Existence of standard models of conic fibrations over non-algebraically-closed fields
Avilov, A A
2014-12-31
We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
Operator algebra in logarithmic conformal field theory
Nagi, Jasbir
2005-10-15
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the extensions of this machinery to the logarithmic case are studied and used. More precisely, from Moebius symmetry constraints, the generic three- and four-point functions of logarithmic quasiprimary fields are calculated in closed form for arbitrary Jordan rank. As an example, c=0 disordered systems with nondegenerate vacua are studied. With the aid of two-, three-, and four-point functions, the operator algebra is obtained and associativity of the algebra studied.
Explicit field realizations of W algebras
NASA Astrophysics Data System (ADS)
Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong
2009-06-01
The fact that certain nonlinear W2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W2,s algebras are presented. The results show that all these realizations are Romans-type realizations.
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki
2010-01-15
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Algebraic complexities and algebraic curves over finite fields
Chudnovsky, D. V.; Chudnovsky, G. V.
1987-01-01
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields. PMID:16593816
Magnetic translation algebra with or without magnetic field
NASA Astrophysics Data System (ADS)
Mudry, Christopher; Chamon, Claudio
2013-03-01
The magnetic translation algebra plays an important role in the quantum Hall effect. Murthy and Shankar have shown how to realize this algebra using fermionic bilinears defined on a two-dimensional square lattice. We show that, in any dimension d, it is always possible to close the magnetic translation algebra using fermionic bilinears, be it in the continuum or on the lattice. We also show that these generators are complete in even, but not odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions that conserves particle number can be represented in terms of the generators of this algebra, whether or not time-reversal symmetry is broken. As an example, we reproduce the f-sum rule of interacting electrons at vanishing magnetic field using this representation. We also show that interactions can significantly change the bare band width of lattice Hamiltonians when represented in terms of the generators of the magnetic translation algebra.
Charge transfer in algebraic quantum field theory
NASA Astrophysics Data System (ADS)
Wright, Jill Dianne
We discuss aspects of the algebraic structure of quantum field theory. We take the view that the superselection structure of a theory should be determinable from the vacuum representation of the observable algebra, and physical properties of the charge. Hence one determines the nature of the charge transfer operations: the automorphisms of the observable algebra corresponding to the movement of charge along space-time paths. New superselection sectors are obtained from the vacuum sector by an automorphism which is a limit of charge transfer operations along paths with an endpoint tending to spacelike infinity. Roberts has shown that for a gauge theory of the first kind, the charge transfer operations for a given charge form a certain kind of 1-cocycle over Minkowski space. The local 1-cohomology group of their equivalence classes corresponds to the superselection structure. The exact definition of the cohomology group depends on the properties of the charge. Using displaced Fock representations of free fields, we develop model field theories which illustrate this structure. The cohomological classification of displaced Fock representations has been elucidated by Araki. For more general representations, explicit determination of the cohomology group is a hard problem. Using our models, we can illustrate ways in which fields with reasonable physical properties depart fromthe abovementioned structure. In 1+1 dimensions, we use the Streater-Wilde model to illustrate explicitly the representation-dependence of the cohomology structure, and the direction-dependence of the limiting charge transfer operation. The cohomology structure may also be representation-dependent in higher-dimensional theories without strict localization of charge, for example the electromagnetic field. The algebraic structure of the electromagnetic field has many other special features, which we discuss in relation to the concept of charge transfer. We also give some indication of the modifications
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
Schertzer, Daniel Tchiguirinskaia, Ioulia
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Vector fields and nilpotent Lie algebras
NASA Technical Reports Server (NTRS)
Grayson, Matthew; Grossman, Robert
1987-01-01
An infinite-dimensional family of flows E is described with the property that the associated dynamical system: x(t) = E(x(t)), where x(0) is a member of the set R to the Nth power, is explicitly integrable in closed form. These flows E are of the form E = E1 + E2, where E1 and E2 are the generators of a nilpotent Lie algebra, which is either free, or satisfies some relations at a point. These flows can then be used to approximate the flows of more general types of dynamical systems.
Algebraically special Einstein-Maxwell fields
NASA Astrophysics Data System (ADS)
Van den Bergh, Norbert
2017-01-01
The Geroch-Held-Penrose formalism is used to re-analyse algebraically special non-null Einstein-Maxwell fields, aligned as well as non-aligned, in the presence of a possible non-vanishing cosmological constant. A new invariant characterization is given of the García-Plebański and Plebański-Hacyan metrics within the family of aligned solutions and of the Griffiths metrics within the family of the non-aligned solutions. As a corollary also the double alignment of the Debever-McLenaghan `class D' metrics with non-vanishing cosmological constant is shown to be equivalent with the shear-free and geodesic behavior of their Debever-Penrose vectors.
Combinatorial Hopf Algebras in Quantum Field Theory I
NASA Astrophysics Data System (ADS)
Figueroa, Héctor; Gracia-Bondía, José M.
This paper stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an elementary invitation to the subject as well. The rest of Sec. 1 is devoted to the basics of Hopf algebra theory and examples in ascending level of complexity. Section 2 turns around the all-important Faà di Bruno Hopf algebra. Section 2.1 contains a first, direct approach to it. Section 2.2 gives applications of the Faà di Bruno algebra to quantum field theory and Lagrange reversion. Section 2.3 rederives the related Connes-Moscovici algebras. In Sec. 3, we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Sec. 3.1, we describe the first. Then in Sec. 3.2, we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Sec. 3.3, general incidence algebras are introduced, and the Faà di Bruno bialgebras are described as incidence bialgebras. In Sec. 3.4, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained. The structure results for commutative Hopf algebras are found in Sec. 4. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.
Field Theoretic Investigations in Current Algebra
NASA Astrophysics Data System (ADS)
Jackiw, Roman
The following sections are included: * Introduction * Canonical and Space-Time Constraints in Current Algebra * Canonical Theory of Currents * Space-Time Constraints on Commutators * Space-Time Constraints on Green's Functions * Space-Time Constraints on Ward Identities * Schwinger Terms * Discussion * The Bjorken-Johnson-Low Limit * The π 0 → 2γ Problem * Preliminaries * Sutherland-Veltman Theorem * Model Calculation * Anomalous Ward Identity * Anomalous Commutators * Anomalous Divergence of Axial Current * Discussion * Electroproduction Sum Rules * Preliminaries * Derivation of Sum Rules, Naive Method * Derivation of Sum Rules, Dispersive Method * Model Calculation * Anomalous Commutators * Discussion * Discussion of Anomalies in Current Algebra * Miscellaneous Anomalies * Non-Perturbative Arguments for Anomalies * Models without Anomalies * Discussion * Approximate Scale Symmetry * Introduction * Canonical Theory of Scale and Conformal Transformations * Ward Identities and Trace Identities * False Theorems * True Theorems * EXERCISES * SOLUTIONS
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Abłamowicz, Rafał; Gonçalves, Icaro; Rocha, Roldão da
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Universal Algebraic Varieties and Ideals in Physics:. Field Theory on Algebraic Varieties
NASA Astrophysics Data System (ADS)
Iguchi, Kazumoto
A class of universal algebraic varieties in physics is discussed herein using the concepts of determinant ideals in algebraic geometry. It is shown that these algebraic varieties arise with very different physical contexts in many branches of physics and mathematics from high energy physics theory to chaos theory. In these physical systems the models are constructed by using the fields on usual manifolds such as vector fields in a Euclidean space and a Minkowskian space. But there is a universal mathematical aspect of linear algebra for linear vector spaces, where the linear independency and dependency are described using the Gramians of the vectors. These Gramians form a class of hypersurfaces in a higher-dimensional mathematical space: If there exist g vectors vi in an n-dimensional Euclidean space, the Gramian Gg is given as a g × g determinant Gg=Det[xij] with the inner products xij=(vi,vj), and exists in a g(g-1)/2-[g(g+1)/2-] dimensional space if the vectors are (not) normalized, xii=1 (xii ≠ 1). It is also shown that the Gramians are invariant under automorphisms of the vectors. The mathematical structure of the Gramians is revealed to be equivalent to the concepts of determinant ideals Ig(v), each element of which is a g × g determinant constructed from components of an arbitrary N×N matrix with N>n and which have inclusion relation: R=I0(v)⊃ I1(v) ⊃···⊃ Ig(v) ⊃···, and Ig(v)=0 if g>n. In the various physical systems the ideals naturally emerge to give us dynamical flows on the hypersurfaces, and therefore, it is called the field theory on algebraic varieties. This viewpoint provides us a grand viewpoint in physics and mathematics.
Algebraic structure of general electromagnetic fields and energy flow
Hacyan, Shahen
2011-08-15
Highlights: > Algebraic structure of general electromagnetic fields in stationary spacetime. > Eigenvalues and eigenvectors of the electomagnetic field tensor. > Energy-momentum in terms of eigenvectors and Killing vector. > Explicit form of reference frame with vanishing Poynting vector. > Application of formalism to Bessel beams. - Abstract: The algebraic structures of a general electromagnetic field and its energy-momentum tensor in a stationary space-time are analyzed. The explicit form of the reference frame in which the energy of the field appears at rest is obtained in terms of the eigenvectors of the electromagnetic tensor and the existing Killing vector. The case of a stationary electromagnetic field is also studied and a comparison is made with the standard short-wave approximation. The results can be applied to the general case of a structured light beams, in flat or curved spaces. Bessel beams are worked out as example.
NASA Astrophysics Data System (ADS)
Chamon, Claudio; Mudry, Christopher
2012-11-01
The magnetic translation algebra plays an important role in the quantum Hall effect. Murthy and Shankar, arXiv:1207.2133, have shown how to realize this algebra using fermionic bilinears defined on a two-dimensional square lattice. We show that, in any dimension d, it is always possible to close the magnetic translation algebra using fermionic bilinears, whether in the continuum or on the lattice. We also show that these generators are complete in even, but not odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions that conserves particle number can be represented in terms of the generators of this algebra, whether or not time-reversal symmetry is broken. As an example, we reproduce the f-sum rule of interacting electrons at vanishing magnetic field using this representation. We also show that interactions can significantly change the bare bandwidth of lattice Hamiltonians when represented in terms of the generators of the magnetic translation algebra.
Operator Algebras and Noncommutative Geometric Aspects in Conformal Field Theory
NASA Astrophysics Data System (ADS)
Longo, Roberto
2010-03-01
The Operator Algebraic approach to Conformal Field Theory has been particularly fruitful in recent years (leading for example to the classification of all local conformal nets on the circle with central charge c < 1, jointly with Y. Kawahigashi). On the other hand the Operator Algebraic viewpoint offers a natural perspective for a Noncommutative Geometric context within Conformal Field Theory. One basic point here is to uncover the relevant structures. In this talk I will explain some of the basic steps in this "Noncommutative Geometrization program" up to the recent construction of a spectral triple associated with certain Ramond representations of the Supersymmetric Virasoro net. So Alain Connes framework enters into play. This is a joint work with S. Carpi, Y. Kawahigashi, and R. Hillier.
Noncommutative Common Cause Principles in algebraic quantum field theory
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{sub 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.
Free-field realisations of the BMS3 algebra and its extensions
NASA Astrophysics Data System (ADS)
Banerjee, Nabamita; Jatkar, Dileep P.; Mukhi, Sunil; Neogi, Turmoli
2016-06-01
We construct an explicit realisation of the BMS3 algebra with nonzero central charges using holomorphic free fields. This can be extended by the addition of chiral matter to a realisation having arbitrary values for the two independent central charges. Via the introduction of additional free fields, we extend our construction to the minimally supersymmetric BMS3 algebra and to the nonlinear higher-spin BMS3-W3 algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS3 via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio
2017-02-01
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of "spacelike linearity". Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.
