra A much larger than U(m), which implies that the energy eigenstates fall into sectors that for open chains (i.e., free boundary conditions) can be labeled by j=0,1,…,L, for the 2 L-site chain such that the degeneracies of all eigenvalues in the jth sector are generically the same and increase rapidly with j. For large j, these degeneracies are much larger than those that would be expected from the U(m) symmetry alone. The enlarged symmetry algebra A(2L) consists of operators that commute in this space of states with the Temperley-Lieb algebra that is generated by the set of nearest-neighbor interaction terms; A(2L) is not a Yangian. There are similar results for supersymmetric chains with gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer representation structure for closed chains (i.e., periodic boundary conditions). The symmetries also apply to the loop models that can be obtained from the spin chains in a spacetime or transfer matrix picture. In the loop language, the symmetries arise because the loops cannot cross. We further define tensor products of representations (for the open chains) by joining chains end to end. The fusion rules for decomposing the tensor product of representations labeled j and j take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra A into a ribbon Hopf algebra, and we show that this is "Morita equivalent" to the quantum group U(sl) for m=q+q. The open-chain results are extended to the cases |m|<2 for which the algebras are no longer semisimple; these possess continuum limits that are critical (conformal) field theories, or massive perturbations thereof. Such models, for open and closed boundary conditions, arise in connection with disordered fermions, percolation, and polymers (self-avoiding walks), and certain non-linear sigma models, all in two dimensions. A product operation is defined in a related way for the Temperley-Lieb representations also, and the fusion rules for this are related to those for A or U(sl) representations; this is useful for the continuum limits also, as we discuss in a companion paper.

From Quantum Fields to Local Von Neumann Algebras

NASA Astrophysics Data System (ADS)

Borchers, H. J.; Yngvason, Jakob

The subject of the paper is an old problem of the general theory of quantized fields: When can the unbounded operators of a Wightman field theory be associated with local algebras of bounded operators in the sense of Haag? The paper reviews and extends previous work on this question, stressing its connections with a noncommutive generalization of the classical Hamburger moment problem. Necessary and sufficient conditions for the existence of a local net of von Neumann algebras corresponding to a given Wightman field are formulated in terms of strengthened versions of the usual positivity property of Wightman functionals. The possibility that the local net has to be defined in an enlarged Hilbert space cannot be ruled out in general. Under additional hypotheses, e.g., if the field operators obey certain energy bounds, such an extension of the Hilbert space is not necessary, however. In these cases a fairly simple condition for the existence of a local net can be given involving the concept of “central positivity” introduced by Powers. The analysis presented here applies to translationally covariant fields with an arbitrary number of components, whereas Lorentz covariance is not needed. The paper contains also a brief discussion of an approach to noncommutative moment problems due to Dubois-Violette, and concludes with some remarks on modular theory for algebras of unbounded operators.

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.

Measurement theory in local quantum physics

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

Okamura, Kazuya, E-mail: okamura@math.cm.is.nagoya-u.ac.jp; Ozawa, Masanao, E-mail: ozawa@is.nagoya-u.ac.jp

In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP, extending the well-known result for type I factors. Moreover, we show that every CP instrument on an injective von Neumann algebra is approximated bymore » CP instruments with the NEP. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Two examples of CP instruments without the NEP are obtained from this result. It is thus concluded that in local quantum physics not every CP instrument represents a measuring process, but in most of physically relevant cases every CP instrument can be realized by a measuring process within arbitrary error limits, as every approximately finite dimensional von Neumann algebra on a separable Hilbert space is injective. To conclude the paper, the concept of local measurement in algebraic quantum field theory is examined in our framework. In the setting of the Doplicher-Haag-Roberts and Doplicher-Roberts theory describing local excitations, we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a CP instrument with the NEP, provided that the split property holds for the net of local algebras.« less

Communication: Analysing kinetic transition networks for rare events.

PubMed

Stevenson, Jacob D; Wales, David J

2014-07-28

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.

A Pulsatile Cardiovascular Computer Model for Teaching Heart-Blood Vessel Interaction.

ERIC Educational Resources Information Center

Campbell, Kenneth; And Others

1982-01-01

Describes a model which gives realistic predictions of pulsatile pressure, flow, and volume events in the cardiovascular system. Includes computer oriented laboratory exercises for veterinary and graduate students; equations of the dynamic and algebraic models; and a flow chart for the cardiovascular teaching program. (JN)

Designing Algebraic Tasks for 7-Year-Old Students--A Pilot Project Inspired by Davydov's "Learning Activity" Concept

ERIC Educational Resources Information Center

Eriksson, Inger; Jansson, Anders

2017-01-01

The issue of this article is to identify and discuss what conditions may be necessary to build into tasks to make it likely for students to be involved in an algebraic Learning Activity inspired by Davydov. Data from a pilot study was used in which a group of students (N = 28) in grade 1 (7-year-olds) were invited to participate in discussions and…

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.

Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis

NASA Astrophysics Data System (ADS)

Martin, J.; Shore, B. W.; Bergmann, K.

1995-07-01

We extend previous theoretical work on coherent population transfer by stimulated Raman adiabatic passage for states involving nonzero angular momentum. The pump and Stokes fields are either copropagating or counterpropagating with the corresponding linearly polarized electric-field vectors lying in a common plane with the magnetic-field direction. Zeeman splitting lifts the magnetic sublevel degeneracy. We present an algebraic analysis of dressed-state properties to explain the behavior noted in numerical studies. In particular, we discuss conditions which are likely to lead to a failure of complete population transfer. The applied strategy, based on simple methods of linear algebra, will also be successful for other types of discrete multilevel systems, provided the rotating-wave and adiabatic approximation are valid.

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2017-06-01

In this paper we show that warped AdS3 black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS3 spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with U(1) current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincides with what we obtain via Cardy’s formula. As we expect, the warped Cardy formula also gives us exactly the same result as we obtain from the usual Cardy’s formula. We calculate mass and angular momentum of the warped black hole and then check that obtained mass, angular momentum and entropy to satisfy the first law of the black hole mechanics. According to the results of this paper we believe that the dual theory of the warped AdS3 black hole solution of GMMG is a warped CFT.

Motion Planning in a Society of Intelligent Mobile Agents

NASA Technical Reports Server (NTRS)

Esterline, Albert C.; Shafto, Michael (Technical Monitor)

2002-01-01

The majority of the work on this grant involved formal modeling of human-computer integration. We conceptualize computer resources as a multiagent system so that these resources and human collaborators may be modeled uniformly. In previous work we had used modal for this uniform modeling, and we had developed a process-algebraic agent abstraction. In this work, we applied this abstraction (using CSP) in uniformly modeling agents and users, which allowed us to use tools for investigating CSP models. This work revealed the power of, process-algebraic handshakes in modeling face-to-face conversation. We also investigated specifications of human-computer systems in the style of algebraic specification. This involved specifying the common knowledge required for coordination and process-algebraic patterns of communication actions intended to establish the common knowledge. We investigated the conditions for agents endowed with perception to gain common knowledge and implemented a prototype neural-network system that allows agents to detect when such conditions hold. The literature on multiagent systems conceptualizes communication actions as speech acts. We implemented a prototype system that infers the deontic effects (obligations, permissions, prohibitions) of speech acts and detects violations of these effects. A prototype distributed system was developed that allows users to collaborate in moving proxy agents; it was designed to exploit handshakes and common knowledge Finally. in work carried over from a previous NASA ARC grant, about fifteen undergraduates developed and presented projects on multiagent motion planning.

Symmetries and the u-condition in Hom-Yetter-Drinfeld categories

PubMed Central

Wang, Shengxiang; Guo, Shuangjian

2014-01-01

Let (H, S, α) be a monoidal Hom-Hopf algebra and \\documentclass[12pt]{minimal}\\begin{document}$^{H}_{H}\\mathcal {HYD}$\\end{document}HYDHH the Hom-Yetter-Drinfeld category over (H, α). Then in this paper, we first find sufficient and necessary conditions for \\documentclass[12pt]{minimal}\\begin{document}$^{H}_{H}\\mathcal {HYD}$\\end{document}HYDHH to be symmetric and pseudosymmetric, respectively. Second, we study the u-condition in \\documentclass[12pt]{minimal}\\begin{document}$^{H}_{H}\\mathcal {HYD}$\\end{document}HYDHH and show that the Hom-Yetter-Drinfeld module (H, adjoint, Δ, α) (resp., (H, m, coadjoint, α)) satisfies the u-condition if and only if S2 = id. Finally, we prove that \\documentclass[12pt]{minimal}\\begin{document}$^{H}_{H}\\mathcal {HYD}$\\end{document}HYDHH over a triangular (resp., cotriangular) Hom-Hopf algebra contains a rich symmetric subcategory. PMID:25278632

Revisiting Ramakrishnan's approach to relatively. [Velocity addition theorem uniqueness

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

Nandi, K.K.; Shankara, T.S.

The conditions under which the velocity addition theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications. 9 references.

Convergence of the standard RLS method and UDUT factorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

NASA Astrophysics Data System (ADS)

Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.

2015-08-01

The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.

Strings on complex multiplication tori and rational conformal field theory with matrix level

NASA Astrophysics Data System (ADS)

Nassar, Ali

Conformal invariance in two dimensions is a powerful symmetry. Two-dimensional quantum field theories which enjoy conformal invariance, i.e., conformal field theories (CFTs) are of great interest in both physics and mathematics. CFTs describe the dynamics of the world sheet in string theory where conformal symmetry arises as a remnant of reparametrization invariance of the world-sheet coordinates. In statistical mechanics, CFTs describe the critical points of second order phase transitions. On the mathematics side, conformal symmetry gives rise to infinite dimensional chiral algebras like the Virasoro algebra or extensions thereof. This gave rise to the study of vertex operator algebras (VOAs) which is an interesting branch of mathematics. Rational conformal theories are a simple class of CFTs characterized by a finite number of representations of an underlying chiral algebra. The chiral algebra leads to a set of Ward identities which gives a complete non-perturbative solution of the RCFT. Identifying the chiral algebra of an RCFT is a very important step in solving it. Particularly interesting RCFTs are the ones which arise from the compactification of string theory as sigma-models on a target manifold M. At generic values of the geometric moduli of M, the corresponding CFT is not rational. Rationality can arise at particular values of the moduli of M. At these special values of the moduli, the chiral algebra is extended. This interplay between the geometric picture and the algebraic description encoded in the chiral algebra makes CFTs/RCFTs a perfect link between physics and mathematics. It is always useful to find a geometric interpretation of a chiral algebra in terms of a sigma-model on some target manifold M. Then the next step is to figure out the conditions on the geometric moduli of M which gives a RCFT. In this thesis, we limit ourselves to the simplest class of string compactifications, i.e., strings on tori. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. On the other hand, the study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of U m,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.

Eisenstein Hecke algebras and Iwasawa theory

NASA Astrophysics Data System (ADS)

Wake, Preston

We show that if an Eisenstein component of the p-adic Hecke algebra associated to modular forms is Gorenstein, then it is necessary that the plus-part of a certain ideal class group is trivial. We also show that this condition is sufficient whenever a conjecture of Sharifi holds. We also formulate a weaker Gorenstein property, and show that this weak Gorenstein property holds if and only if a weak form of Sharifi's conjecture and a weak form of Greenberg's conjecture hold.

Classification of commutator algebras leading to the new type of closed Baker-Campbell-Hausdorff formulas

NASA Astrophysics Data System (ADS)

Matone, Marco

2015-11-01

We show that there are {\\it 13 types} of commutator algebras leading to the new closed forms of the Baker-Campbell-Hausdorff (BCH) formula $$\\exp(X)\\exp(Y)\\exp(Z)=\\exp({AX+BZ+CY+DI}) \\ , $$ derived in arXiv:1502.06589, JHEP {\\bf 1505} (2015) 113. This includes, as a particular case, $\\exp(X) \\exp(Z)$, with $[X,Z]$ containing other elements in addition to $X$ and $Z$. The algorithm exploits the associativity of the BCH formula and is based on the decomposition $\\exp(X)\\exp(Y)\\exp(Z)=\\exp(X)\\exp({\\alpha Y}) \\exp({(1-\\alpha) Y}) \\exp(Z)$, with $\\alpha$ fixed in such a way that it reduces to $\\exp({\\tilde X})\\exp({\\tilde Y})$, with $\\tilde X$ and $\\tilde Y$ satisfying the Van-Brunt and Visser condition $[\\tilde X,\\tilde Y]=\\tilde u\\tilde X+\\tilde v\\tilde Y+\\tilde cI$. It turns out that $e^\\alpha$ satisfies, in the generic case, an algebraic equation whose exponents depend on the parameters defining the commutator algebra. In nine {\\it types} of commutator algebras, such an equation leads to rational solutions for $\\alpha$. We find all the equations that characterize the solution of the above decomposition problem by combining it with the Jacobi identity.

Children's Use of Variables and Variable Notation to Represent Their Algebraic Ideas

ERIC Educational Resources Information Center

Brizuela, Bárbara M.; Blanton, Maria; Sawrey, Katharine; Newman-Owens, Ashley; Murphy Gardiner, Angela

2015-01-01

In this article, we analyze a first grade classroom episode and individual interviews with students who participated in that classroom event to provide evidence of the variety of understandings about variable and variable notation held by first grade children approximately six years of age. Our findings illustrate that given the opportunity,…

Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras

NASA Astrophysics Data System (ADS)

Pirkovskii, Alexei Yu

2012-08-01

We prove the equation \\operatorname{w{.}dg} A=\\operatorname{w{.}db} A for every nuclear Fréchet-Arens-Michael algebra A of finite weak bidimension, where \\operatorname{w{.}dg} A is the weak global dimension and \\operatorname{w{.}db} A the weak bidimension of A. Assuming that A has a projective bimodule resolution of finite type, we establish the estimate \\operatorname{db}A\\le\\operatorname{dg}A+1, where \\operatorname{dg} A is the global dimension and \\operatorname{db} A the bidimension of A. We also prove that \\operatorname{dg}A=\\operatorname{db}A=\\operatorname{w{.}dg}A=\\operatorname{w{.}db} A=n for all nuclear Fréchet-Arens-Michael algebras satisfying the Van den Bergh conditions \\operatorname{VdB}(n). As an application, we calculate the homological dimensions of smooth and complex-analytic quantum tori.

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra by quantum separation of variables

NASA Astrophysics Data System (ADS)

Pezelier, Baptiste

2018-02-01

In this proceeding, we recall the notion of quantum integrable systems on a lattice and then introduce the Sklyanin’s Separation of Variables method. We sum up the main results for the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazanov-Stroganov Lax operator. These results apply as well to the spectral analysis of the lattice sine-Gordon model with open boundary conditions. The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations. We state an equivalent characterization as the set of solutions to a Baxter’s like T-Q functional equation, allowing us to rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form.

Beyond E 11

NASA Astrophysics Data System (ADS)

Bossard, Guillaume; Kleinschmidt, Axel; Palmkvist, Jakob; Pope, Christopher N.; Sezgin, Ergin

2017-05-01

We study the non-linear realisation of E 11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E 11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E 11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E 11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.

Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

NASA Astrophysics Data System (ADS)

Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

2018-04-01

A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

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.

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

Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

Model predictive control of P-time event graphs

NASA Astrophysics Data System (ADS)

Hamri, H.; Kara, R.; Amari, S.

2016-12-01

This paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.

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.

Near-horizon conformal symmetry and black hole entropy.

PubMed

Carlip, S

2002-06-17

Near an event horizon, the action of general relativity acquires a new asymptotic conformal symmetry. For two-dimensional dilaton gravity, this symmetry results in a chiral Virasoro algebra, and Cardy's formula for the density of states reproduces the Bekenstein-Hawking entropy. This lends support to the notion that black hole entropy is controlled universally by conformal symmetry near the horizon.

Symbolic-Numerical Modeling of the Influence of Damping Moments on Satellite Dynamics

NASA Astrophysics Data System (ADS)

Gutnik, Sergey A.; Sarychev, Vasily A.

2018-02-01

The dynamics of a satellite on a circular orbit under the influence of gravitational and active damping torques, which are proportional to the projections of the angular velocity of the satellite, is investigated. Computer algebra Gröbner basis methods for the determination of all equilibrium orientations of the satellite in the orbital coordinate system with given damping torque and given principal central moments of inertia were used. The conditions of the equilibria existence depending on three damping parameters were obtained from the analysis of the real roots of the algebraic equations spanned by the constructed Gröbner basis. Conditions of asymptotic stability of the satellite equilibria and the transition decay processes of the spatial oscillations of the satellite at different damping parameters have also been obtained.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Concerning an application of the method of least squares with a variable weight matrix

NASA Technical Reports Server (NTRS)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

NASA Technical Reports Server (NTRS)

Robertson, D. K.

1985-01-01

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

Necessary and sufficient conditions for R₀ to be a sum of contributions of fertility loops.

PubMed

Rueffler, Claus; Metz, Johan A J

2013-03-01

Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341-1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio R₀ in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end, we develop a fully algebraic counterpart of their graph-reduction method which we actually found more useful in concrete applications. Both methods, if they work, give a simple algebraic formula that can be interpreted as the sum of contributions of all fertility loops. This formula can be used in e.g. pest control and conservation biology, where it can complement sensitivity and elasticity analyses. The simplest of the necessary and sufficient conditions is that, for irreducible projection matrices, all paths from birth to reproduction have to pass through a common state. This state may be visible in the state representation for the chosen sampling time, but the passing may also occur in between sampling times, like a seed stage in the case of sampling just before flowering. Note that there may be more than one birth state, like when plants in their first year can already have different sizes at the sampling time. Also the common state may occur only later in life. However, in all cases R₀ allows a simple interpretation as the expected number of new individuals that in the next generation enter the common state deriving from a single individual in this state. We end with pointing to some alternative algebraically simple quantities with properties similar to those of R₀ that may sometimes be used to good effect in cases where no simple formula for R₀ exists.