NASA Astrophysics Data System (ADS)
Krylyuk, Ya S.
1985-02-01
The maximal dimension is computed for irreducible representations of the Hamiltonian Lie p-algebra and the special Lie p-algebra of an even number of variables over an algebraically closed field of characteristic p>3.Bibliography: 11 titles.
Linear algebraic theory of partial coherence: continuous fields and measures of partial coherence.
Ozaktas, Haldun M; Gulcu, Talha Cihad; Alper Kutay, M
2016-11-01
This work presents a linear algebraic theory of partial coherence for optical fields of continuous variables. This approach facilitates use of linear algebraic techniques and makes it possible to precisely define the concepts of incoherence and coherence in a mathematical way. We have proposed five scalar measures for the degree of partial coherence. These measures are zero for incoherent fields, unity for fully coherent fields, and between zero and one for partially coherent fields.
Integrand Reduction Reloaded: Algebraic Geometry and Finite Fields
NASA Astrophysics Data System (ADS)
Sameshima, Ray D.; Ferroglia, Andrea; Ossola, Giovanni
2017-01-01
The evaluation of scattering amplitudes in quantum field theory allows us to compare the phenomenological prediction of particle theory with the measurement at collider experiments. The study of scattering amplitudes, in terms of their symmetries and analytic properties, provides a theoretical framework to develop techniques and efficient algorithms for the evaluation of physical cross sections and differential distributions. Tree-level calculations have been known for a long time. Loop amplitudes, which are needed to reduce the theoretical uncertainty, are more challenging since they involve a large number of Feynman diagrams, expressed as integrals of rational functions. At one-loop, the problem has been solved thanks to the combined effect of integrand reduction, such as the OPP method, and unitarity. However, plenty of work is still needed at higher orders, starting with the two-loop case. Recently, integrand reduction has been revisited using algebraic geometry. In this presentation, we review the salient features of integrand reduction for dimensionally regulated Feynman integrals, and describe an interesting technique for their reduction based on multivariate polynomial division. We also show a novel approach to improve its efficiency by introducing finite fields. Supported in part by the National Science Foundation under Grant PHY-1417354.
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.
2015-11-15
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Quantum field theory on toroidal topology: Algebraic structure and applications
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
2014-05-01
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RD-d is developed from a Lie-group representation and c*c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real- and imaginary-time versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on
Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.
Ozaktas, Haldun M; Yüksel, Serdar; Kutay, M Alper
2002-08-01
A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.
Closed-field capacitive liquid level sensor
Kronberg, James W.
1998-01-01
A liquid level sensor based on a closed field circuit comprises a ring oscillator using a symmetrical array of plate units that creates a displacement current. The displacement current varies as a function of the proximity of a liquid to the plate units. The ring oscillator circuit produces an output signal with a frequency inversely proportional to the presence of a liquid. A continuous liquid level sensing device and a two point sensing device are both proposed sensing arrangements. A second set of plates may be located inside of the probe housing relative to the sensing plate units. The second set of plates prevent any interference between the sensing plate units.
Closed-field capacitive liquid level sensor
Kronberg, J.W.
1998-03-03
A liquid level sensor based on a closed field circuit comprises a ring oscillator using a symmetrical array of plate units that creates a displacement current. The displacement current varies as a function of the proximity of a liquid to the plate units. The ring oscillator circuit produces an output signal with a frequency inversely proportional to the presence of a liquid. A continuous liquid level sensing device and a two point sensing device are both proposed sensing arrangements. A second set of plates may be located inside of the probe housing relative to the sensing plate units. The second set of plates prevent any interference between the sensing plate units. 12 figs.
Closed-field capacitive liquid level sensor
Kronberg, J.W.
1995-01-01
A liquid level sensor based on a closed field circuit comprises a ring oscillator using a symmetrical array of plate units that creates a displacement current. The displacement current varies as a function of the proximity of a liquid to the plate units. The ring oscillator circuit produces an output signal with a frequency inversely proportional to the presence of a liquid. A continuous liquid level sensing device and a two point sensing device are both proposed sensing arrangements. A second set of plates may be located inside of the probe housing relative to the sensing plate units. The second set of plates prevent any interference between the sensing plate units.
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-11-01
Recently it has been introduced an algorithm for the Baker-Campbell-Hausdorff (BCH) formula, which extends the Van-Brunt and Visser recent results, leading to new closed forms of BCH formula. More recently, it has been shown that there are 13 types of such commutator algebras. We show, by providing the explicit solutions, that these include the generators of the semisimple complex Lie algebras. More precisely, for any pair, X, Y of the Cartan-Weyl basis, we find W, linear combination of X, Y, such that exp (X) exp (Y)=exp (W). The derivation of such closed forms follows, in part, by using the above mentioned recent results. The complete derivation is provided by considering the structure of the root system. Furthermore, if X, Y, and Z are three generators of the Cartan-Weyl basis, we find, for a wide class of cases, W, a linear combination of X, Y and Z, such that exp (X) exp (Y) exp (Z)=exp (W). It turns out that the relevant commutator algebras are type 1c-i, type 4 and type 5. A key result concerns an iterative application of the algorithm leading to relevant extensions of the cases admitting closed forms of the BCH formula. Here we provide the main steps of such an iteration that will be developed in a forthcoming paper.
C*-algebraic scattering theory and explicitly solvable quantum field theories
NASA Astrophysics Data System (ADS)
Warchall, Henry A.
1985-06-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.
Galvao, C.A.; Nutku, Y.
1996-12-01
mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}
Algebraic Characterization of the Vacuum in Light-Front Field Theory
NASA Astrophysics Data System (ADS)
Herrmann, Marc; Polyzou, Wayne
2016-03-01
In the light-front formulation of quantum field theory, the vacuum vector of an interacting field theory has a relatively simple relationship to the vacuum of a free field theory. This is a benefit over the usual equal-time formulation where the interacting vacuum vector has infinite norm with respect to the Hilbert space of the free field theory. By describing the vacuum as a positive linear functional on an operator algebra constructed from free fields with two distinct masses, it can be demonstrated that the complications associated with adding dynamics to the vacuum of a free theory are not present in the construction of the light-front vacuum. Instead, the complications are moved into defining a subalgebra of the light-front algebra which corresponds to the physically relevant algebra of local fields. These results can then be applied to interacting fields by first describing them in terms of asymptotic in or out fields. However, in order to treat local operators products, the vacuum functional may need to be modified to include states with zero eigenvalue of the generator of translations in the direction along the light front, x- =1/√(2) >x0-x3. This work supported by DOE contract No. DE-FG02-86ER40286.
Close Air Support for the Field Army
1964-05-25
90. 76 of the 12th Air Support C omand , for consideration.4 From D plus 4 to D plus 7, requests for attacks on tar,:ets of’ opportunity were not...ibid. 3 8 Ibid. 9o evolved into the "Rover Joe" svstem of close air suooort. Rover Joe was based to an extent on the "Rover David " orinciple used in...tentacles (air sunport oart-4, air sunoort control, and rear links (liaison officer at iir force airfields). Rover David vas intended to be located
Take a Field Trip Close to Home.
ERIC Educational Resources Information Center
Wood, Jacalyn K.
1986-01-01
Describes a simple field trip taken by fourth-grade students to a local park. Aided by volunteers, students go through four learning stations dealing with rock studies, tree identification, following directions (mapping), and observation skills. Presite and postsite activities are discussed. (TW)
Chang, P
2004-09-15
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders.
Does there exist a sensible quantum theory of an ``algebra-valued'' scalar field\\?
NASA Astrophysics Data System (ADS)
Anco, Stephen C.; Wald, Robert M.
1989-04-01
Consider a scalar field φ in Minkowski spacetime, but let φ be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincaré group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a λφ4 field, with φ valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v2=0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincaré group, is evaded here because the finite ``extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail. Thus, although the classical theory is perfectly well behaved, it seems that there does not exist a sensible quantum theory of an algebra-valued scalar field.
ERIC Educational Resources Information Center
Khatri, Daryao
2011-01-01
Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This…
NASA Astrophysics Data System (ADS)
Connes, Alain; Kreimer, Dirk
This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop
Does there exist a sensible quantum theory of an ''algebra-valued'' scalar field
Anco, S.C.; Wald, R.M.
1989-04-15
Consider a scalar field phi in Minkowski spacetime, but let phi be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincare group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a lambdaphi/sup 4/ field, with phi valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v/sup 2/ = 0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincare group, is evaded here because the finite ''extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quasi-closed orbit in a harmonically perturbed magnetic field
Stupakov, G.V. )
1992-11-01
The paper generalizes a notion of the closed orbit for the case when the accelertor lattice is perturbed by a time-dependent harmonic dipole field. The problem is motivated by effects of current ripple in a proton accelerator. Our result allows to estimate the amplitude of the beam excursions as a function of the amplitude and the frequency of the perturbation. It predicts that the deviation of the beam increases as the frequency of the ripple approaches the sideband betatron frequency.
ERIC Educational Resources Information Center
Bal, Ayten Pinar
2016-01-01
Problem Statement: Algebra, which is one of the basic principles of mathematical learning, still maintains its importance in mathematics programmes. However, especially starting from the primary school years, algebra represents a complex mathematical factor in the operational stage for many students. In this scope, a differentiated teaching…
Spinor Field Realizations of Non-critical W2,4 String Based on Linear W1,2,4 Algebra
NASA Astrophysics Data System (ADS)
Zhang, Li-Jie; Liu, Yu-Xiao
2006-10-01
In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical W2,4 string were built with these realizations.
The electric field close to an undulating interface
NASA Astrophysics Data System (ADS)
Kallunki, Jouni; Alava, Mikko; Hellén, E. K. O.
2006-07-01
The electric potential close to a boundary between two dielectric material layers reflects the geometry of such an interface. The local variations arise from the combination of material parameters and from the nature of the inhomogeneity. Here, the arising electric field is considered for both a sinusoidally varying boundary and for a "rough," Gaussian test case. We discuss the applicability of a one-dimensional model with the varying layer thickness as a parameter and the generic scaling of the results. As an application we consider the effect of paper roughness on toner transfer in electrophotographic printing.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines
NASA Technical Reports Server (NTRS)
Lau, Yun-Tung; Finn, John M.
1990-01-01
The present investigation of three-dimensional reconnection of magnetic fields with nulls and of fields with closed lines gives attention to the geometry of the former, with a view to their gamma-line and Sigma-surface structures. The geometric structures of configurations with a pair of type A and B nulls permit reconnection across the null-null lines; these are the field lines which join the two nulls. Also noted is the case of magnetostatic reconnection, in which the magnetic field is time-independent and the electrostatic potential is constant along field lines.
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields
NASA Astrophysics Data System (ADS)
Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs
2015-12-01
We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.
Dynamics of the Open Closed Field Line Boundary
NASA Astrophysics Data System (ADS)
Spanswick, E.; Roy, E.; Nishimura, T.; Unick, C.; Jackel, B. J.; Donovan, E.