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

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

Giorda, Paolo; Zanardi, Paolo; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi and S. Lloyd, e-print quant-ph/0305013. The quantum state space H encoding information decomposes into irreducible sectors and subsystems associated with the group of available evolutions. If this group coincides with the unitary part of the group algebra CK of some group K then universal control is achievable over the K-irreducible components of H. This general strategy is applied to different kinds of bosonic systems. We first consider massive bosons in a double well and show how to achieve universal control over all finite-dimensional Fock sectors. We thenmore » discuss a multimode massless case giving the conditions for generating the whole infinite-dimensional multimode Heisenberg-Weyl enveloping algebra. Finally we show how to use an auxiliary bosonic mode coupled to finite-dimensional systems to generate high-order nonlinearities needed for universal control.« less

The Robustness Analysis of Wireless Sensor Networks under Uncertain Interference

PubMed Central

Deng, Changjian

2013-01-01

Based on the complex network theory, robustness analysis of condition monitoring wireless sensor network under uncertain interference is present. In the evolution of the topology of sensor networks, the density weighted algebraic connectivity is taken into account, and the phenomenon of removing and repairing the link and node in the network is discussed. Numerical simulation is conducted to explore algebraic connectivity characteristics and network robustness performance. It is found that nodes density has the effect on algebraic connectivity distribution in the random graph model; high density nodes carry more connections, use more throughputs, and may be more unreliable. Moreover, the results show that, when network should be more error tolerant or robust by repairing nodes or adding new nodes, the network should be better clustered in median and high scale wireless sensor networks and be meshing topology in small scale networks. PMID:24363613

Construction of Orthonormal Wavelets Using Symbolic Algebraic Methods

NASA Astrophysics Data System (ADS)

Černá, Dana; Finěk, Václav

2009-09-01

Our contribution is concerned with the solution of nonlinear algebraic equations systems arising from the computation of scaling coefficients of orthonormal wavelets with compact support. Specifically Daubechies wavelets, symmlets, coiflets, and generalized coiflets. These wavelets are defined as a solution of equation systems which are partly linear and partly nonlinear. The idea of presented methods consists in replacing those equations for scaling coefficients by equations for scaling moments. It enables us to eliminate some quadratic conditions in the original system and then simplify it. The simplified system is solved with the aid of the Gröbner basis method. The advantage of our approach is that in some cases, it provides all possible solutions and these solutions can be computed to arbitrary precision. For small systems, we are even able to find explicit solutions. The computation was carried out by symbolic algebra software Maple.

RANS modeling of scalar dispersion from localized sources within a simplified urban-area model

NASA Astrophysics Data System (ADS)

Rossi, Riccardo; Capra, Stefano; Iaccarino, Gianluca

2011-11-01

The dispersion of a passive scalar downstream a localized source within a simplified urban-like geometry is examined by means of RANS scalar flux models. The computations are conducted under conditions of neutral stability and for three different incoming wind directions (0°, 45°, 90°) at a roughness Reynolds number of Ret = 391. A Reynolds stress transport model is used to close the flow governing equations whereas both the standard eddy-diffusivity closure and algebraic flux models are employed to close the transport equation for the passive scalar. The comparison with a DNS database shows improved reliability from algebraic scalar flux models towards predicting both the mean concentration and the plume structure. Since algebraic flux models do not increase substantially the computational effort, the results indicate that the use of tensorial-diffusivity can be promising tool for dispersion simulations for the urban environment.

Algebraic and Probabilistic Bases for Fuzzy Sets and the Development of Fuzzy Conditioning

DTIC Science & Technology

1991-08-01

results; and also recently, among others, Bruno & Gilio (1985) bringing forth the basic is- e of combining implicatives compatible with conditional...probabilistic bases for fuzzy sets 67 7. Bruno, G. & Gilio , A. (1985), Confronto fra eventi condizionati di probabililiti nulla nell’ inferenza statistica

Demazure Modules, Fusion Products and Q-Systems

NASA Astrophysics Data System (ADS)

Chari, Vyjayanthi; Venkatesh, R.

2015-01-01

In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the current algebra associated to a simple Lie algebra. These modules are indexed by an -tuple of partitions , where α varies over a set of positive roots of and we assume that they satisfy a natural compatibility condition. In the case when the are all rectangular, for instance, we prove that these modules are Demazure modules in various levels. As a consequence, we see that the defining relations of Demazure modules can be greatly simplified. We use this simplified presentation to relate our results to the fusion products, defined in (Feigin and Loktev in Am Math Soc Transl Ser (2) 194:61-79, 1999), of representations of the current algebra. We prove that the Q-system of (Hatayama et al. in Contemporary Mathematics, vol. 248, pp. 243-291. American Mathematical Society, Providence, 1998) extends to a canonical short exact sequence of fusion products of representations associated to certain special partitions .Finally, in the last section we deal with the case of and prove that the modules we define are just fusion products of irreducible representations of the associated current algebra and give monomial bases for these modules.

Absolute continuity for operator valued completely positive maps on C∗-algebras

NASA Astrophysics Data System (ADS)

Gheondea, Aurelian; Kavruk, Ali Şamil

2009-02-01

Motivated by applicability to quantum operations, quantum information, and quantum probability, we investigate the notion of absolute continuity for operator valued completely positive maps on C∗-algebras, previously introduced by Parthasarathy [in Athens Conference on Applied Probability and Time Series Analysis I (Springer-Verlag, Berlin, 1996), pp. 34-54]. We obtain an intrinsic definition of absolute continuity, we show that the Lebesgue decomposition defined by Parthasarathy is the maximal one among all other Lebesgue-type decompositions and that this maximal Lebesgue decomposition does not depend on the jointly dominating completely positive map, we obtain more flexible formulas for calculating the maximal Lebesgue decomposition, and we point out the nonuniqueness of the Lebesgue decomposition as well as a sufficient condition for uniqueness. In addition, we consider Radon-Nikodym derivatives for absolutely continuous completely positive maps that, in general, are unbounded positive self-adjoint operators affiliated to a certain von Neumann algebra, and we obtain a spectral approximation by bounded Radon-Nikodym derivatives. An application to the existence of the infimum of two completely positive maps is indicated, and formulas in terms of Choi's matrices for the Lebesgue decomposition of completely positive maps in matrix algebras are obtained.

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

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

Bonatsos, Dennis; Karampagia, S.; Casten, R. F.

2011-05-15

Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limit of the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies within the Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices in the midst of chaotic regions. In addition to providing an explanation formore » the existence of the arc of regularity, the present line represents an example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotational band become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.« less

Parametric modelling of cardiac system multiple measurement signals: an open-source computer framework for performance evaluation of ECG, PCG and ABP event detectors.

PubMed

Homaeinezhad, M R; Sabetian, P; Feizollahi, A; Ghaffari, A; Rahmani, R

2012-02-01

The major focus of this study is to present a performance accuracy assessment framework based on mathematical modelling of cardiac system multiple measurement signals. Three mathematical algebraic subroutines with simple structural functions for synthetic generation of the synchronously triggered electrocardiogram (ECG), phonocardiogram (PCG) and arterial blood pressure (ABP) signals are described. In the case of ECG signals, normal and abnormal PQRST cycles in complicated conditions such as fascicular ventricular tachycardia, rate dependent conduction block and acute Q-wave infarctions of inferior and anterolateral walls can be simulated. Also, continuous ABP waveform with corresponding individual events such as systolic, diastolic and dicrotic pressures with normal or abnormal morphologies can be generated by another part of the model. In addition, the mathematical synthetic PCG framework is able to generate the S4-S1-S2-S3 cycles in normal and in cardiac disorder conditions such as stenosis, insufficiency, regurgitation and gallop. In the PCG model, the amplitude and frequency content (5-700 Hz) of each sound and variation patterns can be specified. The three proposed models were implemented to generate artificial signals with varies abnormality types and signal-to-noise ratios (SNR), for quantitative detection-delineation performance assessment of several ECG, PCG and ABP individual event detectors designed based on the Hilbert transform, discrete wavelet transform, geometric features such as area curve length (ACLM), the multiple higher order moments (MHOM) metric, and the principal components analysed geometric index (PCAGI). For each method the detection-delineation operating characteristics were obtained automatically in terms of sensitivity, positive predictivity and delineation (segmentation) error rms and checked by the cardiologist. The Matlab m-file script of the synthetic ECG, ABP and PCG signal generators are available in the Appendix.

Thin-layer approximation and algebraic model for separated turbulent flows

NASA Technical Reports Server (NTRS)

Baldwin, B.; Lomax, H.

1978-01-01

An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

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.

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.

Alternative probability theories for cognitive psychology.

PubMed

Narens, Louis

2014-01-01

Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling. Copyright © 2013 Cognitive Science Society, Inc.

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

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Composite system in rotationally invariant noncommutative phase space

NASA Astrophysics Data System (ADS)

Gnatenko, Kh. P.; Tkachuk, V. M.

2018-03-01

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

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)

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.

On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories

NASA Astrophysics Data System (ADS)

Belletête, J.; Gainutdinov, A. M.; Jacobsen, J. L.; Saleur, H.; Vasseur, R.

2017-12-01

The relationship between bulk and boundary properties is one of the founding features of (rational) conformal field theory (CFT). Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice models. We focus on models based on the Temperley-Lieb algebra, and use the concept of ‘braid translation’, which is a natural way, in physical terms, to ‘close’ an open spin chain by adding an interaction between the first and last spins using braiding to ‘bring’ them next to each other. The interaction thus obtained is in general non-local, but has the key feature that it is expressed solely in terms of the algebra for the open spin chain—the ‘ordinary’ Temperley-Lieb algebra and its blob algebra generalization. This is in contrast with the usual periodic spin chains which involve only local interactions, and are described by the periodic Temperley-Lieb algebra. We show that for the restricted solid-on-solid models, which are known to be described by minimal unitary CFTs (with central charge c<1 ) in the continuum limit, the braid translation in fact does provide the ordinary periodic model starting from the open model with fixed (identical) boundary conditions on the two sides of the strip. This statement has a precise mathematical formulation, which is a pull-back map between irreducible modules of, respectively, the blob algebra and the affine Temperley-Lieb algebra. We then turn to the same kind of analysis for two models whose continuum limits are logarithmic CFTs (LCFTs)—the alternating gl(1\\vert 1) and sl(2\\vert 1) spin chains. We find that the result for minimal models does not hold any longer: braid translation of the relevant (in that case, indecomposable but not irreducible) modules of the Temperley-Lieb algebra does not give rise to the modules known to be present in the periodic chains. In the gl(1\\vert 1) case, the content in terms of the irreducibles is the same, as well as the spectrum, but the detailed structure (like logarithmic coupling) is profoundly different. This carries over to the continuum limit. The situation is similar for the sl(2\\vert 1) case. The problem of relating bulk and boundary lattice models for LCFTs thus remains open.

Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

NASA Astrophysics Data System (ADS)

Zhang, Tianjie; Gao, Xing; Guo, Li

2016-10-01

The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

The Unitality of Quantum B-algebras

NASA Astrophysics Data System (ADS)

Han, Shengwei; Xu, Xiaoting; Qin, Feng

2018-02-01

Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.

Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

NASA Astrophysics Data System (ADS)

Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

2018-03-01

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

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

Suh, Uhi Rinn, E-mail: uhrisu1@math.snu.ac.kr

We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms ofmore » free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.« less

A note on derivations of Murray–von Neumann algebras

PubMed Central

Kadison, Richard V.; Liu, Zhe

2014-01-01

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. PMID:24469831

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

Assessing Algebraic Solving Ability: A Theoretical Framework

ERIC Educational Resources Information Center

Lian, Lim Hooi; Yew, Wun Thiam

2012-01-01

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

On the intersection of irreducible components of the space of finite-dimensional Lie algebras

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

Gorbatsevich, Vladimir V

2012-07-31

The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra ismore » considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.« less

A Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples.

NASA Astrophysics Data System (ADS)

Tate, Ranjeet Shekhar

1992-01-01

General relativity has two features in particular, which make it difficult to apply to it existing schemes for the quantization of constrained systems. First, there is no background structure in the theory, which could be used, e.g., to regularize constraint operators, to identify a "time" or to define an inner product on physical states. Second, in the Ashtekar formulation of general relativity, which is a promising avenue to quantum gravity, the natural variables for quantization are not canonical; and, classically, there are algebraic identities between them. Existing schemes are usually not concerned with such identities. Thus, from the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a general prescription to find the physical inner product, and is flexible enough to accommodate non -canonical variables. In this dissertation I present an algebraic formulation of the Dirac approach to the quantization of constrained systems. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to general relativity, and may give some insight into the pitfalls lurking in quantum gravity. The previous quantizations of one such model had many surprising features. When this model is quantized using the algebraic program, there is no longer any unexpected behaviour. I also construct the complete quantum theory for a previously unsolved relativistic cosmology. All these models indicate that the algebraic formulation provides powerful new tools for quantization. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such "dynamically constrained" systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.

Physical Limits on the Predictability of Erosion and Sediment Transport by Landslides and Debris Flows

NASA Astrophysics Data System (ADS)

Iverson, R. M.

2015-12-01

Episodic landslides and debris flows play a key role in sculpting many steep landscapes, and they also pose significant natural hazards. Field evidence, laboratory experiments, and theoretical analyses show that variations in the quantity, speed, and distance of sediment transport by landslides and debris flows can depend strongly on nuanced differences in initial conditions. Moreover, initial conditions themselves can be strongly dependent on the geological legacy of prior events. The scope of these dependencies is revealed by the results of landslide dynamics experiments [Iverson et al., Science, 2000], debris-flow erosion experiments [Iverson et al., Nature Geosci., 2011], and numerical simulations of the highly destructive 2014 Oso, Washington, landslide [Iverson et al., Earth Planet. Sci. Let., 2015]. In each of these cases, feedbacks between basal sediment deformation and pore-pressure generation cause the speed and distance of sediment transport to be very sensitive to subtle differences in the ambient sediment porosity and water content. On the other hand, the onset of most landslides and debris flows depends largely on pore-water pressure distributions and only indirectly on sediment porosity and water content. Thus, even if perfect predictions of the locations and timing of landslides and debris flows were available, the dynamics of the events - and their consequent hazards and sediment transport - would be difficult to predict. This difficulty is a manifestation of the nonlinear physics involved, rather than of poor understanding of those physics. Consequently, physically based models for assessing the hazards and sediment transport due to landslides and debris flows must take into account both evolving nonlinear dynamics and inherent uncertainties about initial conditions. By contrast, landscape evolution models that use prescribed algebraic formulas to represent sediment transport by landslides and debris flows lack a sound physical basis.

Thermodynamics. [algebraic structure

NASA Technical Reports Server (NTRS)

Zeleznik, F. J.

1976-01-01

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

Invariants of the Jacobi-Porstendorfer room model for radon progeny in indoor air.

PubMed

Thomas, Josef; Jilek, Karel

2012-06-01

The Jacobi-Porstendörfer room model, describing the dynamical behaviour of radon and radon progeny in indoor air, has been successfully used for decades. The inversion of the model-the determination of the five parameters from measured results which provide better information on the room environment than mere ratios of unattached and attached radon progeny-is treated as an algebraic task. The linear interdependence of the used equations strongly limits the algebraic invertibility of experimental results. For a unique solution, the fulfilment of two invariants of the room model for the measured results is required. Non-fulfilment of these model invariants by the measured results leads to a set of non-identical solutions and indicates the violation of the conditions required by the room model or the incorrectness or excessive uncertainties of the measured results. The limited and non-unique algebraic invertibility of the room model is analysed numerically using our own data for the radon progeny.

Minimal models of compact symplectic semitoric manifolds

NASA Astrophysics Data System (ADS)

Kane, D. M.; Palmer, J.; Pelayo, Á.

2018-02-01

A symplectic semitoric manifold is a symplectic 4-manifold endowed with a Hamiltonian (S1 × R) -action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic semitoric manifolds, the helix, and give applications. The helix is a symplectic analogue of the fan of a nonsingular complete toric variety in algebraic geometry, that takes into account the effects of the monodromy near focus-focus singularities. We give two applications of the helix: first, we use it to give a classification of the minimal models of symplectic semitoric manifolds, where "minimal" is in the sense of not admitting any blowdowns. The second application is an extension to the compact case of a well known result of Vũ Ngọc about the constraints posed on a symplectic semitoric manifold by the existence of focus-focus singularities. The helix permits to translate a symplectic geometric problem into an algebraic problem, and the paper describes a method to solve this type of algebraic problem.

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.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

On the central charge for the W algebras

NASA Astrophysics Data System (ADS)

Hornfeck, K.

1991-02-01

For the W algebra that is built besides by the stress-energy tensor T by one additional field W we translate the (WWW) Jacobi-identity (that restricts in general the allowed values for the central charge) into a set of conditions on the structure constants CWWΦ and CΦWW with quasi-primary fields Φ. For the case where the additional field has half-integer dimension >3/2 we give a restriction on the possible central charges that includes that in this case c must be less than one. Address after 1 November 1990: Department of Mathematics, King's College, Strand, London WC2R 2LS, UK.

Quantization of spinor fields. III. Fermions on coherent (Bose) domains

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

1983-02-01

A formulation of the c-number classics-quanta correspondence rule for spinor systems requires all elements of the quantum field algebra to be expanded into power series with respect to the generators of the canonical commutation relation (CCR) algebra. On the other hand, the asymptotic completeness demand would result in the (Haag) expansions with respect to the canonical anticommutation relation (CAR) generators. We establish the conditions under which the above correspondence rule can be reconciled with the existence of Haag expansions in terms of asymptotic free Fermi fields. Then, the CAR become represented on the state space of the Bose (CCR) system.

Matrix preconditioning: a robust operation for optical linear algebra processors.

PubMed

Ghosh, A; Paparao, P

1987-07-15

Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

Low temperature simulation of subliming boundary layer flow in Jupiter atmosphere

NASA Technical Reports Server (NTRS)

Chen, C. J.