2015-12-01
In most cases, large-scale features of the auroral distribution are the projection, along magnetic field lines, of corresponding magnetospheric features. The poleward boundary of the oval is a key example of such a feature. At almost all local times, this is most often interpreted as the ionospheric marker of the latitudinal transition between open lobe and closed central plasma sheet field lines. Earlier work by Blanchard et al. [J. Geophys. Res., 1995 & 1997] used ground-based photometric observations of 630 nm "redline" aurora and in situ particle observations from simultaneous DMSP overflights to demonstrate that the poleward boundary of the redline aurora is a particularly robust signature of the poleward boundary of the plasma sheet. Owing to the orbits of the DMSP spacecraft and the relative newness of the photometer program (CANOPUS) that provided the optical observations, the Blanchard results represent a limited sampling of magnetic local time and a limited number of events. In this paper we revisit the Blanchard et al study, using particle data from the NASA FAST satellite and the DMSP program, together with redline observations obtained by ground-based All-Sky Imagers. Our results indicate that the Blanchard technique for identifying the polar cap boundary holds true for essentially all magnetic local times on the night side, but that the picture is more nuanced than previously appreciated. Here we present these results, and discuss specific examples where the technique does not work (and explore why). Furthermore, this work is motivated by a new extensive network of highly sensitive redline imagers that has been deployed across northern and central Canada which provides high time resolution large-scale snapshots of the instantaneous polar cap boundary. This in turn enables us to explore magnetospheric dynamics at the interface between the lobe and central plasma sheet in fundamentally new and exciting ways.
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
Abdalla, M. Sebawe; Elkasapy, A.I.
2010-08-15
In this paper we consider the problem of a charged harmonic oscillator under the influence of a constant magnetic field. The system is assumed to be isotropic and the magnetic field is applied along the z-axis. The canonical transformation is invoked to remove the interaction term and the system is reduced to a model containing the second harmonic generation. Two classes of the real and complex quadratic invariants (constants of motion) are obtained. We have employed the Lie algebraic technique to find the most general solution for the wave function for both real and complex invariants. Some discussions related to the advantage of using the quadratic invariants to solve the Cauchy problem instead of the direct use of the Hamiltonian itself are also given.
The motion of closed hypersurfaces in the central force fields
NASA Astrophysics Data System (ADS)
Yan, Weiping
2016-08-01
This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. Physically, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by Schnürer and Smoczyk [20]. To study its motion, we introduce a quasi-linear degenerate hyperbolic equation which describes the motion of the surfaces extrinsically. Our main results show the large time existence of such Cauchy problem and the stability with respect to small initial data. When the radially symmetric potential function v ≡ 1, the local existence and stability results have been obtained by Notz [18]. The proof is based on a new Nash-Moser iteration scheme.
Bicovariant quantum algebras and quantum Lie algebras
NASA Astrophysics Data System (ADS)
Schupp, Peter; Watts, Paul; Zumino, Bruno
1993-10-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).
Jordan Algebraic Quantum Categories
NASA Astrophysics Data System (ADS)
Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander
2015-03-01
State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.
78 FR 24765 - Notice of Intent To Close 16 Field Offices
Federal Register 2010, 2011, 2012, 2013, 2014
2013-04-26
... URBAN DEVELOPMENT Notice of Intent To Close 16 Field Offices AGENCY: Office of Field Policy and Management, HUD. ACTION: Notice. SUMMARY: This notice advises the public that HUD intends to close the.... 3535. FOR FURTHER INFORMATION CONTACT: Honor Garcia-Tomchick, Department of Housing and...
Central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, M.; Sheinman, O. K.
2008-08-01
Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K. . Inst. for Theoretical Physics); Sevrin, A. ); van Nieuwenhuizen, P. . Theory Div.)
1991-11-01
In this contribution to Tini Veltman's Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields ( the metric') are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K.; Sevrin, A.; van Nieuwenhuizen, P.
1991-11-01
In this contribution to Tini Veltman`s Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields (`the metric`) are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
An approach to 3D magnetic field calculation using numerical and differential algebra methods
Caspi, S.; Helm, M.; Laslett, L.J.; Brady, V.O.
1992-07-17
Motivated by the need for new means for specification and determination of 3D fields that are produced by electromagnetic lens elements in the region interior to coil windings and seeking to obtain techniques that will be convenient for accurate conductor placement and dynamical study of particle motion, we have conveniently gene the representation of a 2D magnetic field to 3D. We have shown that the 3 dimensioal magnetic field components of a multipole magnet in the curl-fire divergence-fire region near the axis r=0 can be derived from one dimensional functions A{sub n}(z) and their derivatives (part 1). In the region interior to coil windings of accelerator magnets the three spatial components of magnet fields can be expressed in terms of harmonic components'' proportional to functions sin (n{theta}) or cos (n{theta}) of the azimuthal angle. The r,z dependence of any such component can then be expressed in terms of powers of r times functions A{sub n}(z) and their derivatives. For twodimensional configurations B{sub z} of course is identically zero, the derivatives of A{sub n}(z) vanish, and the harmonic components of the transverse field then acquire a simple proportionality B{sub r,n} {proportional to} r{sup n-1} sin (n{theta}),B{sub {theta},n} {proportional to} r{sup n-1} cos (n{theta}), whereas in a 3-D configuration the more complex nature of the field gives rise to additional so-called psuedomultipole'' components as judged by additional powers of r required in the development of the field. Computation of the 3-D magnetic field arising at a sequence of field points, as a direct result of a specified current configuration or coil geometry, can be calculated explicitly through use of the Biot-Savart law and from such data the coefficients can then be derived for a general development of the type indicated above. We indicate, discuss, and illustrate two means by which this development may be performed.
Noncommutative via closed star product
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.; Vitale, P.
2015-08-01
We consider linear star products on of Lie algebra type. First we derive the closed formula for the polydifferential representation of the corresponding Lie algebra generators. Using this representation we define the Weyl star product on the dual of the Lie algebra. Then we construct a gauge operator relating the Weyl star product with the one which is closed with respect to some trace functional, Tr ( f ⋆ g) = Tr ( f · g). We introduce the derivative operator on the algebra of the closed star product and show that the corresponding Leibniz rule holds true up to a total derivative. As a particular example we study the space R {/θ 3} with type noncommutativity and show that in this case the closed star product is the one obtained from the Duflo quantization map. As a result a Laplacian can be defined such that its commutative limit reproduces the ordinary commutative one. The deformed Leibniz rule is applied to scalar field theory to derive conservation laws and the corresponding noncommutative currents.
SOME DUALITY THEOREMS FOR CYCLOTOMIC \\Gamma-EXTENSIONS OF ALGEBRAIC NUMBER FIELDS OF CM TYPE
NASA Astrophysics Data System (ADS)
Kuz'min, L. V.
1980-06-01
For an odd prime l and a cyclotomic \\Gamma{-}l-extension k_\\infty/k of a field k of CM type, a compact periodic \\Gamma-module A_l(k), analogous to the Tate module of a function field, is defined. The analog of the Weil scalar product is constructed on the module A_l(k). The properties of this scalar product are examined, and certain other duality relations are determined on A_l(k). It is proved that, in a finite l-extension k'/k of CM type, the \\mathbf{Z}_l-ranks of A_l(k) and A_l(k') are connected by a relation similar to the Hurwitz formula for the genus of a curve.Bibliography: 7 titles.
NASA Astrophysics Data System (ADS)
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
None, None
2015-09-28
Coulomb interaction between charged particles inside a bunch is one of the most importance collective effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast Electron Microscope (UEM) development currently underway at Michigan State University. In addition, space charge effects are the key limiting factor in the development of ultrafast atomic resolution electron imaging and diffraction technologies and are also correlated with an irreversible growth in rms beam emittance due to fluctuating components of the nonlinear electron dynamics. In the short pulse regime used in the UEM, space charge effects also lead to virtual cathode formation in which the negative charge of the electrons emitted at earlier times, combined with the attractive surface field, hinders further emission of particles and causes a degradation of the pulse properties. Space charge and virtual cathode effects and their remediation are core issues for the development of the next generation of high-brightness UEMs. Since the analytical models are only applicable for special cases, numerical simulations, in addition to experiments, are usually necessary to accurately understand the space charge effect. In this paper we will introduce a grid-free differential algebra based multiple level fast multipole algorithm, which calculates the 3D space charge field for n charged particles in arbitrary distribution with an efficiency of O(n), and the implementation of the algorithm to a simulation code for space charge dominated photoemission processes.
None, None
2015-09-28
Coulomb interaction between charged particles inside a bunch is one of the most importance collective effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast Electron Microscope (UEM) development currently underway at Michigan State University. In addition, space charge effects are the key limiting factor in the development of ultrafast atomic resolution electron imaging and diffraction technologies and are also correlated with an irreversible growth in rms beam emittance due to fluctuating components of the nonlinear electron dynamics.more » In the short pulse regime used in the UEM, space charge effects also lead to virtual cathode formation in which the negative charge of the electrons emitted at earlier times, combined with the attractive surface field, hinders further emission of particles and causes a degradation of the pulse properties. Space charge and virtual cathode effects and their remediation are core issues for the development of the next generation of high-brightness UEMs. Since the analytical models are only applicable for special cases, numerical simulations, in addition to experiments, are usually necessary to accurately understand the space charge effect. In this paper we will introduce a grid-free differential algebra based multiple level fast multipole algorithm, which calculates the 3D space charge field for n charged particles in arbitrary distribution with an efficiency of O(n), and the implementation of the algorithm to a simulation code for space charge dominated photoemission processes.« less
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio
2017-01-01
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of "spacelike linearity". Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.
Twining characters and orbit Lie algebras
Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph
1996-12-05
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.
Closed String S-matrix Elements in Open String Field Theory
NASA Astrophysics Data System (ADS)
Garousi, Mohammad R.; Maktabdaran, G. R.
2005-03-01
We study the S-matrix elements of the gauge invariant operators corresponding to on-shell closed strings, in open string field theory. In particular, we calculate the tree level S-matrix element of two arbitrary closed strings, and the S-matrix element of one closed string and two open strings. By mapping the world-sheet of these amplitudes to the upper half z-plane, and by evaluating explicitly the correlators in the ghost part, we show that these S-matrix elements are exactly identical to the corresponding disk level S-matrix elements in perturbative string theory.
NASA Technical Reports Server (NTRS)
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
Prediction and identification of the magnetic field close to electric machines
NASA Astrophysics Data System (ADS)
Papadopoulos, Peter J.; Ioannides, Maria G.
1999-04-01
The magnetic field around an electric machine operating at full load is predicted numerically and identified experimentally. A precise model of a three-phase induction machine is constructed considering the machine geometry, the windings and the stator and rotor materials. The field distribution close to the machine is determined using the discrete element technique, and actual measurements are carried out for identification purposes. An approximate human model is constructed and the magnetic field inside the human body is computed for a distance of 1 and 5 m from the machine. The magnetic field density is determined at specific points, and the induced current densities are computed.
Translocation of closed polymers through a nanopore under an applied external field
NASA Astrophysics Data System (ADS)
Jiang, Shao-Chuan; Zhang, Lin-Xi; Xia, A.-Gen; Chen, Hong-Ping; Cheng, Jun
2010-01-01
The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ simeq Nα, with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τp and follows a falling exponential function for duration time τ > τp. For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.
NASA Astrophysics Data System (ADS)
Mikhalev, A. V.; Pinchuk, I. A.
2005-06-01
The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.
McComas, D.J.
1994-06-01
For years the field of Space Physics has had a problem, a really big problem for it occurs on the largest spatial scales in Space physics -- across the entire region under the Sun`s influence, the heliosphere. The problem is that the Sun appears to keep opening new magnetic flux into interplanetary space with no obvious way for this flux to close back off again. This state of affairs, without some previously unknown method for closing the open interplanetary magnetic field (IMF), leads to an ever growing amount of magnetic flux in interplanetary space: the magnetic flux catastrophe. Recently, considerable progress has been made in understanding why this catastrophic state is not the observed state of the heliosphere. This brief article paints the newly emerging picture of the opening and closing of the IMF and how these processes may account for the observed variation in the amount of magnetic flux in interplanetary space over the solar cycle.
NASA Astrophysics Data System (ADS)
Cherney, David Matthew
We present a formalism for constructing gauge theories from any representation of a Jacobi (super)algebra. Such representations appear in physics, for example, as the worldline symmetry algebra of (generalized) spinning particle models. We obtain gauge theories of symmetric, antisymmetric, and mixed symmetry tensor fields by applying our formalism to such models in flat space. This provides a unifying and generalizing framework for p-form electromagnetism and the symmetric tensor theory of Curtright and Fronsdal. As another application of the formalism, we presented a quantization of a minisuperspace model of N = 2 supergravity black holes. The quantum spectrum amounts to the cohomology of a certain (purely geometric complex) based on the quaternionic Kahler black hole moduli space. This highly non-trivial construction, relating generalized spinning particles, quantum black holes, and special geometry, is obtained by utilizing the BV formalism for imposing a higher rank first class algebra of constraints; the geometric cohomology is that of the BRST operator. We observe that the constraint algebra becomes rank one in a limit corresponding to hyper-Kahler geometry, and this suggests application of our formalism to generalized spinning particles on arbitrarily curved Kahler and hyper-Kahler manifolds. The former leads us to a theory of (p, q)-form Kahler electromagnetism, while the latter leads to novel gauge theories of "half forms" (antisymmetric tensor products of sections of a rank 2n bundle over a dimension 4n manifold) and "double half forms" (tensor products of half forms with symmetric tensor products of sections of a rank 2 bundle). In the quaternionic-Kahler case, the black hole quantum spectrum is identified finally as the space of double half forms satisfying an equation of motion, generalizing that of p-form electromagnetism and Fronsdal theory, modulo gauge and gauge for gauge symmetries.
On the third cohomology of algebraic groups of rank two in positive characteristic
Dzhumadil'daev, A S; Ibraev, Sh Sh
2014-03-31
We evaluate the third cohomology of simple simply connected algebraic groups of rank 2 over an algebraically closed field of positive characteristic with coefficients in simple modules. It is assumed that the characteristic p of the field is greater than 3 for SL{sub 3}, greater than 5 for Sp{sub 4}, and greater than 11 for G{sub 2}. It follows from the main result that the dimensions of the cohomology spaces do not exceed the rank of the algebraic group in question. To prove the main results we study the properties of the first-quadrant Lyndon-Hochschild-Serre spectral sequence with respect to an infinitesimal subgroup, namely, the Frobenius kernel of the given algebraic group. Bibliography: 49 titles.
Direct observation of closed-loop ferrohydrodynamic pumping under traveling magnetic fields
NASA Astrophysics Data System (ADS)
Mao, Leidong; Elborai, Shihab; He, Xiaowei; Zahn, Markus; Koser, Hur
2011-09-01
Ferrofluid-based liquid manipulation schemes typically actuate an immiscible liquid via a ferrofluid plug, using high magnetic flux (˜1 T) densities and strong field gradients created with bulky permanent magnets. They rely on surface tension effects to maintain the cohesion of the ferrofluid plug, necessitating miniature channels and slow (˜1 μl/min) flow speeds. Here, we demonstrate direct ferrohydrodynamic pumping using traveling magnetic fields at controllable speeds in a simple, closed-loop geometry without any mechanically actuated components. The pumping approach is compact, scalable, and practical. Using moderate field amplitudes (˜10 mT), we obtained a maximum volumetric flow rate of 0.69 ml/s using a readily available commercial ferrofluid. Our closed-loop pumping approach could lead to integrated and efficient liquid manipulation and cooling schemes based on ferrofluids.
NASA Technical Reports Server (NTRS)
Birn, J.; Hones, E. W., Jr.; Craven, J. D.; Frank, L. A.; Elphinstone, R. D.; Stern, D. P.
1991-01-01
The boundary between open and closed field lines is investigated in the empirical Tsyganenko (1987) magnetic field model. All field lines extending to distances beyond -70 R(E), the tailward velocity limit of the Tsyganenko model are defined as open, while all other field lines, which cross the equatorial plane earthward of -70 R(E) and are connected with the earth at both ends, are assumed closed. It is found that this boundary at the surface of the earth, identified as the polar cap boundary, can exhibit the arrowhead shape, pointed toward the sun, which is found in horse collar auroras. For increasing activity levels, the polar cap increases in area and becomes rounder, so that the arrowhead shape is less pronounced. The presence of a net B(y) component can also lead to considerable rounding of the open flux region. The arrowhead shape is found to be closely associated with the increase of B(z) from the midnight region to the flanks of the tail, consistent with a similar increase of the plasma sheet thickness.
ERIC Educational Resources Information Center
Capani, Antonio; De Dominicis, Gabriel
This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…
Birn, J.; Hones, E.W. Jr. ); Craven, J.D.; Frank, L.A. ); Elphinstone, R.D. ); Stern, D.P. )
1991-03-01
Using the empirical Tsyganenko (1987) long model as a prime example of a megnetospheric field model, the authors have attempted to identify the boundary between open and closed field lines. They define as closed all field lines that are connested with the Earth at both ends and cross the equatorial plane earthward of x = {minus}70 R{sub E}, the tailward validity limit of the Tsyganenko model. They find that the form of the open/closed boundary at the Earth's surface, identified with the polar cap boundary, can exhibit the arrowhead shape, pointed toward the Sun, observed in horse collar auroras (Hones et al., 1989). The polar cap size in the Tsyganenko model increases with increasing K{sub p} values, and it becomes rounder and less pointed. The superposition of a net B{sub y} field, which is the expected consequence of an IMF B{sub y}, rotates the polar cap pattern and, for larger values, degrades the arrowhead shape, resulting in polar cap configurations consistent with known asymmetries in the aurora. The pointedness of the polar cap shape also diminishes or even completely disappears if the low-latitude magnetopause is assumed open and located considerably inside of the outermost magnetic flux surface in the Tsyganenko model. The arrowhead shape of the polar cap is found to be associated with a strong increase of B{sub z} from midnight toward the tail flanks, which is observed independently, and is possibly related to the NBZ field-aligned current system, observed during quiet times and strongly northward IMF B{sub z}. The larger B{sub z} values near the flanks of the tail cause more magnetic flux to close through these regions than through the midnight equatorial region.
Array algebra estimation in signal processing
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.
Observations of the Ion Signatures of Double Merging and the Formation of Newly Closed Field Lines
NASA Technical Reports Server (NTRS)
Chandler, Michael O.; Avanov, Levon A.; Craven, Paul D.
2007-01-01
Observations from the Polar spacecraft, taken during a period of northward interplanetary magnetic field (IMF) show magnetosheath ions within the magnetosphere with velocity distributions resulting from multiple merging sites along the same field line. The observations from the TIDE instrument show two separate ion energy-time dispersions that are attributed to two widely separated (-20Re) merging sites. Estimates of the initial merging times show that they occurred nearly simultaneously (within 5 minutes.) Along with these populations, cold, ionospheric ions were observed counterstreaming along the field lines. The presence of such ions is evidence that these field lines are connected to the ionosphere on both ends. These results are consistent with the hypothesis that double merging can produce closed field lines populated by solar wind plasma. While the merging sites cannot be unambiguously located, the observations and analyses favor one site poleward of the northern cusp and a second site at low latitudes.
Quantum field theory in spaces with closed time-like curves
NASA Astrophysics Data System (ADS)
Boulware, D. G.
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Dynamic effects of restoring footpoint symmetry on closed magnetic field lines
NASA Astrophysics Data System (ADS)
Reistad, J. P.; Østgaard, N.; Tenfjord, P.; Laundal, K. M.; Snekvik, K.; Haaland, S.; Milan, S. E.; Oksavik, K.; Frey, H. U.; Grocott, A.
2016-05-01
Here we present an event where simultaneous global imaging of the aurora from both hemispheres reveals a large longitudinal shift of the nightside aurora of about 3 h, being the largest relative shift reported on from conjugate auroral imaging. This is interpreted as evidence of closed field lines having very asymmetric footpoints associated with the persistent positive y component of the interplanetary magnetic field before and during the event. At the same time, the Super Dual Auroral Radar Network observes the ionospheric nightside convection throat region in both hemispheres. The radar data indicate faster convection toward the dayside in the dusk cell in the Southern Hemisphere compared to its conjugate region. We interpret this as a signature of a process acting to restore symmetry of the displaced closed magnetic field lines resulting in flux tubes moving faster along the banana cell than the conjugate orange cell. The event is analyzed with emphasis on Birkeland currents (BC) associated with this restoring process, as recently described by Tenfjord et al. (2015). Using data from the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) during the same conditions as the presented event, the large-scale BC pattern associated with the event is presented. It shows the expected influence of the process of restoring symmetry on BCs. We therefore suggest that these observations should be recognized as being a result of the dynamic effects of restoring footpoint symmetry on closed field lines in the nightside.
Yoshinaga, T.; Uchida, M.; Tanaka, H.; Maekawa, T.
2006-03-31
Spontaneous current jump resulting in the formation of closed field equilibrium has been observed in electron-cyclotron-heated toroidal plasmas under steady external fields composed of a toroidal field and a relatively weak vertical field in the low aspect ratio torus experiment device. This bridges the gap between the open field equilibrium maintained by a pressure-driven current in the external field and the closed field equilibrium at a larger current. Experimental results and theoretical analyses suggest a current jump model that is based on the asymmetric electron confinement along the field line appearing upon simultaneous transitions of field topology and equilibrium.
Field flatness tuning of TM110 mode cavities with closely spaced modes
Leo Bellantoni et al.
2003-10-31
Superconducting cavities for the CKM RF separated kaon beamline at Fermilab have modes that are closely spaced compared to the resonance bandwidths when warm, and this complicates the field flatness (warm) tuning process. Additionally, it is necessary to maintain the azimuthal orientation of the mode during the tuning deformations. the authors present two analytic techniques to warm-tune cavities with overlapping modes, a finite-element analysis of the tuning process, the design of a warm tuner which maintains mode polarization, and the results of tuning a cavity in which initial manufacturing variations caused the desired {pi} and nearby {pi}-1 modes to be indistinguishable before field flatness tuning.
NASA Astrophysics Data System (ADS)
Abd El-Wahab, N. H.; Abdel Rady, A. S.; Osman, Abdel-Nasser A.; Salah, Ahmed
2015-10-01
In this paper, a model is introduced to investigate the interaction between a three-level atom and one-mode of the radiation field. The atomic motion and the classical homogenous gravitational field are taken into consideration. For this purpose, we first introduce a set of new atomic operators obeying an su(3) algebraic structure to derive an effective Hamiltonian for the system under consideration. By solving the Schrödinger equation in the interaction picture, the exact solution is given when the atom and the field are initially prepared in excited state and coherent state, respectively. The influences of the gravity parameter on the collapses-revivals phenomena, the atomic momentum diffusion, the Mandel Q-parameter, the normal squeezing phenomena and the coherent properties for the considered system are examined. It is found that the gravity parameter has important effects on the properties of these phenomena.