1976-01-01

A low-temperature approximate simulation for the sublimation of a graphite heat shield under Jovian entry conditions is studied. A set of algebraic equations is derived to approximate the governing equation and boundary conditions, based on order-of-magnitude analysis. Characteristic quantities such as the wall temperature and the subliming velocity are predicted. Similarity parameters that are needed to simulate the most dominant phenomena of the Jovian entry flow are also given. An approximate simulation of the sublimation of the graphite heat shield is performed with an air-dry-ice model. The simulation with the air-dry-ice model may be carried out experimentally at a lower temperature of 3000 to 6000 K instead of the entry temperature of 14,000 K. The rate of graphite sublimation predicted by the present algebraic approximation agrees to the order of magnitude with extrapolated data. The limitations of the simulation method and its utility are discussed.

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

PubMed

Verburgt, Lukas M

2016-01-01

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

From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

2012-12-01

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, such that each Gn is simply connected. We use the 1-jet of the classifying space W¯ G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The result can be seen as a geometric interpretation of Quillen's (purely algebraic) construction of the adjunction between simplicial Lie algebras and dg-Lie algebras.

Algebra: A Challenge at the Crossroads of Policy and Practice

ERIC Educational Resources Information Center

Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

2011-01-01

The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

Making Algebra Work: Instructional Strategies that Deepen Student Understanding, within and between Algebraic Representations

ERIC Educational Resources Information Center

Star, Jon R.; Rittle-Johnson, Bethany

2009-01-01

Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…

Algebraic K-theory, K-regularity, and -duality of -stable C ∗-algebras

NASA Astrophysics Data System (ADS)

Mahanta, Snigdhayan

2015-12-01

We develop an algebraic formalism for topological -duality. More precisely, we show that topological -duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E ∞ -operad starting from any strongly self-absorbing C ∗-algebra . Then we show that there is a functorial topological K-theory symmetric spectrum construction on the category of separable C ∗-algebras, such that is an algebra over this operad; moreover, is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C ∗-algebras. We also show that -stable C ∗-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of a x+ b-semigroup C ∗-algebras coming from number theory and that of -stabilized noncommutative tori.

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

The probability theory used in quantum mechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantum mechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.

PREFACE: Algebra, Geometry, and Mathematical Physics 2010

NASA Astrophysics Data System (ADS)

Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.

2012-02-01

This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants

The natural mathematics of behavior analysis.

PubMed

Li, Don; Hautus, Michael J; Elliffe, Douglas

2018-04-19

Models that generate event records have very general scope regarding the dimensions of the target behavior that we measure. From a set of predicted event records, we can generate predictions for any dependent variable that we could compute from the event records of our subjects. In this sense, models that generate event records permit us a freely multivariate analysis. To explore this proposition, we conducted a multivariate examination of Catania's Operant Reserve on single VI schedules in transition using a Markov Chain Monte Carlo scheme for Approximate Bayesian Computation. Although we found systematic deviations between our implementation of Catania's Operant Reserve and our observed data (e.g., mismatches in the shape of the interresponse time distributions), the general approach that we have demonstrated represents an avenue for modelling behavior that transcends the typical constraints of algebraic models. © 2018 Society for the Experimental Analysis of Behavior.

Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories

NASA Astrophysics Data System (ADS)

Cheng, Tao; Huang, Hua-Lin; Yang, Yuping

2016-01-01

By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line, Bulacu observed that Clifford algebras are weak Hopf algebras in the aforementioned categories and obtained other interesting properties. The aim of this paper is to study generalized Clifford algebras in a similar manner and extend the results of Albuquerque, Majid and Bulacu to the generalized setting. In particular, by taking full advantage of the gauge transformations in symmetric linear Gr-categories, we derive the decomposition theorem and provide categorical weak Hopf structures for generalized Clifford algebras in a conceptual and simpler manner.

Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation

NASA Astrophysics Data System (ADS)

Trujillo Arredondo, Mariana

2014-06-01

We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

NASA Astrophysics Data System (ADS)

Hermann, Robert

1982-07-01

Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

Convolution Algebra for Fluid Modes with Finite Energy

DTIC Science & Technology

1992-04-01

signals and systems analysis: the evaluation of the initial condition -or input- to a system given its final condition -or output- and its impulse ...Images Corrupted with Gaussian Blur .............. 30 III.. 5 Deblurring with Hermite-Rodriguez Wavelets 34 5.1 Introduction...66 25. Letter "T", which is diffused for t=12, and corrupted by additive noise at SNR’s = 1

The general symmetry algebra structure of the underdetermined equation ux=(vxx)2

NASA Astrophysics Data System (ADS)

Kersten, Paul H. M.

1991-08-01

In a recent paper, Anderson, Kamran, and Olver [``Interior, exterior, and generalized symmetries,'' preprint (1990)] obtained the first- and second-order generalized symmetry algebra for the system ux=(vxx)2, leading to the noncompact real form of the exceptional Lie algebra G2. Here, the structure of the general higher-order symmetry algebra is obtained. Moreover, the Lie algebra G2 is obtained as ordinary symmetry algebra of the associated first-order system. The general symmetry algebra for ux=f(u,v,vx,...,) is established also.

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

Highest-weight representations of Brocherd`s algebras

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

Slansky, R.

1997-01-01

General features of highest-weight representations of Borcherd`s algebras are described. to show their typical features, several representations of Borcherd`s extensions of finite-dimensional algebras are analyzed. Then the example of the extension of affine- su(2) to a Borcherd`s algebra is examined. These algebras provide a natural way to extend a Kac-Moody algebra to include the hamiltonian and number-changing operators in a generalized symmetry structure.

Quantum cluster algebras and quantum nilpotent algebras.

PubMed

Goodearl, Kenneth R; Yakimov, Milen T

2014-07-08

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

Quantum cluster algebras and quantum nilpotent algebras

PubMed Central

Goodearl, Kenneth R.; Yakimov, Milen T.

2014-01-01

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

Transport synthetic acceleration with opposing reflecting boundary conditions

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

Zika, M.R.; Adams, M.L.

2000-02-01

The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iteratingmore » on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.« less

The Feigin Tetrahedron

NASA Astrophysics Data System (ADS)

Rupel, Dylan

2015-03-01

The first goal of this note is to extend the well-known Feigin homomorphisms taking quantum groups to quantum polynomial algebras. More precisely, we define generalized Feigin homomorphisms from a quantum shuffle algebra to quantum polynomial algebras which extend the classical Feigin homomorphisms along the embedding of the quantum group into said quantum shuffle algebra. In a recent work of Berenstein and the author, analogous extensions of Feigin homomorphisms from the dual Hall-Ringel algebra of a valued quiver to quantum polynomial algebras were defined. To relate these constructions, we establish a homomorphism, dubbed the quantum shuffle character, from the dual Hall-Ringel algebra to the quantum shuffle algebra which relates the generalized Feigin homomorphisms. These constructions can be compactly described by a commuting tetrahedron of maps beginning with the quantum group and terminating in a quantum polynomial algebra. The second goal in this project is to better understand the dual canonical basis conjecture for skew-symmetrizable quantum cluster algebras. In the symmetrizable types it is known that dual canonical basis elements need not have positive multiplicative structure constants, while this is still suspected to hold for skew-symmetrizable quantum cluster algebras. We propose an alternate conjecture for the symmetrizable types: the cluster monomials should correspond to irreducible characters of a KLR algebra. Indeed, the main conjecture of this note would establish this ''KLR conjecture'' for acyclic skew-symmetrizable quantum cluster algebras: that is, we conjecture that the images of rigid representations under the quantum shuffle character give irreducible characters for KLR algebras. We sketch a proof in the symmetric case giving an alternative to the proof of Kimura-Qin that all non-initial cluster variables in an acyclic skew-symmetric quantum cluster algebra are contained in the dual canonical basis. With these results in mind we interpret the cluster mutations directly in terms of the representation theory of the KLR algebra.

Form in Algebra: Reflecting, with Peacock, on Upper Secondary School Teaching.

ERIC Educational Resources Information Center

Menghini, Marta

1994-01-01

Discusses algebra teaching by looking back into the history of algebra and the work of George Peacock, who considered algebra from two points of view: symbolic and instrumental. Claims that, to be meaningful, algebra must be linked to real-world problems. (18 references) (MKR)

Rholography, black holes and Scherk-Schwarz

DOE PAGES

Gaddam, Nava; Gnecchi, Alessandra; Vandoren, Stefan; ...

2015-06-10

We present a construction of a class of near-extremal asymptotically flat black hole solutions in four (or five) dimensional gauged supergravity with R-symmetry gaugings obtained from Scherk-Schwarz reductions on a circle. The entropy of these black holes is counted holographically by the well known MSW (or D1/D5) system, with certain twisted boundary conditions labeled by a twist parameter ρ. Here, we find that the corresponding (0, 4) (or (4, 4)) superconformal algebras are exactly those studied by Schwimmer and Seiberg, using a twist on the outer automorphism group. The interplay between R-symmetries, ρ-algebras and holography leads us to name ourmore » construction “Rholography”.« less

Rholography, black holes and Scherk-Schwarz

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

Gaddam, Nava; Gnecchi, Alessandra; Vandoren, Stefan

We present a construction of a class of near-extremal asymptotically flat black hole solutions in four (or five) dimensional gauged supergravity with R-symmetry gaugings obtained from Scherk-Schwarz reductions on a circle. The entropy of these black holes is counted holographically by the well known MSW (or D1/D5) system, with certain twisted boundary conditions labeled by a twist parameter ρ. Here, we find that the corresponding (0, 4) (or (4, 4)) superconformal algebras are exactly those studied by Schwimmer and Seiberg, using a twist on the outer automorphism group. The interplay between R-symmetries, ρ-algebras and holography leads us to name ourmore » construction “Rholography”.« less

Generalized Browder's and Weyl's theorems for Banach space operators

NASA Astrophysics Data System (ADS)

Curto, Raúl E.; Han, Young Min

2007-12-01

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).

On Various Nonlinearity Measures for Boolean Functions*

PubMed Central

Boyar, Joan; Find, Magnus Gausdal; Peralta, René

2016-01-01

A necessary condition for the security of cryptographic functions is to be “sufficiently distant” from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that six common measures, nonlinearity, algebraic degree, annihilator immunity, algebraic thickness, normality, and multiplicative complexity, are incomparable in the sense that for each pair of measures, μ1, μ2, there exist functions f1, f2 with f1 being more nonlinear than f2 according to μ1, but less nonlinear according to μ2. We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions. PMID:27458499

Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

NASA Astrophysics Data System (ADS)

Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

2016-06-01

A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy

NASA Astrophysics Data System (ADS)

Matsushima, Masatomo; Ohmiya, Mayumi

2009-09-01

The stationary KdV hierarchy is constructed using a kind of recursion operator called Λ-operator. The notion of the maximal solution of the n-th stationary KdV equation is introduced. Using this maximal solution, a specific differential polynomial with the auxiliary spectral parameter called the spectral M-function is constructed as the quadratic form of the fundamental system of the eigenvalue problem for the 2-nd order linear ordinary differential equation which is related to the linearizing operator of the hierarchy. By calculating a perfect square condition of the quadratic form by an elementary algebraic method, the complete set of first integrals of this hierarchy is constructed.

Comparison of CFD Predictions with Shuttle Global Flight Thermal Imagery and Discrete Surface Measurements

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.; Tang, chun Y.; Palmer, Grant E.; Hyatt, Andrew J.; Wise, Adam J.; McCloud, Peter L.

2010-01-01

Surface temperature measurements from the STS-119 boundary-layer transition experiment on the space shuttle orbiter Discovery provide a rare opportunity to assess turbulent CFD models at hypersonic flight conditions. This flight data was acquired by on-board thermocouples and by infrared images taken off-board by the Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) team, and is suitable for hypersonic CFD turbulence assessment between Mach 6 and 14. The primary assessment is for the Baldwin-Lomax and Cebeci-Smith algebraic turbulence models in the DPLR and LAURA CFD codes, respectively. A secondary assessment is made of the Shear-Stress Transport (SST) two-equation turbulence model in the DPLR code. Based upon surface temperature comparisons at eleven thermocouple locations, the algebraic-model turbulent CFD results average 4% lower than the measurements for Mach numbers less than 11. For Mach numbers greater than 11, the algebraic-model turbulent CFD results average 5% higher than the three available thermocouple measurements. Surface temperature predictions from the two SST cases were consistently 3 4% higher than the algebraic-model results. The thermocouple temperatures exhibit a change in trend with Mach number at about Mach 11; this trend is not reflected in the CFD results. Because the temperature trends from the turbulent CFD simulations and the flight data diverge above Mach 11, extrapolation of the turbulent CFD accuracy to higher Mach numbers is not recommended.

Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2016-01-01

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

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,…

Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

NASA Astrophysics Data System (ADS)

Liu, Chiu-Chu Melissa; Sheshmani, Artan

2017-07-01

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

Lie algebra of conformal Killing-Yano forms

NASA Astrophysics Data System (ADS)

Ertem, Ümit

2016-06-01

We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing-Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing-Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases.

Generalized Galilean algebras and Newtonian gravity

NASA Astrophysics Data System (ADS)

González, N.; Rubio, G.; Salgado, P.; Salgado, S.

2016-04-01

The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

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.

On special Lie algebras having a faithful module with Krull dimension

NASA Astrophysics Data System (ADS)

Pikhtilkova, O. A.; Pikhtilkov, S. A.

2017-02-01

For special Lie algebras we prove an analogue of Markov's theorem on {PI}-algebras having a faithful module with Krull dimension: the solubility of the prime radical. We give an example of a semiprime Lie algebra that has a faithful module with Krull dimension but cannot be represented as a subdirect product of finitely many prime Lie algebras. We prove a criterion for a semiprime Lie algebra to be representable as such a subdirect product.

Investigating Years 7 to 12 students' knowledge of linear relationships through different contexts and representations

NASA Astrophysics Data System (ADS)

Wilkie, Karina J.; Ayalon, Michal

2018-02-01

A foundational component of developing algebraic thinking for meaningful calculus learning is the idea of "function" that focuses on the relationship between varying quantities. Students have demonstrated widespread difficulties in learning calculus, particularly interpreting and modeling dynamic events, when they have a poor understanding of relationships between variables. Yet, there are differing views on how to develop students' functional thinking over time. In the Australian curriculum context, linear relationships are introduced to lower secondary students with content that reflects a hybrid of traditional and reform algebra pedagogy. This article discusses an investigation into Australian secondary students' understanding of linear functional relationships from Years 7 to 12 (approximately 12 to 18 years old; n = 215) in their approaches to three tasks (finding rate of change, pattern generalisation and interpretation of gradient) involving four different representations (table, geometric growing pattern, equation and graph). From the findings, it appears that these students' knowledge of linear functions remains context-specific rather than becoming connected over time.

Resurgence and dynamics of O(N) and Grassmannian sigma models

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

Dunne, Gerald V.; Unsal, Mithat

Here, we study the non-perturbative dynamics of the two dimensional O( N) and Grassmannian sigma models by using compactification with twisted boundary conditions on R× S 1, semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on R 2, which we call 2d-saddles. On R× S 1, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o( N) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, givenmore » by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O( N) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO( N) gauge theory on R 3×S 1. The Grassmannian sigma models Gr( N, M) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr( N, M), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.« less

Resurgence and dynamics of O(N) and Grassmannian sigma models

DOE PAGES

Dunne, Gerald V.; Unsal, Mithat

2015-09-29

Here, we study the non-perturbative dynamics of the two dimensional O( N) and Grassmannian sigma models by using compactification with twisted boundary conditions on R× S 1, semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on R 2, which we call 2d-saddles. On R× S 1, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o( N) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, givenmore » by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O( N) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO( N) gauge theory on R 3×S 1. The Grassmannian sigma models Gr( N, M) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr( N, M), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.« less

Algebra for Everyone.

ERIC Educational Resources Information Center

Edwards, Edgar L., Jr., Ed.

The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through…

Chinese Algebra: Using Historical Problems to Think about Current Curricula

ERIC Educational Resources Information Center

Tillema, Erik

2005-01-01

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

Conceptualizing Routines of Practice That Support Algebraic Reasoning in Elementary Schools: A Constructivist Grounded Theory

ERIC Educational Resources Information Center

Store, Jessie Chitsanzo

2012-01-01

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…

Derive Workshop Matrix Algebra and Linear Algebra.

ERIC Educational Resources Information Center

Townsley Kulich, Lisa; Victor, Barbara

This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…

Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

ERIC Educational Resources Information Center

Ozgun-Koca, S. Ash

2010-01-01

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

A Richer Understanding of Algebra

ERIC Educational Resources Information Center

Foy, Michelle

2008-01-01

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

A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2016-12-01

Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

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

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.

On the symmetries of integrability

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

Bellon, M.; Maillard, J.M.; Viallet, C.

1992-06-01

In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiatemore » the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.« less

Synchronization Analysis of Master-Slave Probabilistic Boolean Networks.

PubMed

Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W C; Cao, Jinde

2015-08-28

In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results.

Synchronization Analysis of Master-Slave Probabilistic Boolean Networks

PubMed Central

Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W. C.; Cao, Jinde

2015-01-01

In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results. PMID:26315380

Local phase space and edge modes for diffeomorphism-invariant theories

NASA Astrophysics Data System (ADS)

Speranza, Antony J.

2018-02-01

We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel [36]. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, SL(2, ℝ) transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.

The algebra of supertraces for 2+1 super de Sitter gravity

NASA Technical Reports Server (NTRS)

Urrutia, L. F.; Waelbroeck, H.; Zertuche, F.

1993-01-01

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q.

a Triangular Deformation of the Two-Dimensional POINCARÉ Algebra

NASA Astrophysics Data System (ADS)

Khorrami, M.; Shariati, A.; Abolhassani, M. R.; Aghamohammadi, A.

Contracting the h-deformation of SL(2, ℝ), we construct a new deformation of two-dimensional Poincaré's algebra, the algebra of functions on its group and its differential structure. It is seen that these dual Hopf algebras are isomorphic to each other. It is also shown that the Hopf algebra is triangular, and its universal R-matrix is also constructed explicitly. We then find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.

Computer algebra and operators

NASA Technical Reports Server (NTRS)

Fateman, Richard; Grossman, Robert

1989-01-01

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

An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

ERIC Educational Resources Information Center

Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

2016-01-01

This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

Spontaneous Meta-Arithmetic as a First Step toward School Algebra

ERIC Educational Resources Information Center

Caspi, Shai; Sfard, Anna

2012-01-01

Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…

Gender differences in algebraic thinking ability to solve mathematics problems

NASA Astrophysics Data System (ADS)

Kusumaningsih, W.; Darhim; Herman, T.; Turmudi

2018-05-01

This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.

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.

The Growing Importance of Linear Algebra in Undergraduate Mathematics.

ERIC Educational Resources Information Center

Tucker, Alan

1993-01-01

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Conditional Independence in Applied Probability.

ERIC Educational Resources Information Center

Pfeiffer, Paul E.

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

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

PubMed

Yoshida, Hiroshi; Anai, Hirokazu; Horimoto, Katsuhisa

2007-01-01

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

Representing k-graphs as Matrix Algebras

NASA Astrophysics Data System (ADS)

Rosjanuardi, R.

2018-05-01

For any commutative unital ring R and finitely aligned k-graph Λ with |Λ| < ∞ without cycles, we can realise Kumjian-Pask algebra KP R (Λ) as a direct sum of of matrix algebra over some vertices v with properties ν = νΛ, i.e: ⊕ νΛ=ν M |Λv|(R). When there is only a single vertex ν ∈ Λ° such that ν = νΛ, we can realise the Kumjian-Pask algebra as the matrix algebra M |ΛV|(R). Hence the matrix algebra M |vΛ|(R) can be regarded as a representation of the k-graph Λ. In this talk we will figure out the relation between finitely aligned k-graph and matrix algebra.

A description of pseudo-bosons in terms of nilpotent Lie algebras

NASA Astrophysics Data System (ADS)

Bagarello, Fabio; Russo, Francesco G.

2018-02-01

We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we do not find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed into the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behavior of pseudo-bosonic operators in many quantum models.

The hopf algebra of vector fields on complex quantum groups

NASA Astrophysics Data System (ADS)

Drabant, Bernhard; Jurčo, Branislav; Schlieker, Michael; Weich, Wolfgang; Zumino, Bruno

1992-10-01

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A n , B n , C n , and D n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.

Algorithms for computations of Loday algebras' invariants

NASA Astrophysics Data System (ADS)

Hussain, Sharifah Kartini Said; Rakhimov, I. S.; Basri, W.

2017-04-01

The paper is devoted to applications of some computer programs to study structural determination of Loday algebras. We present how these computer programs can be applied in computations of various invariants of Loday algebras and provide several computer programs in Maple to verify Loday algebras' identities, the isomorphisms between the algebras, as a special case, to describe the automorphism groups, centroids and derivations.

Algebra for All: The Effect of Algebra Coursework and Classroom Peer Academic Composition on Low-Achieving Students

ERIC Educational Resources Information Center

Nomi, Takako; Raudenbush, Stephen W.

2014-01-01

Algebra is often considered as a gateway for later achievement. A recent report by the Mathematics Advisory Panel (2008) underscores the importance of improving algebra learning in secondary school. Today, a growing number of states and districts require algebra for all students in ninth grade or earlier. Chicago is at the forefront of this…

Rupture or Continuity: The Arithmetico-Algebraic Thinking as an Alternative in a Modelling Process in a Paper and Pencil and Technology Environment

ERIC Educational Resources Information Center

Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés

2017-01-01

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

Derivation in INK-algebras

NASA Astrophysics Data System (ADS)

Kaviyarasu, M.; Indhira, K.

2018-04-01

In 2017 we introduced a new notion of algebra called IKN-algebra. Motivated by some result on derivations (rightleft)-derivation and (leftright)- derivation in ring. In this paper we introduce derivation in INK-Algebras and investigate some important result.

Roughness in Lattice Ordered Effect Algebras

PubMed Central

Xin, Xiao Long; Hua, Xiu Juan; Zhu, Xi

2014-01-01

Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ordered effect algebra E and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras. PMID:25170523

D{sub {infinity}}-differential E{sub {infinity}}-algebras and spectral sequences of fibrations

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

Lapin, Sergei V

2007-10-31

The notion of an E{sub {infinity}}-algebra with a filtration is introduced. The connections are established between E{sub {infinity}}-algebras with filtrations and the theory of D{sub {infinity}}-differential E{sub {infinity}}-algebras over fields. Based on the technique of D{sub {infinity}}-differential E{sub {infinity}}-algebras, the apparatus of spectral sequences is developed for E{sub {infinity}}-algebras with filtrations, and applications of this apparatus to the multiplicative cohomology spectral sequences of fibrations are given. Bibliography: 21 titles.

q-Derivatives, quantization methods and q-algebras

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

Twarock, Reidun

1998-12-15

Using the example of Borel quantization on S{sup 1}, we discuss the relation between quantization methods and q-algebras. In particular, it is shown that a q-deformation of the Witt algebra with generators labeled by Z is realized by q-difference operators. This leads to a discrete quantum mechanics. Because of Z, the discretization is equidistant. As an approach to a non-equidistant discretization of quantum mechanics one can change the Witt algebra using not the number field Z as labels but a quadratic extension of Z characterized by an irrational number {tau}. This extension is denoted as quasi-crystal Lie algebra, because thismore » is a relation to one-dimensional quasicrystals. The q-deformation of this quasicrystal Lie algebra is discussed. It is pointed out that quasicrystal Lie algebras can be considered also as a 'deformed' Witt algebra with a 'deformation' of the labeling number field. Their application to the theory is discussed.« less

Generalized conformal realizations of Kac-Moody algebras

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

Palmkvist, Jakob

2009-01-15

We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3x3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f{sub 4}, e{sub 6}, e{sub 7}, e{sub 8} for n=2. Moreover, we obtain their infinite-dimensional extensions for n{>=}3. In the casemore » of 2x2 matrices, the resulting Lie algebras are of the form so(p+n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q)« less

Filiform Lie algebras of order 3

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

Navarro, R. M., E-mail: rnavarro@unex.es

2014-04-15

The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de lamore » variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.« less

Labeled trees and the efficient computation of derivations

NASA Technical Reports Server (NTRS)

Grossman, Robert; Larson, Richard G.

1989-01-01

The effective parallel symbolic computation of operators under composition is discussed. Examples include differential operators under composition and vector fields under the Lie bracket. Data structures consisting of formal linear combinations of rooted labeled trees are discussed. A multiplication on rooted labeled trees is defined, thereby making the set of these data structures into an associative algebra. An algebra homomorphism is defined from the original algebra of operators into this algebra of trees. An algebra homomorphism from the algebra of trees into the algebra of differential operators is then described. The cancellation which occurs when noncommuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator. It is shown that the algebra of trees leads naturally to a parallel version of the algorithm.

Differential calculus and gauge transformations on a deformed space

NASA Astrophysics Data System (ADS)

Wess, Julius

2007-08-01

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory.

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.

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

NASA Astrophysics Data System (ADS)

Kaneko, Ryui; Nonomura, Yoshihiko; Kohno, Masanori

2018-05-01

We explore the possibility of a Berezinskii-Kosterlitz-Thouless-like critical phase for the charge degrees of freedom in the intermediate-temperature regime between the charge-ordered and disordered phases in two-dimensional systems with competing short-range Coulomb repulsion. As the simplest example, we investigate the extended Hubbard model with on-site and nearest-neighbor Coulomb interactions on a triangular lattice at half filling in the atomic limit by using a classical Monte Carlo method, and find a critical phase, characterized by algebraic decay of the charge correlation function, belonging to the universality class of the two-dimensional XY model with a Z6 anisotropy. Based on the results, we discuss possible conditions for the critical phase in materials.

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 Characterization of a Unified Notion of Mathematical Function: The Case of High School Function and Linear Transformation

ERIC Educational Resources Information Center

Zandieh, Michelle; Ellis, Jessica; Rasmussen, Chris

2017-01-01

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

Simple nuclear C*-algebras not isomorphic to their opposites

PubMed Central

Hirshberg, Ilan

2017-01-01

We show that it is consistent with Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C∗-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra. PMID:28559339

Implementation of Algebra I in Eighth Grade: An "Ex-Post Facto" Study on Student Achievement

ERIC Educational Resources Information Center

Realdine, Dorothy S.

2010-01-01

Only recently have school districts across the nation begun to offer Algebra I to all eighth grade students. Currently, most eighth grade Algebra I curriculum does not have a national consistent focus of topics or level of rigor. A key issue of implementing Algebra I in eighth grade is defining national Algebra I concepts and skills that students…

The Xs and Whys of Algebra: Key Ideas and Common Misconceptions

ERIC Educational Resources Information Center

Collins, Anne; Dacey, Linda

2011-01-01

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

META: Multi-resolution Framework for Event Summarization

DTIC Science & Technology

2014-05-01

designated by other documentation. 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS ( ES ) U.S. Army Research Office P.O. Box 12211 Research Triangle...storage by removing the lower lev- els of the description nodes. The pruned tree still contains enough details for analysis, and an analyst who analyzes a...similar to the ‘projec- tion’ in relational algebra . It is a unary operator written as Πe(1),e(2),...,e(k)(F). The operation is defined as picking the

The applications of a higher-dimensional Lie algebra and its decomposed subalgebras

PubMed Central

Yu, Zhang; Zhang, Yufeng

2009-01-01

With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra sμ(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras sμ(6) and E is used to directly construct integrable couplings. PMID:20084092

The applications of a higher-dimensional Lie algebra and its decomposed subalgebras.

PubMed

Yu, Zhang; Zhang, Yufeng

2009-01-15

With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Spatial-Operator Algebra For Robotic Manipulators

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

1991-01-01

Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification

NASA Astrophysics Data System (ADS)

Martín–Moruno, Prado; Visser, Matt

2017-11-01

The (generalized) Rainich conditions are algebraic conditions which are polynomial in the (mixed-component) stress-energy tensor. As such they are logically distinct from the usual classical energy conditions (NEC, WEC, SEC, DEC), and logically distinct from the usual Hawking-Ellis (Segré-Plebański) classification of stress-energy tensors (type I, type II, type III, type IV). There will of course be significant inter-connections between these classification schemes, which we explore in the current article. Overall, we shall argue that it is best to view the (generalized) Rainich conditions as a refinement of the classical energy conditions and the usual Hawking-Ellis classification.

Difficulties in initial algebra learning in Indonesia

NASA Astrophysics Data System (ADS)

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-12-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

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.

Algebraic theory of molecules

NASA Technical Reports Server (NTRS)

Iachello, Franco

1995-01-01

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

FRT presentation of the Onsager algebras

NASA Astrophysics Data System (ADS)

Baseilhac, Pascal; Belliard, Samuel; Crampé, Nicolas

2018-03-01

A presentation à la Faddeev-Reshetikhin-Takhtajan (FRT) of the Onsager, augmented Onsager and sl_2 -invariant Onsager algebras is given, using the framework of the nonstandard classical Yang-Baxter algebras. Associated current algebras are identified, and generating functions of mutually commuting quantities are obtained.

The BMS4 algebra at spatial infinity

NASA Astrophysics Data System (ADS)

Troessaert, Cédric

2018-04-01

We show how a global BMS4 algebra appears as part of the asymptotic symmetry algebra at spatial infinity. Using linearised theory, we then show that this global BMS4 algebra is the one introduced by Strominger as a symmetry of the S-matrix.

Post-Lie algebras and factorization theorems

NASA Astrophysics Data System (ADS)

Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

2017-09-01

In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

Comparison of the Effectiveness of a Traditional Intermediate Algebra Course With That of a Less Rigorous Intermediate Algebra Course in Preparing Students for Success in a Subsequent Mathematics Course

ERIC Educational Resources Information Center

Sworder, Steven C.

2007-01-01

An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras

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

Yuan, Lamei, E-mail: lmyuan@hit.edu.cn

2014-04-15

The aim of this paper is to introduce the notions of Hom Gel'fand-Dorfman bialgebra and Hom-Lie conformal algebra. In this paper, we give four constructions of Hom Gel'fand-Dorfman bialgebras. Also, we provide a general construction of Hom-Lie conformal algebras from Hom-Lie algebras. Finally, we prove that a Hom Gel'fand-Dorfman bialgebra is equivalent to a Hom-Lie conformal algebra of degree 2.

Internally connected graphs and the Kashiwara-Vergne Lie algebra

NASA Astrophysics Data System (ADS)

Felder, Matteo

2018-06-01

It is conjectured that the Kashiwara-Vergne Lie algebra \\widehat{krv}_2 is isomorphic to the direct sum of the Grothendieck-Teichmüller Lie algebra grt_1 and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of \\widehat{krv}_2 whose intersection is grt_1, thus giving a way to interpolate between these two Lie algebras.

Discrimination in a General Algebraic Setting

PubMed Central

Fine, Benjamin; Lipschutz, Seymour; Spellman, Dennis

2015-01-01

Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421

Exploring Optimal Conditions of Instructional Guidance in an Algebra Tutor

ERIC Educational Resources Information Center

Lee, Hee Seung; Anderson, John R.; Berman, Susan R.; Ferris-Glick, Jennifer; Joshi, Ambarish; Nixon, Tristan; Ritter, Steve

2013-01-01

In designing learning environments that support student learning, there are many instructional design decisions. These include when and how to provide examples, verbal explanations, feedback, and other scaffolding features. In this paper, the authors investigate instructional guidance as it relates to Cognitive Tutor, an intelligent tutoring…

Hom-associative Ore extensions

NASA Astrophysics Data System (ADS)

Bäck, P.; Richter, J.; Silvestrov, S.

2018-02-01

We introduce hom-associative Ore extensions as non-associative, non-unital Ore extensions with a hom-associative multiplication, as well as give some necessary and sufficient conditions when such exist. Within this framework, we also construct a family of hom-associative Weyl algebras as generalizations of the classical analogue, and prove that they are simple.

An algebra of reversible computation.

PubMed

Wang, Yong

2016-01-01

We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

Macdonald index and chiral algebra

NASA Astrophysics Data System (ADS)

Song, Jaewon

2017-08-01

For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

Macdonald index and chiral algebra

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

Song, Jaewon

For any 4dN = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. Here, we conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A 1, A 2n) and (A 1, D 2n+1) where the chiral algebras are given by Virasoro andmore » $$ˆ\\atop{su}$$(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.« less

Macdonald index and chiral algebra

DOE PAGES

Song, Jaewon

2017-08-10

For any 4dN = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. Here, we conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A 1, A 2n) and (A 1, D 2n+1) where the chiral algebras are given by Virasoro andmore » $$ˆ\\atop{su}$$(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.« less

Line defect Schur indices, Verlinde algebras and U(1) r fixed points

NASA Astrophysics Data System (ADS)

Neitzke, Andrew; Yan, Fei

2017-11-01

Given an N=2 superconformal field theory, we reconsider the Schur index ℐ L ( q) in the presence of a half line defect L. Recently Cordova-Gaiotto-Shao found that ℐ L ( q) admits an expansion in terms of characters of the chiral algebra A introduced by Beem et al., with simple coefficients υ L, β ( q). We report a puzzling new feature of this expansion: the q → 1 limit of the coefficients υ L, β ( q) is linearly related to the vacuum expectation values 〈 L〉 in U(1) r -invariant vacua of the theory compactified on S 1. This relation can be expressed algebraically as a commutative diagram involving three algebras: the algebra generated by line defects, the algebra of functions on U(1) r -invariant vacua, and a Verlindelike algebra associated to A . Our evidence is experimental, by direct computation in the Argyres-Douglas theories of type ( A 1, A 2), ( A 1, A 4), ( A 1, A 6), ( A 1, D 3) and ( A 1, D 5). In the latter two theories, which have flavor symmetries, the Verlinde-like algebra which appears is a new deformation of algebras previously considered.

Constraint-Referenced Analytics of Algebra Learning

ERIC Educational Resources Information Center

Sutherland, Scot M.; White, Tobin F.

2016-01-01

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

Teaching Strategies to Improve Algebra Learning

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Larson, Matthew R.

2015-01-01

Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

Preparing Elementary Prospective Teachers to Teach Early Algebra

ERIC Educational Resources Information Center

Hohensee, Charles

2017-01-01

Researchers have argued that integrating early algebra into elementary grades will better prepare students for algebra. However, currently little research exists to guide teacher preparation programs on how to prepare prospective elementary teachers to teach early algebra. This study examines the insights and challenges that prospective teachers…

Difficulties in Initial Algebra Learning in Indonesia

ERIC Educational Resources Information Center

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-01-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

Visual Salience of Algebraic Transformations

ERIC Educational Resources Information Center

Kirshner, David; Awtry, Thomas

2004-01-01

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

Quantum walled Brauer algebra: commuting families, Baxterization, and representations

NASA Astrophysics Data System (ADS)

Semikhatov, A. M.; Tipunin, I. Yu

2017-02-01

For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys-Murphy elements. We also propose a Baxterization prescription; it involves representing the quantum walled Brauer algebra in terms of morphisms in a braided monoidal category and introducing parameters into these morphisms, which allows constructing a ‘universal transfer matrix’ that generates commuting elements of the algebra.

Abstract Numeric Relations and the Visual Structure of Algebra

ERIC Educational Resources Information Center

Landy, David; Brookes, David; Smout, Ryan

2014-01-01

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

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…

UCSMP Algebra. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2007

2007-01-01

"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

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…

Abstract Algebra to Secondary School Algebra: Building Bridges

ERIC Educational Resources Information Center

Christy, Donna; Sparks, Rebecca

2015-01-01

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

A Proposed Algebra Assessment for Use in a Problem-Analysis Framework

ERIC Educational Resources Information Center

Walick, Christopher M.; Burns, Matthew K.