Recursion and feedback in image algebra
NASA Astrophysics Data System (ADS)
Ritter, Gerhard X.; Davidson, Jennifer L.
1991-04-01
Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.
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.
NASA Astrophysics Data System (ADS)
Lupyan, Dmitry; Abramov, Yuriy A.; Sherman, Woody
2012-11-01
The Cambridge Structural Database (CSD) offers an excellent data source to study small molecule conformations and molecular interactions. We have analyzed 130 small molecules from the CSD containing an intramolecular sulfur-oxygen distance less than the sum of their van der Waals (vdW) radii. Close S···O distances are observed in several important medicinal chemistry motifs (e.g. a carbonyl oxygen connected by a carbon or nitrogen linker to a sulfur) and are not treated well with existing parameters in the MMFFs or OPLS_2005 force fields, resulting in suboptimal geometries and energetics. In this work, we develop modified parameters for the OPLS_2005 force field to better treat this specific interaction in order to generate conformations close to those found in the CSD structures. We use a combination of refitting a force field torsional parameter, adding a specific atom pair vdW term, and attenuating the electrostatic interactions to obtain an improvement in the accuracy of geometry minimizations and conformational searches for these molecules. Specifically, in a conformational search 58 % of the cases produced a conformation less than 0.25 Å from the CSD crystal conformation with the modified OPLS force field parameters developed in this work. In contrast, 25 and 37 % produced a conformation less than 0.25 Å with the MMFFs and OPLS_2005 force fields, respectively. As an application of the new parameters, we generated conformations for the tyrosine kinase inhibitor axitinib (trade name Inlyta) that could be correctly repacked into three observed polymorphic structures, which was not possible with conformations generated using MMFFs or OPLS_2005. The improved parameters can be mapped directly onto physical characteristics of the systems that are treated inadequately with the molecular mechanics force fields used in this study and potentially other force fields as well.
Lupyan, Dmitry; Abramov, Yuriy A; Sherman, Woody
2012-11-01
The Cambridge Structural Database (CSD) offers an excellent data source to study small molecule conformations and molecular interactions. We have analyzed 130 small molecules from the CSD containing an intramolecular sulfur-oxygen distance less than the sum of their van der Waals (vdW) radii. Close S···O distances are observed in several important medicinal chemistry motifs (e.g. a carbonyl oxygen connected by a carbon or nitrogen linker to a sulfur) and are not treated well with existing parameters in the MMFFs or OPLS_2005 force fields, resulting in suboptimal geometries and energetics. In this work, we develop modified parameters for the OPLS_2005 force field to better treat this specific interaction in order to generate conformations close to those found in the CSD structures. We use a combination of refitting a force field torsional parameter, adding a specific atom pair vdW term, and attenuating the electrostatic interactions to obtain an improvement in the accuracy of geometry minimizations and conformational searches for these molecules. Specifically, in a conformational search 58 % of the cases produced a conformation less than 0.25 Å from the CSD crystal conformation with the modified OPLS force field parameters developed in this work. In contrast, 25 and 37 % produced a conformation less than 0.25 Å with the MMFFs and OPLS_2005 force fields, respectively. As an application of the new parameters, we generated conformations for the tyrosine kinase inhibitor axitinib (trade name Inlyta) that could be correctly repacked into three observed polymorphic structures, which was not possible with conformations generated using MMFFs or OPLS_2005. The improved parameters can be mapped directly onto physical characteristics of the systems that are treated inadequately with the molecular mechanics force fields used in this study and potentially other force fields as well.
Harbach, Philipp H P; Wormit, Michael; Dreuw, Andreas
2014-08-14
The implementation of an efficient program of the algebraic diagrammatic construction method for the polarisation propagator in third-order perturbation theory (ADC(3)) for the computation of excited states is reported. The accuracies of ADC(2) and ADC(3) schemes have been investigated with respect to Thiel's recently established benchmark set for excitation energies and oscillator strengths. The calculation of 141 vertical excited singlet and 71 triplet states of 28 small to medium-sized organic molecules has revealed that ADC(3) exhibits mean error and standard deviation of 0.12 ± 0.28 eV for singlet states and -0.18 ± 0.16 eV for triplet states when the provided theoretical best estimates are used as benchmark. Accordingly, the ADC(2)-s and ADC(2)-x calculations revealed accuracies of 0.22 ± 0.38 eV and -0.70 ± 0.37 eV for singlets and 0.12 ± 0.16 eV and -0.55 ± 0.20 eV for triplets, respectively. For a comparison of CC3 and ADC(3), only non-CC3 benchmark values were considered, which comprise 84 singlet states and 19 triplet states. For these singlet states CC3 exhibits an accuracy of 0.23 ± 0.21 eV and ADC(3) an accuracy of 0.08 ± 0.27 eV, and accordingly for the triplet states of 0.12 ± 0.10 eV and -0.10 ± 0.13 eV, respectively. Hence, based on the quality of the existing benchmark set it is practically not possible to judge whether ADC(3) or CC3 is more accurate, however, ADC(3) has a much larger range of applicability due to its more favourable scaling of O(N(6)) with system size.
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Ramond-Ramond Central Charges in the Supersymmetry Algebra of the Superstring
Berkovits, N.
1997-09-01
The free action for the massless sector of the type II superstring was recently constructed using closed Ramond-Neveo-Schwarz superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N=2 D=10 supersymmetry algebra with Ramond-Ramond central charges. {copyright} {ital 1997} {ital The American Physical Society}
A New Bench Concept for Measuring Magnetic Fields of Big Closed Structure
NASA Astrophysics Data System (ADS)
Campmany, Josep; Ribó, Llibert; Colldelram, Carles; Becheri, Fulvio; Marcos, Jordi; Massana, Valentí
The measurement of big closed magnetic structures is becoming a challenge of great interest. The main reason is the tendency towards building accelerators with high magnetic fields produced by small gap magnets, as well as the development of cryogenic or superconducting narrow-gap insertion devices. Usual approach, based on side-measurements made with a Hall probe mounted on the tip of a motorized arm based on a long granite bench is no more applicable to such closed structures. So, new concepts and approaches have been developed, mainly based on complex devices that insert a Hall probe inside the magnetic structure maintaining the desired position by close-loop controls. We present in this paper the characterization of a new bench that has been built at ALBA synchrotron that is simple, multi-purpose and can be a general solution for measuring big closed structures. Motion control is done via ICEpap motion driver system using the new trigger feature that has been implemented in this motor controller.
Closed-loop flow test Miravalles Geothermal Field well log results
Dennis, B.; Eden, G.; Lawton, R.
1992-10-01
The Instituto Costarricense de Electricidad (ICE) conducted a closed-loop flow test in the Miravalles Geothermal Field. The closed-loop test was started in May and ran through August of 1990. The effluent from the production well PG-11 was carried by a pipeline through a monitor station to the injection well PG-2. Before starting the long-term flow test in May, cold-water injection experiments were performed in each well to determine the pressure and temperature response. A series of downhole measurements were made in each well to obtain background information. The downhole measurements were repeated in August just before terminating the flow test to evaluate the results.
Closed-loop flow test Miravalles Geothermal Field well log results
Dennis, B.; Eden, G.; Lawton, R.
1992-01-01
The Instituto Costarricense de Electricidad (ICE) conducted a closed-loop flow test in the Miravalles Geothermal Field. The closed-loop test was started in May and ran through August of 1990. The effluent from the production well PG-11 was carried by a pipeline through a monitor station to the injection well PG-2. Before starting the long-term flow test in May, cold-water injection experiments were performed in each well to determine the pressure and temperature response. A series of downhole measurements were made in each well to obtain background information. The downhole measurements were repeated in August just before terminating the flow test to evaluate the results.
Acceleration of plasma flows in the closed magnetic fields: Simulation and analysis
Mahajan, Swadesh M.; Shatashvili, Nana L.; Mikeladze, Solomon V.; Sigua, Ketevan I.
2006-06-15
Within the framework of a two-fluid description, possible pathways for the generation of fast flows (dynamical as well as steady) in the closed magnetic fields are established. It is shown that a primary plasma flow (locally sub-Alfvenic) is accelerated while interacting with ambient arcade-like closed field structures. The time scale for creating reasonably fast flows (> or approx. 100 km/s) is dictated by the initial ion skin depth, while the amplification of the flow depends on local plasma {beta}. It is shown that distances over which the flows become 'fast' are {approx}0.01R{sub 0} from the interaction surface (R{sub 0} being a characteristic length of the system); later, the fast flow localizes (with dimensions < or approx. 0.05R{sub 0}) in the upper central region of the original arcade. For fixed initial temperature, the final speed (> or approx. 500 km/s) of the accelerated flow and the modification of the field structure are independent of the time duration (lifetime) of the initial flow. In the presence of dissipation, these flows are likely to play a fundamental role in the heating of the finely structured stellar atmospheres; their relevance to the solar wind is also obvious.
NASA Astrophysics Data System (ADS)
Sobral, R. R.; Guimarães, A. P.; da Silva, X. A.
1994-10-01
The eigenvalues of the Crystalline Electric Field (CEF) Hamiltonian with cubic symmetry are analytically obtained for trivalent rare-earth ions of ground state J= {5}/{2}, {7}/{2}, 4, {9}/{2}, 6, {15}/{2} and 8, via a Computer Algebra approach. In the presence of both CEF and an effective exchange field, Computer Algebra still allows a partial factorization of the characteristic polynomial equation associated to the total Hamiltonian, a result of interest to the study of the magnetic behavior of rare-earth intermetallics. An application to the PrX2 intermetallic compounds ( X = Mg, Al, Ru, Rh, Pt) is reported.
Remarks on Virasoro and Kac-Moody Algebras
NASA Astrophysics Data System (ADS)
Grabowski, J.; Marmo, G.; Perelomov, A.; Simoni, A.
Parametric realizations of Virasoro or Kac-Moody algebras are constructed on a generic manifold carrying an appropriate vector field. It is shown that the centrally extended algebras cannot be realized as algebras of vector fields on finite-dimensional manifolds.
Current algebra and the nonlinear σ-model
NASA Astrophysics Data System (ADS)
Ghosh, S.
2007-06-01
We present the current algebra of a particular form in the nonlinear σ-model. The algebra has a non-Abelian form with field-dependent structure functions. We comment on the connection of the model with noncommutative space.
Study of magnetic thin films deposited by closed-field unbalanced magnetron sputtering
NASA Astrophysics Data System (ADS)
Ormston, M. W.; Petford-Long, A. K.; Teer, D. G.
1999-04-01
Closed-field unbalanced magnetron sputtering, developed by TEER Coatings Ltd., uses a novel plasma confinement system, which allows controllable high-rate deposition from a wide range of target materials. We report the first use of this technique using ferromagnetic target materials to grow films of nanometer thickness. A study was carried out on a series of Py/Cu/Py and Py/Au/Py magnetic multilayer films, with and without underlayers of Ti or Ta. High-resolution electron microscopy showed that 5 nm of Ti or 15 nm of Ta did not change the structure of the trilayers. The use of Au as a spacer layer induced a texture in the upper Py layer, which decreased its saturation field by half. In situ experiments to observe the effects of an applied field on the domain structure of the films were carried out using Lorentz transmission electron microscopy. Variations in the switching field of the Py layers and of the coupling strength between the Py layers were observed when the thicknesses of the three layers were varied. Double domain wall structures with different wall intensities were observed in some cases. The roughness of the interfaces were increased by ion bombardment; this increased the saturation field of the Py layers.