2017-01-01

Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

A Relational Algebra Query Language for Programming Relational Databases

ERIC Educational Resources Information Center

McMaster, Kirby; Sambasivam, Samuel; Anderson, Nicole

2011-01-01

In this paper, we describe a Relational Algebra Query Language (RAQL) and Relational Algebra Query (RAQ) software product we have developed that allows database instructors to teach relational algebra through programming. Instead of defining query operations using mathematical notation (the approach commonly taken in database textbooks), students…

Assessing Mathematics Automatically Using Computer Algebra and the Internet

ERIC Educational Resources Information Center

Sangwin, Chris

2004-01-01

This paper reports some recent developments in mathematical computer-aided assessment which employs computer algebra to evaluate students' work using the Internet. Technical and educational issues raised by this use of computer algebra are addressed. Working examples from core calculus and algebra which have been used with first year university…

The detection and stabilisation of limit cycle for deterministic finite automata

NASA Astrophysics Data System (ADS)

Han, Xiaoguang; Chen, Zengqiang; Liu, Zhongxin; Zhang, Qing

2018-04-01

In this paper, the topological structure properties of deterministic finite automata (DFA), under the framework of the semi-tensor product of matrices, are investigated. First, the dynamics of DFA are converted into a new algebraic form as a discrete-time linear system by means of Boolean algebra. Using this algebraic description, the approach of calculating the limit cycles of different lengths is given. Second, we present two fundamental concepts, namely, domain of attraction of limit cycle and prereachability set. Based on the prereachability set, an explicit solution of calculating domain of attraction of a limit cycle is completely characterised. Third, we define the globally attractive limit cycle, and then the necessary and sufficient condition for verifying whether all state trajectories of a DFA enter a given limit cycle in a finite number of transitions is given. Fourth, the problem of whether a DFA can be stabilised to a limit cycle by the state feedback controller is discussed. Criteria for limit cycle-stabilisation are established. All state feedback controllers which implement the minimal length trajectories from each state to the limit cycle are obtained by using the proposed algorithm. Finally, an illustrative example is presented to show the theoretical results.

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

PubMed Central

Omar, Mohamed A.

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732

Remediating Number Combination and Word Problem Deficits Among Students With Mathematics Difficulties: A Randomized Control Trial

PubMed Central

Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Cirino, Paul T.; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.; Zumeta, Rebecca O.

2009-01-01

The purposes of this study were to assess the efficacy of remedial tutoring for 3rd graders with mathematics difficulty, to investigate whether tutoring is differentially efficacious depending on students’ math difficulty status (mathematics difficulty alone vs. mathematics plus reading difficulty), to explore transfer from number combination (NC) remediation, and to examine the transportability of the tutoring protocols. At 2 sites, 133 students were stratified on mathematics difficulty status and site and then randomly assigned to 3 conditions: control (no tutoring), tutoring on automatic retrieval of NCs (i.e., Math Flash), or tutoring on word problems with attention to the foundational skills of NCs, procedural calculations, and algebra (i.e., Pirate Math). Tutoring occurred for 16 weeks, 3 sessions per week and 20–30 min per session. Math Flash enhanced fluency with NCs with transfer to procedural computation but without transfer to algebra or word problems. Pirate Math enhanced word problem skill as well as fluency with NCs, procedural computation, and algebra. Tutoring was not differentially efficacious as a function of students’ mathematics difficulty status. The tutoring protocols proved transportable across sites. PMID:19865600

Branes and the Kraft-Procesi transition: classical case

NASA Astrophysics Data System (ADS)

Cabrera, Santiago; Hanany, Amihay

2018-04-01

Moduli spaces of a large set of 3 d N=4 effective gauge theories are known to be closures of nilpotent orbits. This set of theories has recently acquired a special status, due to Namikawa's theorem. As a consequence of this theorem, closures of nilpotent orbits are the simplest non-trivial moduli spaces that can be found in three dimensional theories with eight supercharges. In the early 80's mathematicians Hanspeter Kraft and Claudio Procesi characterized an inclusion relation between nilpotent orbit closures of the same classical Lie algebra. We recently [1] showed a physical realization of their work in terms of the motion of D3-branes on the Type IIB superstring embedding of the effective gauge theories. This analysis is restricted to A-type Lie algebras. The present note expands our previous discussion to the remaining classical cases: orthogonal and symplectic algebras. In order to do so we introduce O3-planes in the superstring description. We also find a brane realization for the mathematical map between two partitions of the same integer number known as collapse. Another result is that basic Kraft-Procesi transitions turn out to be described by the moduli space of orthosymplectic quivers with varying boundary conditions.

Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.

PubMed

Omar, Mohamed A

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

Algebraic independence results for reciprocal sums of Fibonacci and Lucas numbers

NASA Astrophysics Data System (ADS)

Stein, Martin

2011-09-01

Let Fn and Ln denote the Fibonacci and Lucas numbers, respectively. D. Duverney, Ke. Nishioka, Ku. Nishioka and I. Shiokawa proved that the values of the Fibonacci zeta function ζF(2s) = Σn = 1∞Fn-2s are transcendental for any s∈N using Nesterenko's theorem on Ramanujan functions P(q), Q(q), and R(q). They obtained similar results for the Lucas zeta function ζL(2s) = Σn = 1∞Ln-2s and some related series. Later, C. Elsner, S. Shimomura and I. Shiokawa found conditions for the algebraic independence of these series. In my PhD thesis I generalized their approach and treated the following problem: We investigate all subsets of { ∑ n = 1∞1/Fn2s1, ∑ n = 1∞(-1)n+1/Fn2s2, ∑ n = 1∞1/Ln2s3, ∑ n = 1∞(-1)n+1/Ln2s4:s1,s2,s3,s4∈N} and decide on their algebraic independence over Q. Actually this is a special case of a more general theorem for reciprocal sums of binary recurrent sequences.

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…

Quiver W-algebras

NASA Astrophysics Data System (ADS)

Kimura, Taro; Pestun, Vasily

2018-06-01

For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

Symmetries and stochastic symmetry breaking in multifractal geophysics: analysis and simulation with the help of the Lévy-Clifford algebra of cascade generators..

NASA Astrophysics Data System (ADS)

Schertzer, D. J. M.; Tchiguirinskaia, I.

2016-12-01

Multifractal fields, whose definition is rather independent of their domain dimension, have opened a new approach of geophysics enabling to explore its spatial extension that is of prime importance as underlined by the expression "spatial chaos". However multifractals have been until recently restricted to be scalar valued, i.e. to one-dimensional codomains. This has prevented to deal with the key question of complex component interactions and their non trivial symmetries. We first emphasize that the Lie algebra of stochastic generators of cascade processes enables us to generalize multifractals to arbitrarily large codomains, e.g. flows of vector fields on large dimensional manifolds. In particular, we have recently investigated the neat example of stable Levy generators on Clifford algebra that have a number of seductive properties, e.g. universal statistical and robust algebra properties, both defining the basic symmetries of the corresponding fields (Schertzer and Tchiguirinskaia, 2015). These properties provide a convenient multifractal framework to study both the symmetries of the fields and how they stochastically break the symmetries of the underlying equations due to boundary conditions, large scale rotations and forcings. These developments should help us to answer to challenging questions such as the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013), to fully address the question of the limitations of quasi- geostrophic turbulence (Schertzer et al., 2012) and to explore the peculiar phenomenology of turbulent dynamics of the atmosphere or oceans that is neither two- or three-dimensional. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.8183. Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

NASA Astrophysics Data System (ADS)

Fuentealba, Oscar; Matulich, Javier; Pérez, Alfredo; Pino, Miguel; Rodríguez, Pablo; Tempo, David; Troncoso, Ricardo

2018-01-01

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for isl(2,R) , being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the Hirota-Satsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k. Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is then recovered from the corresponding surface integrals in the canonical approach.

On split regular BiHom-Lie superalgebras

NASA Astrophysics Data System (ADS)

Zhang, Jian; Chen, Liangyun; Zhang, Chiping

2018-06-01

We introduce the class of split regular BiHom-Lie superalgebras as the natural extension of the one of split Hom-Lie superalgebras and the one of split Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Lie superalgebra L is of the form L = U +∑ [ α ] ∈ Λ / ∼I[α] with U a subspace of the Abelian (graded) subalgebra H and any I[α], a well described (graded) ideal of L, satisfying [I[α] ,I[β] ] = 0 if [ α ] ≠ [ β ] . Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its simple (graded) ideals.

General algebraic method applied to control analysis of complex engine types

NASA Technical Reports Server (NTRS)

Boksenbom, Aaron S; Hood, Richard

1950-01-01

A general algebraic method of attack on the problem of controlling gas-turbine engines having any number of independent variables was utilized employing operational functions to describe the assumed linear characteristics for the engine, the control, and the other units in the system. Matrices were used to describe the various units of the system, to form a combined system showing all effects, and to form a single condensed matrix showing the principal effects. This method directly led to the conditions on the control system for noninteraction so that any setting disturbance would affect only its corresponding controlled variable. The response-action characteristics were expressed in terms of the control system and the engine characteristics. The ideal control-system characteristics were explicitly determined in terms of any desired response action.

Generalizations of the Toda molecule

NASA Astrophysics Data System (ADS)

Van Velthoven, W. P. G.; Bais, F. A.

1986-12-01

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

On τ-Compactness of Products of τ-Measurable Operators

NASA Astrophysics Data System (ADS)

Bikchentaev, Airat M.

2017-12-01

Let M be a von Neumann algebra of operators on a Hilbert space H, τ be a faithful normal semifinite trace on M. We obtain some new inequalities for rearrangements of τ-measurable operators products. We also establish some sufficient τ-compactness conditions for products of selfadjoint τ-measurable operators. Next we obtain a τ-compactness criterion for product of a nonnegative τ-measurable operator with an arbitrary τ-measurable operator. We construct an example that shows importance of nonnegativity for one of the factors. The similar results are obtained also for elementary operators from M. We apply our results to symmetric spaces on (M, τ ). The results are new even for the *-algebra B(H) of all linear bounded operators on H endowed with the canonical trace τ = tr.

A novel approach for analyzing data on recurrent events with duration to estimate the combined cumulative rate of both variables over time.

PubMed

Bhattacharya, Sudipta

2018-06-01

Recurrent adverse events, once occur often continue for some duration of time in clinical trials; and the number of events along with their durations is clinically considered as a measure of severity of a disease under study. While there are methods available for analyzing recurrent events or durations or for analyzing both side by side, no effort has been made so far to combine them and present as a single measure. However, this single-valued combined measure may help clinicians assess the wholesome effect of recurrence of incident comprising events and durations. Non-parametric approach is adapted here to develop an estimator for estimating the combined rate of both, the recurrence of events as well as the event-continuation, that is the duration per event. The proposed estimator produces a single numerical value, the interpretation and meaningfulness of which are discussed through the analysis of a real-life clinical dataset. The algebraic expression of variance is derived, asymptotic normality of the estimator is noted, and demonstration is provided on how the estimator can be used in the setup of testing of statistical hypothesis. Further possible development of the estimator is also noted, to adjust for the dependence of event occurrences on the history of the process generating recurrent events through covariates and for the case of dependent censoring.

An Algebraic Formulation of Level One Wess-Zumino Models

NASA Astrophysics Data System (ADS)

Böckenhauer, Jens

The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven.

On Correspondence of BRST-BFV, Dirac, and Refined Algebraic Quantizations of Constrained Systems

NASA Astrophysics Data System (ADS)

Shvedov, O. Yu.

2002-11-01

The correspondence between BRST-BFV, Dirac, and refined algebraic (group averaging, projection operator) approaches to quantizing constrained systems is analyzed. For the closed-algebra case, it is shown that the component of the BFV wave function corresponding to maximal (minimal) value of number of ghosts and antighosts in the Schrodinger representation may be viewed as a wave function in the refined algebraic (Dirac) quantization approach. The Giulini-Marolf group averaging formula for the inner product in the refined algebraic quantization approach is obtained from the Batalin-Marnelius prescription for the BRST-BFV inner product, which should be generally modified due to topological problems. The considered prescription for the correspondence of states is observed to be applicable to the open-algebra case. The refined algebraic quantization approach is generalized then to the case of nontrivial structure functions. A simple example is discussed. The correspondence of observables for different quantization methods is also investigated.

Toward the classification of differential calculi on κ-Minkowski space and related field theories

NASA Astrophysics Data System (ADS)

Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel; Štrajn, Rina

2015-07-01

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

Eighth Grade Algebra Placement Policies: Promoting Equity, Achievement, and Access

ERIC Educational Resources Information Center

Wambsgans, Cynthia

2014-01-01

This study was an investigation of a standardized 8th grade Algebra I placement policy across multiple educational districts. Researchers have documented benefits of students' 8th grade Algebra I education, while others have detailed the consequences of algebra enrollment without necessary prerequisite skills. The purpose of this study was to…

Designing Virtual Worlds for Use in Mathematics Education: The Example of Experiential Algebra.

ERIC Educational Resources Information Center

Winn, William; Bricken, William

1992-01-01

Discussion of the use of virtual reality (VR) to help students learn highlights the use of VR with elementary algebra. Learning theory is examined, including knowledge construction; knowledge representation is discussed, including the symbol systems of algebra; and spatial algebra is described and illustrated. (34 references) (LRW)

Meanings Given to Algebraic Symbolism in Problem-Posing

ERIC Educational Resources Information Center

Cañadas, María C.; Molina, Marta; del Río, Aurora

2018-01-01

Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic…

Build an Early Foundation for Algebra Success

ERIC Educational Resources Information Center

Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

2016-01-01

Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

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…

Unifying the Algebra for All Movement

ERIC Educational Resources Information Center

Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

2015-01-01

There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

A Meta-Analysis of Algebra Interventions for Learners with Disabilities and Struggling Learners

ERIC Educational Resources Information Center

Hughes, Elizabeth M.; Witzel, Bradley S.; Riccomini, Paul J.; Fries, Karen M.; Kanyongo, Gibbs Y.

2014-01-01

The need for global competence in mathematics is apparent. Algebra is considered a gateway course to prepare students for the demands of a competitive global market. Many students demonstrate low performance in algebra; this is especially true for students with disabilities. Effective algebra instruction is essential to increase algebra…

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…

Using Linguistics in the Teaching of Developmental and Remedial Algebra.

ERIC Educational Resources Information Center

Lesnak, Richard J.

Basic algebra at Robert Morris College (RMC) in Pittsburgh, Pennsylvania, is a remedial course for students with virtually no algebra background, and for students whose previous experiences with algebra have created math blocks and math anxiety. A study was conducted in an effort to measure quantitatively the benefits of using linguistic methods…

How Middle Grade Teachers Think about Algebraic Reasoning

ERIC Educational Resources Information Center

Glassmeyer, David; Edwards, Belinda

2016-01-01

Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

Assessing Elementary Algebra with STACK

ERIC Educational Resources Information Center

Sangwin, Christopher J.

2007-01-01

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

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

NASA Astrophysics Data System (ADS)

Aryani, F.; Amin, S. M.; Sulaiman, R.

2018-01-01

Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

The Dixmier Map for Nilpotent Super Lie Algebras

NASA Astrophysics Data System (ADS)

Herscovich, Estanislao

2012-07-01

In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by {Prim({U}({g}))} the set of (graded) primitive ideals of the enveloping algebra {{U}({g})} of a nilpotent Lie superalgebra {{g}} and {{A}d0} the adjoint group of {{g}0}, we prove that the usual Dixmier map for nilpotent Lie algebras can be naturally extended to the context of nilpotent super Lie algebras, i.e. there exists a bijective map I : {g}0^{*}/{A}d0 rightarrow Prim({U}({g})) defined by sending the equivalence class [ λ] of a functional λ to a primitive ideal I( λ) of {{U}({g})}, and which coincides with the Dixmier map in the case of nilpotent Lie algebras. Moreover, the construction of the previous map is explicit, and more or less parallel to the one for Lie algebras, a major difference with a previous approach ( cf. [18]). One key fact in the construction is the existence of polarizations for super Lie algebras, generalizing the concept defined for Lie algebras. As a corollary of the previous description, we obtain the isomorphism {{U}({g})/I(λ) ˜eq Cliffq(k) ⊗ Ap(k)}, where {(p,q) = (dim({g}0/{g}0^{λ})/2,dim({g}1/{g}1^{λ}))}, we get a direct construction of the maximal ideals of the underlying algebra of {{U}({g})} and also some properties of the stabilizers of the primitive ideals of {{U}({g})}.

Zero Forcing Conditions for Nonlinear channel Equalisation using a pre-coding scheme

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

Arfa, Hichem; Belghith, Safya; El Asmi, Sadok

2009-03-05

This paper shows how we can present a zero forcing conditions for a nonlinear channel equalisation. These zero forcing conditions based on the rank of nonlinear system are issued from an algebraic approach based on the module theoretical approach, in which the rank of nonlinear channel is clearly defined. In order to improve the performance of equalisation and reduce the complexity of used nonlinear systems, we will apply a pre-coding scheme. Theoretical results are given and computer simulation is used to corroborate the theory.

Residus de 2-formes differentielles sur les surfaces algebriques et applications aux codes correcteurs d'erreurs

NASA Astrophysics Data System (ADS)

Couvreur, A.

2009-05-01

The theory of algebraic-geometric codes has been developed in the beginning of the 80's after a paper of V.D. Goppa. Given a smooth projective algebraic curve X over a finite field, there are two different constructions of error-correcting codes. The first one, called "functional", uses some rational functions on X and the second one, called "differential", involves some rational 1-forms on this curve. Hundreds of papers are devoted to the study of such codes. In addition, a generalization of the functional construction for algebraic varieties of arbitrary dimension is given by Y. Manin in an article of 1984. A few papers about such codes has been published, but nothing has been done concerning a generalization of the differential construction to the higher-dimensional case. In this thesis, we propose a differential construction of codes on algebraic surfaces. Afterwards, we study the properties of these codes and particularly their relations with functional codes. A pretty surprising fact is that a main difference with the case of curves appears. Indeed, if in the case of curves, a differential code is always the orthogonal of a functional one, this assertion generally fails for surfaces. Last observation motivates the study of codes which are the orthogonal of some functional code on a surface. Therefore, we prove that, under some condition on the surface, these codes can be realized as sums of differential codes. Moreover, we show that some answers to some open problems "a la Bertini" could give very interesting informations on the parameters of these codes.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

SH c realization of minimal model CFT: triality, poset and Burge condition

NASA Astrophysics Data System (ADS)

Fukuda, M.; Nakamura, S.; Matsuo, Y.; Zhu, R.-D.

2015-11-01

Recently an orthogonal basis of {{W}}_N -algebra (AFLT basis) labeled by N-tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH c which is universal for any N. We show that it has an {{S}}_3 automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by N or M Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH c . Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the N-Burge condition in the Hilbert space.

Attributions for Success and Failure in Algebra of Samoan Community College Students: A Profile Analysis.

ERIC Educational Resources Information Center

Powers, Stephen; And Others

Sex differences in attributions for success and failure in algebra of Samoan community college students were examined and compared with attributions of a large group of mainland U.S. students. study included the Mathematics Attribution Scale: Algebra Version (MAS), which assessed students' attributions of achievement in algebra to their effort,…

Using CRA to Teach Algebra to Students with Math Difficulties in Inclusive Settings

ERIC Educational Resources Information Center

Witzel, Bradley S.

2005-01-01

The importance of algebra instruction has increased in the United States in the past few years. Thus, in most states, middle school students are required to take Algebra 1. Middle school students with math difficulties in inclusion algebra settings may require a different instructional approach. The purpose of this research was to compare student…

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

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2016-01-01

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…

Capitalizing on Basic Brain Processes in Developmental Algebra--Part 2

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand its basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain processes…

Capitalizing on Basic Brain Processes in Developmental Algebra--Part One

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

Reinventing Fractions and Division as They Are Used in Algebra: The Power of Preformal Productions

ERIC Educational Resources Information Center

Peck, Frederick; Matassa, Michael

2016-01-01

In this paper, we explore algebra students' mathematical realities around fractions and division, and the ways in which students reinvented mathematical productions involving fractions and division. We find that algebra students' initial realities do not include the fraction-as-quotient sub-construct. This can be problematic because in algebra,…

The Development of Children's Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade

ERIC Educational Resources Information Center

Blanton, Maria; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy; Isler, Isil; Kim, Jee-Seon

2015-01-01

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

Algebra? A Gate! A Barrier! A Mystery!

ERIC Educational Resources Information Center

Mathematics Educatio Dialogues, 2000

2000-01-01

This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

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

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2014-01-01

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

The State of the Gate: A Description of Instructional Practice in Algebra in Five Urban Districts

ERIC Educational Resources Information Center

Litke, Erica G.

2015-01-01

Algebra is considered a linchpin for success in secondary mathematics, serving as a gatekeeper to higher-level courses. Access to algebra is also considered an important lever for educational equity. Yet despite its prominence, large-scale examinations of algebra instruction are rare. In my dissertation, I endeavor to better understand what…

Relationships between Classroom Schedule Types and Performance on the Algebra I Criterion-Referenced Test

ERIC Educational Resources Information Center

Murray, Gregory V.; Moyer-Packenham, Patricia S.

2014-01-01

One option for length of individual mathematics class periods is the schedule type selected for Algebra I classes. This study examined the relationship between student achievement, as indicated by Algebra I Criterion-Referenced Test scores, and the schedule type for Algebra I classes. Data obtained from the Utah State Office of Education included…

Grade 11 Students' Interconnected Use of Conceptual Knowledge, Procedural Skills, and Strategic Competence in Algebra: A Mixed Method Study of Error Analysis

ERIC Educational Resources Information Center

Egodawatte, Gunawardena; Stoilescu, Dorian

2015-01-01

The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…

The Ideas of Algebra, K-12. 1988 Yearbook.

ERIC Educational Resources Information Center

Coxford, Arthur F., Ed.; Shulte, Albert P., Ed.

This volume is organized into six parts. Chapters 1-5, which make up Part 1, first discuss the forces impinging on algebra in the curriculum and suggest possible directions for change. Chapters 6-8, Part 2, concentrate on concepts and teaching possibilities available prior to the formal introduction of algebra. The notion that algebraic ideas are…

Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R

ERIC Educational Resources Information Center

Actuarial Foundation, 2013

2013-01-01

"Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…

Developing "Algebraic Thinking": Two Key Ways to Establish Some Early Algebraic Ideas in Primary Classrooms

ERIC Educational Resources Information Center

Ormond, Christine

2012-01-01

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…

Investigating Students' Modes of Thinking in Linear Algebra: The Case of Linear Independence

ERIC Educational Resources Information Center

Çelik, Derya

2015-01-01

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

Exploring Teacher Noticing of Student Algebraic Thinking in a Video Club

ERIC Educational Resources Information Center

Walkoe, Janet

2015-01-01

Learning algebra is critical for students in the USA today, yet many students in the USA struggle in algebra classes. Researchers claim that one reason for these difficulties is that algebra classes often focus on symbol manipulation and procedures above, and many times at the expense of, a more conceptual understanding of the content. Teaching…

Algebra and Algebraic Thinking in School Math: 70th YB

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2008

2008-01-01

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

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…

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong

2018-06-01

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

Literal algebra for satellite dynamics. [perturbation analysis

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

1975-01-01

A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.

Contractions from grading

NASA Astrophysics Data System (ADS)

Krishnan, Chethan; Raju, Avinash

2018-04-01

We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically via identifying appropriate Zm-gradings (and their generalizations) on the parent algebra. This includes various types of flat space/Carroll limits of finite and infinite dimensional (A)dS algebras, as well as Galilean and Galilean conformal algebras. Our observations can be regarded as providing a natural context for the Grassmann approach of Krishnan et al. [J. High Energy Phys. 2014(3), 36]. We also introduce a related notion, which we call partial grading, that arises naturally in this context.

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

Mozrzymas, Marek; Horodecki, Michał; Studziński, Michał

We consider the structure of algebra of operators, acting in n-fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its regular representation, we derive basic properties of the algebra. In particular, we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations. It appears that there are two kinds of irreducible representations of the algebra. The first one is strictly connected with the representations of the group S(n − 1) induced by irreduciblemore » representations of the group S(n − 2). The second kind is structurally connected with irreducible representations of the group S(n − 1)« less

Separated transonic airfoil flow calculations with a nonequilibrium turbulence model

NASA Technical Reports Server (NTRS)

King, L. S.; Johnson, D. A.

1985-01-01

Navier-Stokes transonic airfoil calculations based on a recently developed nonequilibrium, turbulence closure model are presented for a supercritical airfoil section at transonic cruise conditions and for a conventional airfoil section at shock-induced stall conditions. Comparisons with experimental data are presented which show that this nonequilibrium closure model performs significantly better than the popular Baldwin-Lomax and Cebeci-Smith equilibrium algebraic models when there is boundary-layer separation that results from the inviscid-viscous interactions.

Linearized stability of extreme black holes

NASA Astrophysics Data System (ADS)

Burko, Lior M.; Khanna, Gaurav

2018-03-01

Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar ψ4 blows up along their event horizons at very late advanced times. We show numerically, by solving the Teukolsky equation in 2 +1 D , that all algebraically independent curvature scalar polynomials approach limits that exist when advanced time along the event horizon approaches infinity. Therefore, the horizons of extreme black holes are stable against linearized gravitational perturbations. We argue that the divergence of ψ4 is a consequence of the choice of a fixed tetrad, and that in a suitable dynamical tetrad all Weyl scalars, including ψ4, approach their background extreme Kerr values. We make similar conclusions also for the case of scalar field perturbations of extreme Kerr.

Asymptotic structure of the Einstein-Maxwell theory on AdS3

NASA Astrophysics Data System (ADS)

Pérez, Alfredo; Riquelme, Miguel; Tempo, David; Troncoso, Ricardo

2016-02-01

The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to {R}⊗ U(1)⊗ U(1) . Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and U (1). This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.

Developing Meaning for Algebraic Procedures: An Exploration of the Connections Undergraduate Students Make between Algebraic Rational Expressions and Basic Number Properties

ERIC Educational Resources Information Center

Yantz, Jennifer

2013-01-01

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study…

Curricula Alignment and Its Impact on End of Course Assessment Scores

ERIC Educational Resources Information Center

Burti, Neil, Jr.

2011-01-01

The purpose of this mixed methods study was to examine the alignment of the written, enacted, and tested Algebra I curricula in the Cherry Hill (NJ) Public School District. Furthermore, this QUAN-QUAL study sought to determine the impact of course selection (Algebra I, Enriched Algebra) on achievement as measured by the Algebra I End of Course…

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…

Card Games and Algebra Tic Tacmatics on Achievement of Junior Secondary II Students in Algebraic Expressions

ERIC Educational Resources Information Center

Okpube, Nnaemeka Michael; Anugwo, M. N.

2016-01-01

This study investigated the Card Games and Algebra tic-Tacmatics on Junior Secondary II Students' Achievement in Algebraic Expressions. Three research questions and three null hypotheses guided the study. The study adopted the pre-test, post-test control group design. A total of two hundred and forty (240) Junior Secondary School II students were…

A Study of Improving Eighth Graders' Learning Deficiency in Algebra by Applying a Realistic Context Instructional Design

ERIC Educational Resources Information Center

Chang, Yu-Liang; Huang, Yu-I

2014-01-01

The intention of this study was to improve the learning deficiency in algebraic learning and to enhance Taiwanese middle students' learning achievement and interest in algebra. By using a grade skipping experimental design, the research team intended to find out an effective way to benefit these students' leaning in abstract algebraic concepts.…

Effects of Comparison and Game-Challenge on Sixth Graders' Algebra Variable Learning Achievement, Learning Attitude, and Meta-Cognitive Awareness

ERIC Educational Resources Information Center

Sun Lin, Hong-Zheng; Chiou, Guey-Fa

2017-01-01

This study examined the effects of comparison and game-challenge strategies on sixth graders' learning achievement of algebra variable, learning attitude towards algebra variable learning, and meta-cognitive awareness of algebra variable learning. A 2 × 2 factorial design was used, and 86 students were invited to participate in the experimental…

Middle School Math Acceleration and Equitable Access to Eighth-Grade Algebra: Evidence from the Wake County Public School System

ERIC Educational Resources Information Center

Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.

2015-01-01

Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…

It's a Wonderful Life: Using Public Domain Cinema Clips To Teach Affective Objectives and Illustrate Real-World Algebra Applications.

ERIC Educational Resources Information Center

Palmer, Loretta

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…

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.

Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students. Educator's Practice Guide. What Works Clearinghouse.™ NCEE 2015-4010

ERIC Educational Resources Information Center

Star, Jon R.; Foegen, Anne; Larson, Matthew R.; McCallum, William G.; Porath, Jane; Zbiek, Rose Mary; Caronongan, Pia; Furgeson, Joshua,; Keating, Betsy; Lyskawa, Julia

2015-01-01

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…

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.

A Geometric Construction of Cyclic Cocycles on Twisted Convolution Algebras

NASA Astrophysics Data System (ADS)

Angel, Eitan

2010-09-01

In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the action of a discrete group into the periodic cyclic cohomology of the associated convolution algebra. Furthermore, for proper étale groupoids, J.-L. Tu and P. Xu provide a map between the periodic cyclic cohomology of a gerbe twisted convolution algebra and twisted cohomology groups. Our focus will be the convolution algebra with a product defined by a gerbe over a discrete translation groupoid. When the action is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial notions related to ideas of J. Dupont to construct a simplicial form representing the Dixmier-Douady class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial Dixmier-Douady form to the mixed bicomplex of certain matrix algebras. Finally, we define a morphism from this complex to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras.

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

PubMed Central

Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

On the quantum symmetry of the chiral Ising model

NASA Astrophysics Data System (ADS)

Vecsernyés, Peter

1994-03-01

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of rational quantum field theories. As an example we show that a six-dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the role of the global symmetry algebra of the chiral Ising model in the following sense: (1) a simple field algebra F and a representation π on Hπ of it is given, which contains the c = {1}/{2} unitary representations of the Virasoro algebra as subrepresentations; (2) the embedding U: H → B( Hπ) is such that the observable algebra π( A) - is the invariant subalgebra of B( Hπ) with respect to the left adjoint action of H and U(H) is the commutant of π( A); (3) there exist H-covariant primary fields in B( Hπ), which obey generalized Cuntz algebra properties and intertwine between the inequivalent sectors of the observables.

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

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

PubMed

Simzar, Rahila M; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

A natural history of mathematics: George Peacock and the making of English algebra.

PubMed

Lambert, Kevin

2013-06-01

In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's "principle of equivalent forms," which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra.

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

PubMed

Sialaros, Michalis; Christianidis, Jean

2016-06-01

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

Visualizing the inner product space ℝm×n in a MATLAB-assisted linear algebra classroom

NASA Astrophysics Data System (ADS)

Caglayan, Günhan

2018-05-01

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space ? in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools that complement the algebraic approach. As implemented in linear algebra lessons in a university in the Unites States, the article also incorporates algebraic and visual work of students who experienced these activities with MATLAB software. The connection between the Frobenius norm and the Euclidean norm is also emphasized.

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.

Graph C ∗-algebras and Z2-quotients of quantum spheres

NASA Astrophysics Data System (ADS)

Hajac, Piotr M.; Matthes, Rainer; Szymański, Wojciech

2003-06-01

We consider two Z2-actions on the Podleś generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesmewski q-disc and the quantum real projective space, respectively. The C ∗-algebas of all these quantum spaces are described as graph C ∗-algebras. The K-groups of the thus presented C ∗-algebras are then easily determined from the general theory of graph C ∗-algebas. For the quantum real projective space, we also recall the classification of the classes of irreducible ∗-representations of its algebra and give a linear basis for this algebra.

Quiver elliptic W-algebras

NASA Astrophysics Data System (ADS)

Kimura, Taro; Pestun, Vasily

2018-06-01

We define elliptic generalization of W-algebras associated with arbitrary quiver using our construction (Kimura and Pestun in Quiver W-algebras, 2015. arXiv:1512.08533 [hep-th]) with six-dimensional gauge theory.

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.

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.

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.

The Great Debate: Should All 8th Graders Take Algebra?

ERIC Educational Resources Information Center

McKibben, Sarah

2009-01-01

While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…

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…

The Effects of Teacher Collective Responsibility on the Mathematics Achievement of Students Who Repeat Algebra

ERIC Educational Resources Information Center

Morales-Chicas, Jessica; Agger, Charlotte

2017-01-01

In this article, the authors use the national High School Longitudinal Study of 2009 (HSLS:09) dataset to explore (a) if repeating algebra in the eighth grade was associated with overall mathematics grades and course-taking patterns by twelfth grade, (b) if repeating algebra in the eighth grade was associated with students' final grade in algebra,…

Quantum mechanics on periodic and non-periodic lattices and almost unitary Schwinger operators

NASA Astrophysics Data System (ADS)

Arik, Metin; Ildes, Medine

2018-05-01

In this work, we uncover the mathematical structure of the Schwinger algebra and introduce almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations between these algebras and show that the almost unitary Schwinger operators are equivalent to the Schwinger algebra. We introduce new representations for MN(C) in terms of these algebras.

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…

Change in Peer Ability as a Mediator and Moderator of the Effect of the Algebra-For-All Policy on Ninth Graders' Math Outcomes

ERIC Educational Resources Information Center

Hong, Guanglei; Nomi, Takako

2011-01-01

A recent report by the Mathematics Advisory Panel referred to algebra as a "gateway" to later achievement (National Mathematics Advisory Panel, 2008). To address the problem of low academic performance in algebra, an increasing number of states and districts have started to implement a policy of requiring algebra for all students in…

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…

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Extended Riemannian geometry II: local heterotic double field theory

NASA Astrophysics Data System (ADS)

Deser, Andreas; Heller, Marc Andre; Sämann, Christian

2018-04-01

We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold that captures heterotic Generalized Geometry which leads to new observations on the generalized metric and its twists. We then give a symplectic pre-N Q-manifold that captures the symmetries and the geometry of local heterotic DFT. We derive a weakened form of the section condition, which arises algebraically from consistency of the symmetry Lie 2-algebra and its action on extended tensors. We also give appropriate notions of twists — which are required for global formulations — and of the torsion and Riemann tensors. Finally, we show how the observed α'-corrections are interpreted naturally in our framework.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

NASA Astrophysics Data System (ADS)

Alazzawi, Sabina; Lechner, Gandalf

2017-09-01

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.

Deformed coset models from gauged WZW actions

NASA Astrophysics Data System (ADS)

Park, Q.-Han

1994-06-01

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTg -1overlineT) , where algebra elements T, overlineT belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the deformed coset model can be identified with the integrability condition of certain linear equations which makes the use of the inverse scattering method possible. Using the linear equation, we give a systematic way to construct infinitely many conserved currents as well as soliton solutions. In the case of the parafermionic SU(2)/U(1)-coset model, we derive n-solitons and conserved currents explicitly.

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

PubMed

Cierniak, Robert; Lorent, Anna

2016-09-01

The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Deformed twistors and higher spin conformal (super-)algebras in four dimensions

DOE PAGES

Govil, Karan; Gunaydin, Murat

2015-03-05

Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5.more » The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS 5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4,R) admits only two massless representations (minreps), namely the scalar and spinor singletons.« less

Combinatorial Formulas for Characteristic Classes, and Localization of Secondary Topological Invariants.