Studies of Dynamic, Radiative Macroscopic Magnetized HED Plasmas with Closed B-Field Lines
Frese, Michael H.; Frese, Sherry D.
2013-11-01
The purpose of this research has been to study the physics of macroscopic magnetized high-energy-density laboratory plasmas (HEDLPs) created through the compression of a high-beta compact toroid (CT) plasma having closed magnetic field lines. The high-beta CT chosen for this work is a field-reversed configuration (FRC). The basic approach is to investigate CT plasmas as they are compressed to a HED state by the electromagnetic implosion of a surrounding metallic shell or solid liner (Figure 1). The shell provides an axisymmetric, electrically-conducting boundary around the plasma and its supporting magnetic field and is imploded by means of the magnetic pressure force arising from axial current flow in the liner interacting with its associated azimuthal magnetic field. Compression of the CT will bring the plasma to fusion temperatures at higher densities and magnetic fields (multi-MegaGauss [MG]) than have previously been present in conventional magnetic fusion approaches. The resulting energy densities will be ~1 Mbar or greater and thus will place the plasma in a parameter space intermediate to MFE and IFE. This work has been a collaboration between the Air Force Research Laboratory, Los Alamos National Laboratory, and NumerEx, LLC.
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,…
Pinyon, Jeremy L; Tadros, Sherif F; Froud, Kristina E; Y Wong, Ann C; Tompson, Isabella T; Crawford, Edward N; Ko, Myungseo; Morris, Renée; Klugmann, Matthias; Housley, Gary D
2014-04-23
The cochlear implant is the most successful bionic prosthesis and has transformed the lives of people with profound hearing loss. However, the performance of the "bionic ear" is still largely constrained by the neural interface itself. Current spread inherent to broad monopolar stimulation of the spiral ganglion neuron somata obviates the intrinsic tonotopic mapping of the cochlear nerve. We show in the guinea pig that neurotrophin gene therapy integrated into the cochlear implant improves its performance by stimulating spiral ganglion neurite regeneration. We used the cochlear implant electrode array for novel "close-field" electroporation to transduce mesenchymal cells lining the cochlear perilymphatic canals with a naked complementary DNA gene construct driving expression of brain-derived neurotrophic factor (BDNF) and a green fluorescent protein (GFP) reporter. The focusing of electric fields by particular cochlear implant electrode configurations led to surprisingly efficient gene delivery to adjacent mesenchymal cells. The resulting BDNF expression stimulated regeneration of spiral ganglion neurites, which had atrophied 2 weeks after ototoxic treatment, in a bilateral sensorineural deafness model. In this model, delivery of a control GFP-only vector failed to restore neuron structure, with atrophied neurons indistinguishable from unimplanted cochleae. With BDNF therapy, the regenerated spiral ganglion neurites extended close to the cochlear implant electrodes, with localized ectopic branching. This neural remodeling enabled bipolar stimulation via the cochlear implant array, with low stimulus thresholds and expanded dynamic range of the cochlear nerve, determined via electrically evoked auditory brainstem responses. This development may broadly improve neural interfaces and extend molecular medicine applications.
Quasilinear theory of interchange modes in a closed field line configuration
Kouznetsov, A.; Freidberg, J. P.; Kesner, J.
2007-10-15
Two important issues for any magnetic fusion configuration are the maximum achievable values of {beta} and energy confinement time when ideal magnetohydrodynamic (MHD) modes are excited. It is well known that the excitation of the MHD unstable modes typically can lead to violent restructuring of the plasma profiles. The particle and energy transport associated with these modes normally dominates all other transport mechanisms and can lead to plasma disruptions and a rapid loss of energy. This paper analytically investigates the transport of particle density, energy, and magnetic field due to the ideal MHD interchange mode in a closed-line system using the quasilinear approximation. The transport equations are derived for a static plasma in a hardcore Z-pinch configuration and generalized to an arbitrary axisymmetric toroidal closed poloidal field line configuration. It is shown that violation of the marginal stability criterion leads to rapid quasilinear transport that drives the pressure profile back to its marginal profile and forces the particle density to be inversely proportional to {integral}dl/B. The applicability of the quasilinear approximation is numerically tested for the hardcore Z-pinch magnetic configuration using a full nonlinear code.
The close lightning electromagnetic environment: Dart-leader electric field change versus distance
NASA Astrophysics Data System (ADS)
Crawford, David E.; Rakov, Vladimir A.; Uman, Martin A.; Schnetzer, George H.; Rambo, Keith J.; Stapleton, Michael V.; Fisher, Richard J.
2001-07-01
Net electric field changes due to dart leaders in triggered lightning from experiments conducted in 1997, 1998, and 1999 at the International Center for Lightning Research and Testing at Camp Blanding, Florida, are analyzed and compared with similar data obtained in 1993 at Camp Blanding and at Fort McClellan, Alabama. In 1997-1999 the fields were measured at 2-10 stations with distances from the lightning channel ranging from 10 to 621 m, while in 1993 the fields were measured at three distances, 30, 50, and 110 m, in Florida and at two distances, about 10 and 20 m, in Alabama. With a few exceptions, the 1997-1999 data indicate that the distance dependence of the leader electric field change is close to an inverse proportionality (r-1), in contrast to the 1993 data in which a somewhat weaker distance dependence was observed. The typically observed r-1 dependence is consistent with a uniform distribution of leader charge along the bottom kilometer or so of the channel.
Application of closed-form solutions to a mesh point field in silicon solar cells
NASA Technical Reports Server (NTRS)
Lamorte, M. F.
1985-01-01
A computer simulation method is discussed that provides for equivalent simulation accuracy, but that exhibits significantly lower CPU running time per bias point compared to other techniques. This new method is applied to a mesh point field as is customary in numerical integration (NI) techniques. The assumption of a linear approximation for the dependent variable, which is typically used in the finite difference and finite element NI methods, is not required. Instead, the set of device transport equations is applied to, and the closed-form solutions obtained for, each mesh point. The mesh point field is generated so that the coefficients in the set of transport equations exhibit small changes between adjacent mesh points. Application of this method to high-efficiency silicon solar cells is described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing, carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been investigated using Fermi-Dirac statistics, and these results show that bandgap narrowing is more pronounced and that it is temperature-dependent in contrast to the results based on Boltzmann statistics.
The Influence of Magnetic Field Geometry on the Formation of Close-in Exoplanets
NASA Astrophysics Data System (ADS)
Simon, Jacob B.
2016-08-01
Approximately half of Sun-like stars harbor exoplanets packed within a radius of ˜0.3 au, but the formation of these planets and why they form in only half of known systems are still not well understood. We employ a one-dimensional steady-state model to gain physical insight into the origin of these close-in exoplanets. We use Shakura & Sunyaev α values extracted from recent numerical simulations of protoplanetary disk accretion processes in which the magnitude of α, and thus the steady-state gas surface density, depend on the orientation of large-scale magnetic fields with respect to the disk’s rotation axis. Solving for the metallicity as a function of radius, we find that for fields anti-aligned with the rotation axis, the inner regions of our model disk often fall within a region of parameter space that is not suitable for planetesimal formation, whereas in the aligned case, the inner disk regions are likely to produce planetesimals through some combination of streaming instability and gravitational collapse, though the degree to which this is true depends on the assumed parameters of our model. More robustly, the aligned field case always produces higher concentrations of solids at small radii compared to the anti-aligned case. In the in situ formation model, this bimodal distribution of solid enhancement leads directly to the observed dichotomy in exoplanet orbital distances.
Cartan calculus on quantum Lie algebras
Schupp, P.; Watts, P.; Zumino, B.
1993-12-09
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ``Cartan Calculus.``
Open and closed loop manipulation of charged microchiplets in an electric field
Lu, J. P. Thompson, J. D.; Whiting, G. L.; Biegelsen, D. K.; Raychaudhuri, S.; Lujan, R.; Veres, J.; Lavery, L. L.; Völkel, A. R.; Chow, E. M.
2014-08-04
We demonstrate the ability to orient, position, and transport microchips (“chiplets”) with electric fields. In an open-loop approach, modified four phase traveling wave potential patterns manipulate chiplets in a dielectric solution using dynamic template agitation techniques. Repeatable parallel assembly of chiplets is demonstrated to a positional accuracy of 6.5 μm using electrodes of 200 μm pitch. Chiplets with dipole surface charge patterns are used to show that orientation can be controlled by adding unique charge patterns on the chiplets. Chip path routing is also demonstrated. With a closed-loop control system approach using video feedback, dielectric, and electrophoretic forces are used to achieve positioning accuracy of better than 1 μm with 1 mm pitch driving electrodes. These chip assembly techniques have the potential to enable future printer systems where inputs are electronic chiplets and the output is a functional electronic system.
Moving frames and prolongation algebras
NASA Technical Reports Server (NTRS)
Estabrook, F. B.
1982-01-01
Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
Upper bound for the length of commutative algebras
NASA Astrophysics Data System (ADS)
Markova, Ol'ga V.
2009-12-01
By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field one means the least positive integer k such that the words of length not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, an upper bound for the length of a commutative algebra in terms of a function of two invariants of the algebra, the dimension and the maximal degree of the minimal polynomial for the elements of the algebra, is obtained. As a corollary, a formula for the length of the algebra of diagonal matrices over an arbitrary field is obtained. Bibliography: 8 titles.
Quantum cluster algebras and quantum nilpotent algebras
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
Gauged Ads-Maxwell Algebra and Gravity
NASA Astrophysics Data System (ADS)
Durka, R.; Kowalski-Glikman, J.; Szczachor, M.
We deform the anti-de Sitter algebra by adding additional generators {Z}ab, forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein-Cartan action with Holst term, and the gauge fields associated with the Maxwell generators {Z}ab appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.
NASA Astrophysics Data System (ADS)
Dickinson, M.; Kremens, R.; Bova, A. S.
2012-12-01
Closing the wildland fire heat budget involves characterizing the heat source and energy dissipation across the range of variability in fuels and fire behavior. Meeting this challenge will lay the foundation for predicting direct ecological effects of fires and fire-atmosphere coupling. Here, we focus on the relationships between the fire radiation field, as measured from the zenith, fuel consumption, and the behavior of spreading flame fronts. Experiments were conducted in 8 m x 8 m outdoor plots using pre-conditioned wildland fuels characteristic of mixed-oak forests of the eastern United States. Using dual-band radiometers with a field of view of about 18.5 m^2 at a height of 4.2 m, we found a near-linear increase in fire radiative energy density (FRED) over a range of fuel consumption between 0.15 kg m^-2 to 3.25 kg m^-2. Using an integrated heat budget, we estimate that the fraction of total theoretical combustion energy density radiated from the plot averaged 0.17, the fraction of latent energy transported in the plume averaged 0.08, and the fraction accounted for by the combination of fire convective energy transport and soil heating averaged 0.72. Future work will require, at minimum, instantaneous and time-integrated estimates of energy transported by radiation, convection, and soil heating across a range of fuels. We introduce the Rx-CADRE project through which such measurements are being made.
Methods of Using a Magnetic Field Response Sensor Within Closed, Electrically Conductive Containers
NASA Technical Reports Server (NTRS)
Woodward, Stanley E.; Taylor, Bryant D.