NASA Astrophysics Data System (ADS)

Smirnov, Mikhail

1995-01-01

The problems solved in this thesis originated from combinatorial formulas for characteristic classes. This thesis deals with Chern-Simons classes, their generalizations and related algebraic and analytic problems. (1) In this thesis, I describe a new class of algebras whose elements contain Chern and generalized Chern -Simons classes. There is a Poisson bracket in these algebras, similar to the bracket in Kontsevich's noncommutative symplectic geometry (Kon). I prove that the Poisson bracket gives rise to a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. This is a new result. I describe algebraic analogs of the dilogarithm and higher polylogarithms in the algebra corresponding to Chern-Simons classes. (2) I study the properties of this bracket. It is possible to write the exterior differential and other operations in the algebra using this bracket. The bracket of any two Chern classes is zero and the bracket of a Chern class and a Chern-Simons class is d-closed. The construction developed here easily gives explicit formulas for known secondary classes and makes it possible to construct new ones. (3) I develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action (see theorem 3 page xi). (4) It is possible give new explicit formulas for cocycles on a gauge group of a bundle and for the corresponding cocycles on the Lie algebra of the gauge group. I use formulas for secondary characteristic classes and an algebraic approach developed in chapter 1. I also use the work of Faddeev, Reiman and Semyonov-Tian-Shanskii (FRS) on cocycles as quantum anomalies. (5) I apply the methods of differential geometry of formal power series to construct universal characteristic and secondary characteristic classes. Given a pair of gauge equivalent connections using local formulas I obtain dilogarithmic and trilogarithmic analogs of Chern-Simons classes.

Algebra for Gifted Third Graders.

ERIC Educational Resources Information Center

Borenson, Henry

1987-01-01

Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

Using Student Work to Develop Teachers' Knowledge of Algebra

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth A.; Phillips, Elizabeth Difanis

2005-01-01

This article describes a set of learning activities that use algebraic problems and written student work to help preservice and in-service teachers understand students' algebraic thinking. (Contains 4 figures.)

Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds

NASA Astrophysics Data System (ADS)

Blumen, Sacha C.

2006-01-01

The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra U_q(osp(1|2n)) over C is considered with q a primitive N^th root of unity for all integers N >= 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U_q^(N)(osp(1|2n)) = U_q(osp(1|2n)) / I is a Z_2-graded ribbon Hopf algebra. For all n and all N >= 3, a finite collection of finite dimensional representations of U_q^(N)(osp(1|2n)) is defined. Each such representation of U_q^(N)(osp(1|2n)) is labelled by an integral dominant weight belonging to the truncated dominant Weyl chamber. Properties of these representations are considered: the quantum superdimension of each representation is calculated, each representation is shown to be self-dual, and more importantly, the decomposition of the tensor product of an arbitrary number of such representations is obtained for even N. It is proved that the quotient algebra U_q^(N)(osp(1|2n)), together with the set of finite dimensional representations discussed above, form a pseudo-modular Hopf algebra when N >= 6 is twice an odd number. Using this pseudo-modular Hopf algebra, we construct a topological invariant of 3-manifolds. This invariant is shown to be different to the topological invariants of 3-manifolds arising from quantum so(2n+1) at roots of unity.

On controllability of homogeneous and inhomogeneous discrete-time multi-input bilinear systems in dimension two

NASA Astrophysics Data System (ADS)

Tie, Lin

2017-08-01

In this paper, the controllability problem of two-dimensional discrete-time multi-input bilinear systems is completely solved. The homogeneous and the inhomogeneous cases are studied separately and necessary and sufficient conditions for controllability are established by using a linear algebraic method, which are easy to apply. Moreover, for the uncontrollable systems, near-controllability is considered and similar necessary and sufficient conditions are also obtained. Finally, examples are provided to demonstrate the results of this paper.

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Symmetries and Invariants of Twisted Quantum Algebras and Associated Poisson Algebras

NASA Astrophysics Data System (ADS)

Molev, A. I.; Ragoucy, E.

We construct an action of the braid group BN on the twisted quantized enveloping algebra U q'( {o}N) where the elements of BN act as automorphisms. In the classical limit q → 1, we recover the action of BN on the polynomial functions on the space of upper triangular matrices with ones on the diagonal. The action preserves the Poisson bracket on the space of polynomials which was introduced by Nelson and Regge in their study of quantum gravity and rediscovered in the mathematical literature. Furthermore, we construct a Poisson bracket on the space of polynomials associated with another twisted quantized enveloping algebra U q'( {sp}2n). We use the Casimir elements of both twisted quantized enveloping algebras to reproduce and construct some well-known and new polynomial invariants of the corresponding Poisson algebras.

Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn

NASA Astrophysics Data System (ADS)

Nurhayati, D. M.; Herman, T.; Suhendra, S.

2017-09-01

This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.

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.

Minimal unitary representation of 5d superconformal algebra F(4) and AdS 6/CFT 5 higher spin (super)-algebras

DOE PAGES

Fernando, Sudarshan; Günaydin, Murat

2014-11-28

We study the minimal unitary representation (minrep) of SO(5, 2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5, 2) describes a massless conformal scalar field in five dimensions and admits a unique “deformation” which describes a massless conformal spinor. Scalar and spinor minreps of SO(5, 2) are the 5d analogs of Dirac’s singletons of SO(3, 2). We then construct the minimal unitary representation of the unique 5d supercon-formal algebra F(4) with the even subalgebra SO(5, 2) ×SU(2). The minrep of F(4) describes a massless conformal supermultiplet consisting of two scalar andmore » one spinor fields. We then extend our results to the construction of higher spin AdS 6/CFT 5 (super)-algebras. The Joseph ideal of the minrep of SO(5, 2) vanishes identically as operators and hence its enveloping algebra yields the AdS 6/CFT 5 bosonic higher spin algebra directly. The enveloping algebra of the spinor minrep defines a “deformed” higher spin algebra for which a deformed Joseph ideal vanishes identically as operators. These results are then extended to the construction of the unique higher spin AdS 6/CFT 5 superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.« less

Higher-dimensional lifts of Killing-Yano forms with torsion

NASA Astrophysics Data System (ADS)

Chow, David D. K.

2017-01-01

Using a Kaluza-Klein-type lift, it is shown how Killing-Yano forms with torsion can remain symmetries of a higher-dimensional geometry, subject to an algebraic condition between the Kaluza-Klein field strength and the Killing-Yano form. The lift condition’s significance is highlighted, and is satisfied by examples of black holes in supergravity.

Towards Direct Simulations of Counterflow Flames with Consistent Numerical Differential-Algebraic Boundary Conditions

DTIC Science & Technology

2015-05-18

First, the gov - erning equations of the problem are presented. A detailed discussion on the construction of the initial profile of the flow follows...time from the DoD HPCMP Open Research Systems and JPL/ NASA is gratefully acknowledged. References [1] H. Tsuji, Prog. Energ. Combust.8(2) (1982) 93-119

Application of fuzzy fault tree analysis based on modified fuzzy AHP and fuzzy TOPSIS for fire and explosion in the process industry.

PubMed

Yazdi, Mohammad; Korhan, Orhan; Daneshvar, Sahand

2018-05-09

This study aimed at establishing fault tree analysis (FTA) using expert opinion to compute the probability of an event. To find the probability of the top event (TE), all probabilities of the basic events (BEs) should be available when the FTA is drawn. In this case, employing expert judgment can be used as an alternative to failure data in an awkward situation. The fuzzy analytical hierarchy process as a standard technique is used to give a specific weight to each expert, and fuzzy set theory is engaged for aggregating expert opinion. In this regard, the probability of BEs will be computed and, consequently, the probability of the TE obtained using Boolean algebra. Additionally, to reduce the probability of the TE in terms of three parameters (safety consequences, cost and benefit), the importance measurement technique and modified TOPSIS was employed. The effectiveness of the proposed approach is demonstrated with a real-life case study.

A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement

ERIC Educational Resources Information Center

Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.

2009-01-01

The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

Students' Perceptions about the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Government Girls Secondary School Karachi

ERIC Educational Resources Information Center

Samo, Mashooque Ali

2009-01-01

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the…

Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities

PubMed Central

Yau, Stephen S.-T.

1983-01-01

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra. PMID:16593401

A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras

NASA Astrophysics Data System (ADS)

Alshammari, Fahad; Isaac, Phillip S.; Marquette, Ian

2018-02-01

We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and (2) the Schrödinger Lie algebras. We find that an abstract form of dimensional analysis assists us in our algorithm, and greatly reduces the complexity of the problem.

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.

Working memory, worry, and algebraic ability.

PubMed

Trezise, Kelly; Reeve, Robert A

2014-05-01

Math anxiety (MA)-working memory (WM) relationships have typically been examined in the context of arithmetic problem solving, and little research has examined the relationship in other math domains (e.g., algebra). Moreover, researchers have tended to examine MA/worry separate from math problem solving activities and have used general WM tasks rather than domain-relevant WM measures. Furthermore, it seems to have been assumed that MA affects all areas of math. It is possible, however, that MA is restricted to particular math domains. To examine these issues, the current research assessed claims about the impact on algebraic problem solving of differences in WM and algebraic worry. A sample of 80 14-year-old female students completed algebraic worry, algebraic WM, algebraic problem solving, nonverbal IQ, and general math ability tasks. Latent profile analysis of worry and WM measures identified four performance profiles (subgroups) that differed in worry level and WM capacity. Consistent with expectations, subgroup membership was associated with algebraic problem solving performance: high WM/low worry>moderate WM/low worry=moderate WM/high worry>low WM/high worry. Findings are discussed in terms of the conceptual relationship between emotion and cognition in mathematics and implications for the MA-WM-performance relationship. Copyright © 2013 Elsevier Inc. All rights reserved.

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

Miyadera, Takayuki; Imai, Hideki; Graduate School of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551

This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloningmore » on effect algebras and hidden variables.« less

The noncommutative Poisson bracket and the deformation of the family algebras

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

Wei, Zhaoting, E-mail: zhaotwei@indiana.edu

The family algebras are introduced by Kirillov in 2000. In this paper, we study the noncommutative Poisson bracket P on the classical family algebra C{sub τ}(g). We show that P controls the first-order 1-parameter formal deformation from C{sub τ}(g) to Q{sub τ}(g) where the latter is the quantum family algebra. Moreover, we will prove that the noncommutative Poisson bracket is in fact a Hochschild 2-coboundary, and therefore, the deformation is infinitesimally trivial. In the last part of this paper, we discuss the relation between Mackey’s analogue and the quantization problem of the family algebras.

Gopakumar-Vafa Invariants Do Not Determine Flops

NASA Astrophysics Data System (ADS)

Brown, Gavin; Wemyss, Michael

2017-11-01

Two 3-fold flops are exhibited, both of which have precisely one flopping curve. One of the two flops is new and is distinct from all known algebraic D 4-flops. It is shown that the two flops are neither algebraically nor analytically isomorphic, yet their curve-counting Gopakumar-Vafa invariants are the same. We further show that the contraction algebras associated to both are not isomorphic, so the flops are distinguished at this level. This shows that the contraction algebra is a finer invariant than various curve-counting theories, and it also provides more evidence for the proposed analytic classification of 3-fold flops via contraction algebras.

Homomorphisms in C*-ternary algebras and JB*-triples

NASA Astrophysics Data System (ADS)

Park, Choonkil; Rassias, Themistocles M.

2008-01-01

In this paper, we investigate homomorphisms between C*-ternary algebras and derivations on C*-ternary algebras, and homomorphisms between JB*-triples and derivations on JB*-triples, associated with the following Apollonius type additive functional equation

Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.

ERIC Educational Resources Information Center

Leitze, Annette Ricks; Kitt, Nancy A.

2000-01-01

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

A critical evaluation of various turbulence models as applied to internal fluid flows

NASA Technical Reports Server (NTRS)

Nallasamy, M.

1985-01-01

Models employed in the computation of turbulent flows are described and their application to internal flows is evaluated by examining the predictions of various turbulence models in selected flow configurations. The main conclusions are: (1) the k-epsilon model is used in a majority of all the two-dimensional flow calculations reported in the literature; (2) modified forms of the k-epsilon model improve the performance for flows with streamline curvature and heat transfer; (3) for flows with swirl, the k-epsilon model performs rather poorly; the algebraic stress model performs better in this case; and (4) for flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well for fully developed flow, for developing flow, the algebraic stress model performance is not good; a Reynolds stress model should be used. False diffusion and inlet boundary conditions are discussed. Countergradient transport and its implications in turbulence modeling is mentioned. Two examples of recirculating flow predictions obtained using PHOENICS code are discussed. The vortex method, large eddy simulation (modeling of subgrid scale Reynolds stresses), and direct simulation, are considered. Some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.

On generalized Melvin solution for the Lie algebra E_6

NASA Astrophysics Data System (ADS)

Bolokhov, S. V.; Ivashchuk, V. D.

2017-10-01

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H_s(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H_s(z), s = 1,\\ldots ,6, for the Lie algebra E_6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q_s, s = 1,\\ldots ,6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E_6-polynomials at large z are governed by the integer-valued matrix ν = A^{-1} (I + P), where A^{-1} is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z_2-group of symmetry of the Dynkin diagram. The 2-form fluxes Φ ^s, s = 1,\\ldots ,6, are calculated.

Saturation of the magnetorotational instability at large Elsasser number

NASA Astrophysics Data System (ADS)

Jamroz, B.; Julien, K.; Knobloch, E.

2008-09-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still but not negligible. The regime explored retains the condition that (viscous and ohmic) dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

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

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

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

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

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.

Linear {GLP}-algebras and their elementary theories

NASA Astrophysics Data System (ADS)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Workflows in bioinformatics: meta-analysis and prototype implementation of a workflow generator.

PubMed

Garcia Castro, Alexander; Thoraval, Samuel; Garcia, Leyla J; Ragan, Mark A

2005-04-07

Computational methods for problem solving need to interleave information access and algorithm execution in a problem-specific workflow. The structures of these workflows are defined by a scaffold of syntactic, semantic and algebraic objects capable of representing them. Despite the proliferation of GUIs (Graphic User Interfaces) in bioinformatics, only some of them provide workflow capabilities; surprisingly, no meta-analysis of workflow operators and components in bioinformatics has been reported. We present a set of syntactic components and algebraic operators capable of representing analytical workflows in bioinformatics. Iteration, recursion, the use of conditional statements, and management of suspend/resume tasks have traditionally been implemented on an ad hoc basis and hard-coded; by having these operators properly defined it is possible to use and parameterize them as generic re-usable components. To illustrate how these operations can be orchestrated, we present GPIPE, a prototype graphic pipeline generator for PISE that allows the definition of a pipeline, parameterization of its component methods, and storage of metadata in XML formats. This implementation goes beyond the macro capacities currently in PISE. As the entire analysis protocol is defined in XML, a complete bioinformatic experiment (linked sets of methods, parameters and results) can be reproduced or shared among users. http://if-web1.imb.uq.edu.au/Pise/5.a/gpipe.html (interactive), ftp://ftp.pasteur.fr/pub/GenSoft/unix/misc/Pise/ (download). From our meta-analysis we have identified syntactic structures and algebraic operators common to many workflows in bioinformatics. The workflow components and algebraic operators can be assimilated into re-usable software components. GPIPE, a prototype implementation of this framework, provides a GUI builder to facilitate the generation of workflows and integration of heterogeneous analytical tools.

Computer Algebra Systems in Undergraduate Instruction.

ERIC Educational Resources Information Center

Small, Don; And Others

1986-01-01

Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

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.

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.

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

Ermakov's Superintegrable Toy and Nonlocal Symmetries

NASA Astrophysics Data System (ADS)

Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.

2005-11-01

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.

Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

NASA Astrophysics Data System (ADS)

Suga, Tetsuya; Iijima, Junichi

2018-03-01

Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.

Teaching Structure in Algebra

ERIC Educational Resources Information Center

Merlin, Ethan M.

2013-01-01

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

Error-Detecting Identification Codes for Algebra Students.

ERIC Educational Resources Information Center

Sutherland, David C.

1990-01-01

Discusses common error-detecting identification codes using linear algebra terminology to provide an interesting application of algebra. Presents examples from the International Standard Book Number, the Universal Product Code, bank identification numbers, and the ZIP code bar code. (YP)

Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

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

Burdik, C., E-mail: burdik@kmlinux.fjfi.cvut.cz; Navratil, O.

2011-06-15

We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

Elliptic biquaternion algebra

NASA Astrophysics Data System (ADS)

Özen, Kahraman Esen; Tosun, Murat

2018-01-01

In this study, we define the elliptic biquaternions and construct the algebra of elliptic biquaternions over the elliptic number field. Also we give basic properties of elliptic biquaternions. An elliptic biquaternion is in the form A0 + A1i + A2j + A3k which is a linear combination of {1, i, j, k} where the four components A0, A1, A2 and A3 are elliptic numbers. Here, 1, i, j, k are the quaternion basis of the elliptic biquaternion algebra and satisfy the same multiplication rules which are satisfied in both real quaternion algebra and complex quaternion algebra. In addition, we discuss the terms; conjugate, inner product, semi-norm, modulus and inverse for elliptic biquaternions.

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.

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.

Algebraic Algorithm Design and Local Search

DTIC Science & Technology

1996-12-01

method for performing algorithm design that is more purely algebraic than that of KIDS. This method is then applied to local search. Local search is a...synthesis. Our approach was to follow KIDS in spirit, but to adopt a pure algebraic formalism, supported by Kestrel’s SPECWARE environment (79), that...design was developed that is more purely algebraic than that of KIDS. This method was then applied to local search. A general theory of local search was

Quantum walks, deformed relativity and Hopf algebra symmetries.

PubMed

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

2016-05-28

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. © 2016 The Author(s).

From rational numbers to algebra: separable contributions of decimal magnitude and relational understanding of fractions.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2015-05-01

To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

An Algebraic Approach to the Eigenstates of the Calogero Model

NASA Astrophysics Data System (ADS)

Ujino, Hideaki

2002-11-01

An algebraic treatment of the eigenstates of the (AN-1-) Calogero model is presented, which provides an algebraic construction of the nonsymmetric orthogonal eigenvectors, symmetrization, antisymmetrization and calculation of square norms in a unified way.

Solving Our Algebra Problem: Getting All Students through Algebra I to Improve Graduation Rates

ERIC Educational Resources Information Center

Schachter, Ron

2013-01-01

graduation as well as admission to most colleges. But taking algebra also can turn into a pathway for failure, from which some students never recover. In 2010, a national U.S. Department of Education study…

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners.