2010-01-01
Magnetic field response sensors are a class of sensors that are powered via oscillating magnetic fields, and when electrically active, respond with their own magnetic fields with attributes dependent upon the magnitude of the physical quantity being measured. A magnetic field response recorder powers and interrogates the magnetic sensors [see Magnetic-Field-Response Measurement- Acquisition System, NASA Tech Briefs Vol. 30, No, 6 (June 2006, page 28)]. Electrically conductive containers have low transmissivity for radio frequency (RF) energy and thus present problems for magnetic field response sensors. It is necessary in some applications to have a magnetic field response sensor s capacitor placed in these containers. Proximity to conductive surfaces alters the inductance and capacitance of the sensors. As the sensor gets closer to a conductive surface, the electric field and magnetic field energy of the sensor is reduced due to eddy currents being induced in the conductive surface. Therefore, the capacitors and inductors cannot be affixed to a conductive surface or embedded in a conductive material. It is necessary to have a fixed separation away from the conductive material. The minimum distance for separation is determined by the desired sensor response signal to noise ratio. Although the inductance is less than what it would be if it were not in proximity to the conductive surface, the inductance is fixed. As long as the inductance is fixed, all variations of the magnetic field response are due to capacitance changes. Numerous variations of inductor mounting can be utilized, such as providing a housing that provides separation from the conductive material as well as protection from impact damage. The sensor can be on the same flexible substrate with a narrow throat portion of the sensor between the inductor and the capacitor, Figure 1. The throat is of sufficient length to allow the capacitor to be appropriately placed within the container and the inductor
ERIC Educational Resources Information Center
Vaninsky, Alexander
2011-01-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…
Salvaging dipmeters using an oil field {open_quotes}Dinosaur{close_quotes}
Breimayer, A.R.P.; Puzio, L.B.
1996-09-01
Although state-of-the-art methods such as 3-D seismic and formation imaging tools are widely used, the advantages of the old standard dipmeter should not be dismissed. Seismic dip is subject to velocity errors, and formation imagers cannot be run in all borehole conditions. The dipmeter offers a relatively low cost, highly effective alternative for defining geologic features. The 60{double_prime}= 100{prime} scale playback of the raw dipmeter data may be an oil field {open_quotes}dinosaur,{close_quotes} but it is also the key to assessing the reliability of a dipmeter. This playback should be used to determine CORRELATION QUALITY, critical to the accuracy of any dipmeter. Computer computation of the raw dipmeter data does not always yield reliable dip information, particularly when dipmeters are run under adverse hole conditions or in complex geology. This data can be often salvaged by optical correlation of the 60{close_quote} playback - the process of manually correlating raw dipmeter resistivity curves to determine the attitude of bedding planes in the subsurface. Problems such as tool noise, tool pulls, and poor pad contact compromise data quality. These problems can be recognized and compensated for using optical correlation. Finally, at the 60{double_prime} scale many formation textures and structural characteristics visible on the formation imaging logs are also discernible on the standard dipmeter traces. We will offer many Gulf Coast examples and some hands-on demonstrations using the 60{double_prime} data, and show improved tadpole plots which result from optical correlation.
Measured close lightning leader-step electric-field-derivative waveforms.
Jordan, Doug M.; Hill, Dustin; Biagi, Christopher J.; Howard, Joseph Sean; Uman, Martin A.; Rakov, Vladimir A.
2010-12-01
We characterize the measured electric field-derivative (dE/dt) waveforms of lightning stepped-leader steps from three negative lightning flashes at distances of tens to hundreds of meters. Electromagnetic signatures of leader steps at such close distances have rarely been documented in previous literature. Individual leader-step three-dimensional locations are determined by a dE/dt TOA system. The leader-step field derivative is typically a bipolar pulse with a sharp initial half-cycle of the same polarity as that of the return stroke, followed by an opposite polarity overshoot that decays relatively slowly to background level. This overshoot increases in amplitude relative to the initial peak and becomes dominant as range decreases. The initial peak is often preceded by a 'slow front,' similar to the slow front that precedes the fast transition to peak in first return stroke dE/dt and E waveforms. The overall step-field waveform duration is typically less than 1 {micro}s. The mean initial peak of dE/dt, range-normalized to 100 km, is 7.4 V m{sup -1} {micro}s{sup -1} (standard deviation (S.D.), 3.7 V m{sup -1} {micro}s{sup -1}, N = 103), the mean half-peak width is 33.5 ns (S.D., 11.9 ns, N = 69), and the mean 10-to-90% risetime is 43.6 ns (S.D., 24.2 ns, N = 69). From modeling, we determine the properties of the leader step currents which produced two typical measured field derivatives, and we use one of these currents to calculate predicted leader step E and dE/dt as a function of source range and height, the results being in good agreement with our observations. The two modeled current waveforms had maximum rates of current rise-to-peak near 100 kA {micro}s{sup -1}, peak currents in the 5-7 kA range, current half-peak widths of about 300 ns, and charge transfers of {approx}3 mC. As part of the modeling, those currents were propagated upward at 1.5 x 10{sup 8} m s{sup -1}, with their amplitudes decaying exponentially with a decay height constant of 25 m.
NASA Astrophysics Data System (ADS)
Jackson, B. V.; Yu, H. S.; Hick, P. P.; Buffington, A.; Bisi, M. M.; Tokumaru, M.; Kim, J.; Hong, S.; Lee, B.; Yi, J.; Yun, J.
2015-12-01
We find that a portion of the north-south interplanetary magnetic field measured in situ near Earth is present from a direct outward mapping of closed fields from the low solar corona. Using the Current-Sheet Source Surface (CSSS) model (Zhao & Hoeksema, 1995 JGR 100, 19), these lower coronal fields are extrapolated upward from near the solar surface. Global velocities inferred from a combination of observations of interplanetary scintillation (IPS) matched to in-situ velocities and densities measured by spacecraft instrumentation provide an accurate outward timing to 1 AU from a model assuming conservation of mass and mass flux. The north-south field component at 1 AU is compared with the appropriate ACE magnetometer in-situ Normal (RTN) or Bn field coordinate (Jackson et al., 2015, ApJL, 803:L1). From a significant positive correlation between this method of determining the Bn field compared with in-situ measurements over a three-year period during the last solar minimum, we find that a small fraction of the low-coronal Bn component flux (~1%) regularly escapes from closed-field regions. Since the Bn field provides the major portion of the Geocentric Solar Magnetospheric (GSM) Bz field component that couples most closely to the Earth's geomagnetic field, the prospects for its determination using this technique for space weather use are being actively developed by our many colleague groups.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Applications: Using Algebra in an Accounting Practice.
ERIC Educational Resources Information Center
Eisner, Gail A.
1994-01-01
Presents examples of algebra from the field of accounting including proportional ownership of stock, separation of a loan payment into principal and interest portions, depreciation methods, and salary withholdings computations. (MKR)
Jackson, B. V.; Hick, P. P.; Buffington, A.; Yu, H.-S.; Bisi, M. M.; Tokumaru, M.; Zhao, X. E-mail: pphick@ucsd.edu E-mail: hsyu@ucsd.edu
2015-04-10
A component of the magnetic field measured in situ near the Earth in the solar wind is present from north–south fields from the low solar corona. Using the Current-sheet Source Surface model, these fields can be extrapolated upward from near the solar surface to 1 AU. Global velocities inferred from a combination of interplanetary scintillation observations matched to in situ velocities and densities provide the extrapolation to 1 AU assuming mass and mass flux conservation. The north–south field component is compared with the same ACE in situ magnetic field component—the Normal (Radial Tangential Normal) Bn coordinate—for three years throughout the solar minimum of the current solar cycle. We find a significant positive correlation throughout this period between this method of determining the Bn field compared with in situ measurements. Given this result from a study during the latest solar minimum, this indicates that a small fraction of the low-coronal Bn component flux regularly escapes from closed field regions. The prospects for Space Weather, where the knowledge of a Bz field at Earth is important for its geomagnetic field effects, is also now enhanced. This is because the Bn field provides the major portion of the Geocentric Solar Magnetospheric Bz field coordinate that couples most closely to the Earth’s geomagnetic field.
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
ERIC Educational Resources Information Center
Miller, L. Diane; England, David A.
1989-01-01
Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)
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.
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
2016-07-01
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
SAYD Modules over Lie-Hopf Algebras
NASA Astrophysics Data System (ADS)
Rangipour, Bahram; Sütlü, Serkan
2012-11-01
In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.
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.
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.
Conformal current algebra in two dimensions
NASA Astrophysics Data System (ADS)
Ashok, Sujay K.; Benichou, Raphael; Troost, Jan
2009-06-01
We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
NASA Astrophysics Data System (ADS)
Mosaddeghi, A.; Pavanello, D.; Rachidi, F.; Rubinstein, M.
2007-10-01
In this paper, we show that the electric field generated by a lightning return stroke to a tall structure can change polarity at very close distance range, typically at distances of about one tenth the height or so of the struck object. This change in the polarity seems to be a specific signature of the very close vertical electric field. Two different theoretical explanations of such an inversion of polarity are given, the first based on general field equations for a perfectly conducting ground and the second based on the equation derived by Baba and Rakov (2005a) for the case when the return stroke wavefront speed is assumed to be equal to the speed of light and the reflection coefficient at the top of the tall structure is zero. A simple equation is derived which provides an estimate of the critical distance below which such an inversion of polarity might occur. It is also shown that the inversion of polarity depends on the value of the reflection coefficient at the base of the tower and disappears for reflection coefficients close to 1. On the other hand, other parameters such as the return stroke speed, the reflection coefficient at the top of the strike object, and the adopted return stroke model seem not to have an impact on the inversion of polarity. The need of obtaining experimental data on electromagnetic fields at very close range to a tower struck by lightning is emphasized in order to confirm the theoretical finding.
Algebras with convergent star products and their representations in Hilbert spaces
NASA Astrophysics Data System (ADS)
Soloviev, M. A.
2013-07-01
We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We consider different star products in a unifying way and present results on the structure and basic properties of these algebras, which are useful for applications. Special attention is given to the Hilbert space representation of the algebras and to the exact description of their corresponding operator algebras.
Closely-spaced double-row microstrip RF arrays for parallel MR imaging at ultrahigh fields
Yan, Xinqiang; Xue, Rong; Zhang, Xiaoliang
2015-01-01
Radiofrequency (RF) coil arrays with high count of elements, e.g., closely-spaced multi-row arrays, exhibit superior parallel imaging performance in MRI. However, it is technically challenging and time-consuming to build multi-row arrays due to complex coupling issues. This paper presents a novel and simple method for closely-spaced multi-row RF array designs. Induced current elimination (ICE) decoupling method has shown the capability of reducing coupling between microstrip elements from different rows. In this study, its capability for decoupling array elements from the same row was investigated and validated by bench tests, with an isolation improvement from −8.9 dB to −20.7 dB. Based on this feature, a closely-spaced double-row microstrip array with 16 elements was built at 7T. S21 between any two elements of the 16-channel closely-spaced was better than −14 dB. In addition, its feasibility and performance was validated by MRI experiments. No significant image reconstruction- related noise amplifications were observed for parallel imaging even when reduced factor (R) achieves 4. The experimental results demonstrated that the proposed design might be a simple and efficient approach in fabricating closely-spaced multi-row RF arrays. PMID:26508810
Closely-spaced double-row microstrip RF arrays for parallel MR imaging at ultrahigh fields.