PubMed

Powell, Sarah R; Fuchs, Lynn S; Cirino, Paul T; Fuchs, Douglas; Compton, Donald L; Changas, Paul C

2015-07-01

The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2 nd -grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge.

Head Pose Estimation Using Multilinear Subspace Analysis for Robot Human Awareness

NASA Technical Reports Server (NTRS)

Ivanov, Tonislav; Matthies, Larry; Vasilescu, M. Alex O.

2009-01-01

Mobile robots, operating in unconstrained indoor and outdoor environments, would benefit in many ways from perception of the human awareness around them. Knowledge of people's head pose and gaze directions would enable the robot to deduce which people are aware of the its presence, and to predict future motions of the people for better path planning. To make such inferences, requires estimating head pose on facial images that are combination of multiple varying factors, such as identity, appearance, head pose, and illumination. By applying multilinear algebra, the algebra of higher-order tensors, we can separate these factors and estimate head pose regardless of subject's identity or image conditions. Furthermore, we can automatically handle uncertainty in the size of the face and its location. We demonstrate a pipeline of on-the-move detection of pedestrians with a robot stereo vision system, segmentation of the head, and head pose estimation in cluttered urban street scenes.

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.

Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

NASA Astrophysics Data System (ADS)

Abdalla, M. Sebaweh; Khalil, E. M.; Obada, A.-S. F.

2017-06-01

The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

2014-01-01

The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2nd-grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge. PMID:26097244

Contractions of AdS brane algebra and superGalileon Lagrangians

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

Kamimura, Kiyoshi; Onda, Seiji

2013-06-15

We examine AdS Galileon Lagrangians using the method of nonlinear realization. By contractions (1) flat curvature limit, (2) non-relativistic brane algebra limit, and (3) (1) + (2) limits we obtain DBI, Newton-Hoock, and Galilean Galileons, respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino (WZ) terms using Maurer-Cartan (MC) equations on the coset G/SO(3, 1). We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using amore » supercoset SU(2, 2 Double-Vertical-Line 1)/(SO(3, 1) Multiplication-Sign U(1)) and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates for supersymmetric Galileon action.« less

Simultaneous Heat and Mass Transfer Model for Convective Drying of Building Material

NASA Astrophysics Data System (ADS)

Upadhyay, Ashwani; Chandramohan, V. P.

2018-04-01

A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss-Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.

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

Govil, Karan; Gunaydin, Murat

Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5.more » The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS 5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4,R) admits only two massless representations (minreps), namely the scalar and spinor singletons.« less

Extending a Property of Cubic Polynomials to Higher-Degree Polynomials

ERIC Educational Resources Information Center

Miller, David A.; Moseley, James

2012-01-01

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Special Bohr-Sommerfeld Lagrangian submanifolds

NASA Astrophysics Data System (ADS)

Tyurin, N. A.

2016-12-01

We introduce a new notion in symplectic geometry, that of speciality for Lagrangian submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr- Sommerfeld Lagrangian submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.

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.

Massless conformal fields, AdS (d+1)/CFT d higher spin algebras and their deformations

DOE PAGES

Fernando, Sudarshan; Gunaydin, Murat

2016-02-04

Here, we extend our earlier work on the minimal unitary representation of SO(d, 2)and its deformations for d=4, 5and 6to arbitrary dimensions d. We show that there is a one-to-one correspondence between the minrep of SO(d, 2)and its deformations and massless conformal fields in Minkowskian spacetimes in ddimensions. The minrep describes a massless conformal scalar field, and its deformations describe massless conformal fields of higher spin. The generators of Joseph ideal vanish identically as operators for the quasiconformal realization of the minrep, and its enveloping algebra yields directly the standard bosonic AdS (d+1)/CFT d higher spin algebra. For deformed minrepsmore » the generators of certain deformations of Joseph ideal vanish as operators and their enveloping algebras lead to deformations of the standard bosonic higher spin algebra. In odd dimensions there is a unique deformation of the higher spin algebra corresponding to the spinor singleton. In even dimensions one finds infinitely many deformations of the higher spin algebra labelled by the eigenvalues of Casimir operator of the little group SO(d–2)for massless representations.« less

Individual Differences in Algebraic Cognition: Relation to the Approximate Number and Sematic Memory Systems

PubMed Central

Geary, David C.; Hoard, Mary K.; Nugent, Lara; Rouder, Jeffrey N.

2015-01-01

The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 (92 girls) 9th graders, controlling parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation, but not schema memory. Frequency of fact-retrieval errors was related to schema memory but not coordinate plane or expression evaluation accuracy. The results suggest the ANS may contribute to or is influenced by spatial-numerical and numerical only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest different brain and cognitive systems are engaged during the learning of different components of algebraic competence, controlling demographic and domain general abilities. PMID:26255604

Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

NASA Astrophysics Data System (ADS)

Bufalo, R.; Cardoso, T. R.; Nogueira, A. A.; Pimentel, B. M.

2018-05-01

We establish the multiplicative renormalization procedure of generalized scalar Duffin-Kemmer-Petiau electrodynamics (GSDKP4 ) in the mass shell. We show an explicit calculation of the first radiative corrections (one-loop) associated with the photon propagator, meson propagator, vertex function, and photon-photon four-point function utilizing the dimensional regularization method, where the gauge symmetry is manifest. As we will see, one of the consequences of the study is that, from the complete photon propagator renormalization condition, imposing that it behaves as a massless field, an energy range where GSDKP4 is well defined is m2≪k2

Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

NASA Astrophysics Data System (ADS)

Mata-Machuca, Juan L.; Aguilar-López, Ricardo

2018-01-01

This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator-chiral medium

NASA Astrophysics Data System (ADS)

Shoukat, Sobia; Naqvi, Qaisar A.

2016-12-01

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)-chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber-Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

Numerical Solutions for the CAWAPI Configuration on Structured Grids at NASA LaRC, United States. Chapter 7

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa A.; Abdol-Hamid, Khaled S.; Massey, Steven J.

2009-01-01

In this chapter numerical simulations of the flow around F-16XL are performed as a contribution to the Cranked Arrow Wing Aerodynamic Project International (CAWAPI) using the PAB3D CFD code. Two turbulence models are used in the calculations: a standard k-epsilon model, and the Shih-Zhu-Lumley (SZL) algebraic stress model. Seven flight conditions are simulated for the flow around the F-16XL where the free stream Mach number varies from 0.242 to 0.97. The range of angles of attack varies from 0 deg to 20 deg. Computational results, surface static pressure, boundary layer velocity profiles, and skin friction are presented and compared with flight data. Numerical results are generally in good agreement with flight data, considering that only one grid resolution is utilized for the different flight conditions simulated in this study. The Algebraic Stress Model (ASM) results are closer to the flight data than the k-epsilon model results. The ASM predicted a stronger primary vortex, however, the origin of the vortex and footprint is approximately the same as in the k-epsilon predictions.

Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times

NASA Astrophysics Data System (ADS)

Finster, Felix; Strohmaier, Alexander

2015-08-01

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta-Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time.

Proceedings of the International Conference on Algebraic Methodology and Software Technology (3rd) Held in The Netherlands on June 21 - 25, 1993

DTIC Science & Technology

1993-06-25

one). Other ones from the concrete implementation of the abstract data types: implementation of the heap • as a stack, optimal memory allocation of the...Utah, U. Iowa): Rea-time progrm synthes from specifications 16:10-16:30 Tea break SssioN: Testing theory and applications (Chair: Christine Choppy) 16...protocols via testing -proectio evening 19.30-20:30 System demonstratics 21.00- Surprise event v•0 0 Thursday 24 June min ing0 09𔃺-0:50 lNXizITLK: Rob J

Nonlinear External Kink Computing with NIMROD

NASA Astrophysics Data System (ADS)

Bunkers, K. J.; Sovinec, C. R.

2016-10-01

Vertical displacement events (VDEs) during disruptions often include non-axisymmetric activity, including external kink modes, which are driven unstable as contact with the wall eats into the q-profile. The NIMROD code is being applied to study external-kink-unstable tokamak profiles in toroidal and cylindrical geometries. Simulations with external kinks show the plasma swallowing a vacuum bubble, similar to. NIMROD reproduces external kinks in both geometries, using an outer vacuum region (modeled as a plasma with a large resistivity), but as the boundary between the vacuum and plasma regions becomes more 3D, the resistivity becomes a 3D function, and it becomes more difficult for algebraic solves to converge. To help allow non-axisymmetric, nonlinear VDE calculations to proceed without restrictively small time-steps, several computational algorithms have been tested. Flexible GMRES, using a Fourier and real space representation for the toroidal angle has shown improvements. Off-diagonal preconditioning and a multigrid approach were tested and showed little improvement. A least squares finite element method (LSQFEM) has also helped improve the algebraic solve. This effort is supported by the U.S. Dept. of Energy, Award Numbers DE-FG02-06ER54850 and DE-FC02-08ER54975.

Modular operads and the quantum open-closed homotopy algebra

NASA Astrophysics Data System (ADS)

Doubek, Martin; Jurčo, Branislav; Münster, Korbinian

2015-12-01

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

Elementary maps on nest algebras

NASA Astrophysics Data System (ADS)

Li, Pengtong

2006-08-01

Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.

On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2017-06-01

Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

Towards classical spectrum generating algebras for f-deformations

NASA Astrophysics Data System (ADS)

Kullock, Ricardo; Latini, Danilo

2016-01-01

In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.

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…

Geometry of quantum state manifolds generated by the Lie algebra operators

NASA Astrophysics Data System (ADS)

Kuzmak, A. R.

2018-03-01

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results, we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

On Non-Abelian Extensions of 3-Lie Algebras

NASA Astrophysics Data System (ADS)

Song, Li-Na; Makhlouf, Abdenacer; Tang, Rong

2018-04-01

In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed. Supported by National Natural Science Foundation of China under Grant No. 11471139 and National Natural Science Foundation of Jilin Province under Grant No. 20170101050JC

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.

A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets

DTIC Science & Technology

2014-11-01

linear hybrid systems by linear algebraic methods. In SAS, volume 6337 of LNCS, pages 373–389. Springer, 2010. [19] E. W. Mayr. Membership in polynomial...383–394, 2009. [31] A. Tarski. A decision method for elementary algebra and geometry. Bull. Amer. Math. Soc., 59, 1951. [32] A. Tiwari. Abstractions...A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 November 2014 CMU

Topology-preserving quantum deformation with non-numerical parameter

NASA Astrophysics Data System (ADS)

Aukhadiev, Marat; Grigoryan, Suren; Lipacheva, Ekaterina

2013-11-01

We introduce a class of compact quantum semigroups, that we call semigroup deformations of compact Abelian qroups. These objects arise from reduced semigroup -algebras, the generalization of the Toeplitz algebra. We study quantum subgroups, quantum projective spaces and quantum quotient groups for such objects, and show that the group is contained as a compact quantum subgroup in the deformation of itself. The connection with the weak Hopf algebra notion is described. We give a grading on the -algebra of the compact quantum semigroups constructed.

A Study to Determine Differences in the Level of Perceived Preparedness in Teaching Algebra to Eighth Graders between Teachers in the United States and Teachers in Lebanon

ERIC Educational Resources Information Center

Khajarian, Seta

2011-01-01

Algebra is a branch in mathematics and taking Algebra in middle school is often a gateway to advanced courses in high school. The problem is that the United States and Lebanon had low scores in Algebra in the 2007 Trends in Mathematics and Sciences Study (TIMSS), an international assessment administered to 4th and 8th graders every 4 years. On the…

Realization of Uq(sp(2n)) within the Differential Algebra on Quantum Symplectic Space

NASA Astrophysics Data System (ADS)

Zhang, Jiao; Hu, Naihong

2017-10-01

We realize the Hopf algebra U_q({sp}_{2n}) as an algebra of quantum differential operators on the quantum symplectic space X(f_s;R) and prove that X(f_s;R) is a U_q({sp}_{2n})-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of U_q({sp}_{2n}).

Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory

NASA Astrophysics Data System (ADS)

Hoefel, Eduardo; Livernet, Muriel

2012-08-01

Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.

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.

Structure of Lie point and variational symmetry algebras for a class of odes

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2018-04-01

It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced by a point transformation to the trivial equation y(n)=0. For arbitrary systems of ordinary differential equations of order n ≥ 3 reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the maximal dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.

An embedding of the universal Askey-Wilson algebra into Uq (sl2) ⊗Uq (sl2) ⊗Uq (sl2)

NASA Astrophysics Data System (ADS)

Huang, Hau-Wen

2017-09-01

The Askey-Wilson algebras were used to interpret the algebraic structure hidden in the Racah-Wigner coefficients of the quantum algebra Uq (sl2). In this paper, we display an injection of a universal analog △q of Askey-Wilson algebras into Uq (sl2) ⊗Uq (sl2) ⊗Uq (sl2) behind the application. Moreover we establish the decomposition rules for 3-fold tensor products of irreducible Verma Uq (sl2)-modules and of finite-dimensional irreducible Uq (sl2)-modules into the direct sums of finite-dimensional irreducible △q-modules. As an application, we derive a formula for the Racah-Wigner coefficients of Uq (sl2).

The Effects of History of Mathematics on Attitudes Toward Mathematics of College Algebra Students

ERIC Educational Resources Information Center

McBride, Cecil; Rollins, James H.

1977-01-01

Two college algebra classes were exposed to items from mathematics history in their classroom instruction, while two other college algebra classes received no such exposure. Results showed a significant positive attitude change of the mathematics history group. (DT)

A Worked Example for Creating Worked Examples

ERIC Educational Resources Information Center

McGinn, Kelly M.; Lange, Karin E.; Booth, Julie L.

2015-01-01

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Earth Algebra: Real-Life Mathematics in Navajoland.

ERIC Educational Resources Information Center

Schaufele, Christopher; Srivastava, Ravindra

1995-01-01

An algebra class at Navajo Community College (Shiprock, New Mexico) uses traditional algebra topics to study real-life situations, focuses on environmental issues, encourages collaborative learning, uses modern technology, and promotes development of critical thinking and decision-making skills. Students follow principles of Dine educational…

Learning Activity Package, Algebra.

ERIC Educational Resources Information Center

Evans, Diane

A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

Algebra 1r, Mathematics (Experimental): 5215.13.

ERIC Educational Resources Information Center

Strachan, Florence

This third of six guidebooks on minimum course content for first-year algebra includes work with laws of exponents; multiplication, division, and factoring of polynomials; and fundamental operations with rational algebraic expressions. Course goals are stated, performance objectives listed, a course outline provided, testbook references specified…

Relational Algebra and SQL: Better Together

ERIC Educational Resources Information Center

McMaster, Kirby; Sambasivam, Samuel; Hadfield, Steven; Wolthuis, Stuart

2013-01-01

In this paper, we describe how database instructors can teach Relational Algebra and Structured Query Language together through programming. Students write query programs consisting of sequences of Relational Algebra operations vs. Structured Query Language SELECT statements. The query programs can then be run interactively, allowing students to…

Using Students' Interests as Algebraic Models

ERIC Educational Resources Information Center

Whaley, Kenneth A.

2012-01-01

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

Oleanna Math Program Materials.

ERIC Educational Resources Information Center

Coole, Walter A.

This document is a collection of course outlines, syllabi, and test materials designed for several high school level and lower division mathematics courses taught in an auto-tutorial learning laboratory at Skagit Valley College (Washington). The courses included are: Pre-Algebra, Basic Algebra, Plan Geometry, Intermediate Algebra, Probability and…

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.

Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

2012-01-01

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. PMID:22409764

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.

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

Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl{sub -1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from the q{yields}-1 limit of the dual q-Hahn polynomials. The Hopf algebra sl{sub -1}(2) has four generators including an involution, it is also a q{yields}-1 limit of the quantum algebra sl{sub q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of themore » -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl{sub -1}(2) algebras, so that the Clebsch-Gordan coefficients of sl{sub -1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.« less

Proper Conformal Killing Vectors in Kantowski-Sachs Metric

NASA Astrophysics Data System (ADS)

Hussain, Tahir; Farhan, Muhammad

2018-04-01

This paper deals with the existence of proper conformal Killing vectors (CKVs) in Kantowski-Sachs metric. Subject to some integrability conditions, the general form of vector filed generating CKVs and the conformal factor is presented. The integrability conditions are solved generally as well as in some particular cases to show that the non-conformally flat Kantowski-Sachs metric admits two proper CKVs, while it admits a 15-dimensional Lie algebra of CKVs in the case when it becomes conformally flat. The inheriting conformal Killing vectors (ICKVs), which map fluid lines conformally, are also investigated.

Symplecticity in Beam Dynamics: An Introduction

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

Rees, John R

2003-06-10

A particle in a particle accelerator can often be considered a Hamiltonian system, and when that is the case, its motion obeys the constraints of the Symplectic Condition. This tutorial monograph derives the condition from the requirement that a canonical transformation must yield a new Hamiltonian system from an old one. It then explains some of the consequences of symplecticity and discusses examples of its applications, touching on symplectic matrices, phase space and Liouville's Theorem, Lagrange and Poisson brackets, Lie algebra, Lie operators and Lie transformations, symplectic maps and symplectic integrators.

Stability properties of a general class of nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Numerical simulation of supersonic flow using a new analytical bleed boundary condition

NASA Technical Reports Server (NTRS)

Harloff, G. J.; Smith, G. E.

1995-01-01

A new analytical bleed boundary condition is used to compute flowfields for a strong oblique shock wave/boundary layer interaction with a baseline and three bleed rates at a freestream Mach number of 2.47 with an 8 deg shock generator. The computational results are compared to experimental Pitot pressure profiles and wall static pressures through the interaction region. An algebraic turbulence model is employed for the bleed and baseline cases, and a one equation model is also used for the baseline case where the boundary layer is separated.

Algebraic Thinking through Koch Snowflake Constructions

ERIC Educational Resources Information Center

Ghosh, Jonaki B.

2016-01-01

Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

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,…