Yan, Xinqiang; Xue, Rong; Zhang, Xiaoliang
2015-11-01
Radiofrequency (RF) coil arrays with high count of elements, e.g., closely-spaced multi-row arrays, exhibit superior parallel imaging performance in MRI. However, it is technically challenging and time-consuming to build multi-row arrays due to complex coupling issues. This paper presents a novel and simple method for closely-spaced multi-row RF array designs. Induced current elimination (ICE) decoupling method has shown the capability of reducing coupling between microstrip elements from different rows. In this study, its capability for decoupling array elements from the same row was investigated and validated by bench tests, with an isolation improvement from -8.9 dB to -20.7 dB. Based on this feature, a closely-spaced double-row microstrip array with 16 elements was built at 7T. S21 between any two elements of the 16-channel closely-spaced was better than -14 dB. In addition, its feasibility and performance was validated by MRI experiments. No significant image reconstruction- related noise amplifications were observed for parallel imaging even when reduced factor (R) achieves 4. The experimental results demonstrated that the proposed design might be a simple and efficient approach in fabricating closely-spaced multi-row RF arrays.
Algebra and topology for applications to physics
NASA Technical Reports Server (NTRS)
Rozhkov, S. S.
1987-01-01
The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.
Open and closed string vertices for branes with magnetic field and T-duality
NASA Astrophysics Data System (ADS)
Pesando, Igor
2010-02-01
We discuss carefully the vertices which describe the dipole open strings and closed strings on a D-brane with magnetic flux on a torus. Translation invariance along closed cycles forces surprisingly closed string vertices written in open string formalism to acquire Chan-Paton like matrices. Moreover the one loop amplitudes have a single trace for the part of gauge group with the magnetic flux. These peculiarities are also required by consistency of the action of T-duality in the open string sector. In this way we can show to all orders in perturbation theory the equivalence of the T-dual open string theories, gravitational interactions included. We provide also a new and direct derivation of the bosonic boundary state in presence of constant magnetic and Kalb-Ramond background based on Sciuto-Della Selva-Saito vertex formalism.
Involved field radiation for Hodgkin's lymphoma: The actual dose to breasts in close proximity
Dabaja, Bouthaina; Wang Zhonglo; Stovall, Marilyn; Baker, Jamie S.; Smith, Susan A.; Khan, Meena; Ballas, Leslie; Salehpour, Mohammad R.
2012-01-01
To decrease the risk of late toxicities in Hodgkin's lymphoma (HL) patients treated with radiation therapy (RT) (HL), involved field radiation therapy (IFRT) has largely replaced the extended fields. To determine the out-of-field dose delivered from a typical IFRT to surrounding critical structures, we measured the dose at various points in an anthropomorphic phantom. The phantom is divided into 1-inch-thick slices with the ability to insert TLDs at 3-cm intervals grid spacing. Two treatment fields were designed, and a total of 45 TLDs were placed (equally spaced) at the margin of the each of the 2 radiation fields. After performing a computed tomography simulation, 2 treatment plans targeting the mediastinum, a typical treatment field in patients with early stage HL, were generated. A total dose of 3060 cGy was delivered to the gross tumor volume for each field consecutively. The highest measured dose detected at 1 cm from the field edge in the planning target volume was 496 cGy, equivalent to 16% of the isocentric dose. The dose dropped significantly with increasing distance from the field edge. It ranged from 1.1-3.9% of the isocentric dose at a distance of 3.2-4 cm to <1.6% at a distance of >6 cm. Although the computer treatment planning system (CTPS) frequently underestimated the dose delivered, the difference in dose between measured and generated by CTPS was <2.5% in 90 positions measured. The collateral dose of radiation to breasts from IFRT is minimal. The out-of-field dose, although mildly underestimated by CTPS, becomes insignificant at >3 cm from the field edge of the radiation field.
Prediction of Algebraic Instabilities
NASA Astrophysics Data System (ADS)
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
NASA Astrophysics Data System (ADS)
Kharin, Stanislav; Sarsengeldin, Merey; Kassabek, Samat
2016-08-01
We represent mathematical models of electromagnetic field dynamics and heat transfer in closed symmetric and asymmetric electrical contacts including Thomson effect, which are essentially nonlinear due to the dependence of thermal and electrical conductivities on temperature. Suggested solutions are based on the assumption of identity of equipotentials and isothermal surfaces, which agrees with experimental data and valid for both linear and nonlinear cases. Well known Kohlrausch temperature-potential relation is analytically justified.
Quan, Wei; Yuan, MingHu; Yu, ShaoGang; Xu, SongPo; Chen, YongJu; Wang, YanLan; Sun, RenPing; Xiao, ZhiLei; Gong, Cheng; Hua, LinQiang; Lai, XuanYang; Liu, XiaoJun; Chen, Jing
2016-10-03
We conceive an improved procedure to determine the laser intensity with the momentum distributions from nonadiabatic tunneling ionization of atoms in the close-to-circularly polarized laser fields. The measurements for several noble gas atoms are in accordance with the semiclassical calculations, where the nonadiabatic effect and the influence of Coulomb potential are included. Furthermore, the high-order above-threshold ionization spectrum in linearly polarized laser fields for Ar is measured and compared with the numerical calculation of the time-dependent Schrödinger equation in the single-active-electron approximation to test the accuracy of the calibrated laser intensity.
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
Parastatistics Algebras and Combinatorics
NASA Astrophysics Data System (ADS)
Popov, T.
2005-03-01
We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
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,…
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…
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…
Aspects of infinite dimensional ℓ-super Galilean conformal algebra
NASA Astrophysics Data System (ADS)
Aizawa, N.; Segar, J.
2016-12-01
In this work, we construct an infinite dimensional ℓ-super Galilean conformal algebra, which is a generalization of the ℓ = 1 algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation, and the operator product expansion of the infinite dimensional ℓ-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.
Close-range photogrammetry with light field camera: from disparity map to absolute distance.
Yang, Peng; Wang, Zhaomin; Yan, Yizhen; Qu, Weijuan; Zhao, Hongying; Asundi, Anand; Yan, Lei
2016-09-20
A new approach to measure the 3D profile of a texture object is proposed utilizing light field imaging, in which three key steps are required: a disparity map is first obtained by detecting the slopes in the epipolar plane image with the multilabel technique; the intrinsic parameters of the light field camera are then extracted by camera calibration; at last, the relationship between disparity values and real distances is built up by depth calibration. In the last step, a linear calibration method is proposed to achieve accurate results. Furthermore, the depth error is also investigated and compensated for by reusing the checkerboard pattern. The experimental results are in good agreement with the 3D models, and also indicate that the light field imaging is a promising 3D measurement technique.
Closing the superconducting gap in small Pb nanoislands with high magnetic fields
NASA Astrophysics Data System (ADS)
Rolf-Pissarczyk, Steffen; Burgess, Jacob A. J.; Yan, Shichao; Loth, Sebastian
2016-12-01
Superconducting properties change in confined geometries. Here we study the effects of strong confinement in nanosized Pb islands on Si(111) 7 ×7 . Small hexagonal islands with diameters less than 50 nm and a uniform height of seven atomic layers are formed by depositing Pb at low temperature and annealing at 300 K. We measure the tunneling spectra of individual Pb nanoislands using a low-temperature scanning tunneling microscope operated at 0.6 K and follow the narrowing of the superconducting gap as a function of magnetic field. We find the critical magnetic field, at which the superconducting gap vanishes, reaches several Tesla, which represents a greater than 50-fold enhancement compared to the bulk value. By independently measuring the size of the superconducting gap, and the critical magnetic field that quenches superconductivity for a range of nanoislands, we can correlate these two fundamental parameters and estimate the maximal achievable critical field for 7 ML Pb nanoislands to be 7 T.
Closed-loop torque feedback for a universal field-oriented controller
De Doncker, Rik W. A. A.; King, Robert D.; Sanza, Peter C.; Haefner, Kenneth B.
1992-01-01
A torque feedback system is employed in a universal field-oriented (UFO) controller to tune a torque-producing current command and a slip frequency command in order to achieve robust torque control of an induction machine even in the event of current regulator errors and during transitions between pulse width modulated (PWM) and square wave modes of operation.
Closed-loop torque feedback for a universal field-oriented controller
De Doncker, R.W.A.A.; King, R.D.; Sanza, P.C.; Haefner, K.B.
1992-11-24
A torque feedback system is employed in a universal field-oriented (UFO) controller to tune a torque-producing current command and a slip frequency command in order to achieve robust torque control of an induction machine even in the event of current regulator errors and during transitions between pulse width modulated (PWM) and square wave modes of operation. 1 figure.
Huang, Yu; Zhang, Xian; Ringe, Emilie; Hou, Mengjing; Ma, Lingwei; Zhang, Zhengjun
2016-01-01
Considering the nanogap and lattice effects, there is an attractive structure in plasmonics: closely spaced metallic nanoarrays. In this work, we demonstrate experimentally and theoretically the lattice coupling of multipole plasmon modes for closely spaced gold nanorod arrays, offering a new insight into the higher order cavity modes coupled with each other in the lattice. The resonances can be greatly tuned by changes in inter-rod gaps and nanorod heights while the influence of the nanorod diameter is relatively insignificant. Experimentally, pronounced suppressions of the reflectance are observed. Meanwhile, the near-field enhancement can be further enhanced, as demonstrated through surface enhanced Raman scattering (SERS). We then confirm the correlation between the near-field and far-field plasmonic responses, which is significantly important for maximizing the near-field enhancement at a specific excitation wavelength. This lattice coupling of multipole plasmon modes is of broad interest not only for SERS but also for other plasmonic applications, such as subwavelength imaging or metamaterials. PMID:26983501
Closing of the Midcontinent-Rift - a far-field effect on Grenvillian compression
Cannon, W.F.
1994-01-01
The Midcontinent rift formed in the Laurentian supercontinent between 1109 and 1094 Ma. Soon after rifting, stresses changed from extensional to compressional, and the central graben of the rift was partly inverted by thrusting on original extensional faults. Thrusting culminated at about 1060 Ma but may have begun as early as 1080 Ma. On the southwest-trending arm of the rift, the crust was shortened about 30km; on the southeast-trending arm, strike-slip motion was dominant. The rift developed adjacent to the tectonically active Grenville province, and its rapid evolution from an extensional to a compressional feature at c1080 Ma was coincident with renewal of northwest-directed thrusting in the Grenville, probably caused by continent-continent collision. A zone of weak lithosphere created by rifting became the locus for deformation within the otherwise strong continental lithosphere. Stresses transmitted from the Grenville province utilized this weak zone to close and invert the rift. -Author
On a Equation in Finite Algebraically Structures
ERIC Educational Resources Information Center
Valcan, Dumitru
2013-01-01
Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…
Numerical field model simulation of full scale fire tests in a closed spherical/cylindrical vessel
NASA Astrophysics Data System (ADS)
Raycraft, Janet K.
1987-12-01
Most of the casualties incurred during a fire are due to the smoke generated. An understanding of the way smoke and fire spread during a fire would provide a valuable tool to save lives and minimize damage. The Naval Research Laboratory maintains a full scale test facility called Fire-1. The computer model developed in this thesis is based on the actual geometry of Fire-1 and uses field modeling. It is a three dimensional, finite difference model using primitive variables. The model includes local and global pressure corrections, surface radiation, turbulence, strong buoyancy, and conjugate boundary conditions. Given heat input data, the computer code produces pressure, temperature, density, and velocity fields. Experimental fire tests conducted in Fire-1 are used to validate the computer code. Reasonable agreement in the results has been found. Because of the model's ability to account for pressure, temperature and smoke buildup, its envisioned use is to predict fires aboard ships and submarines.
Closing the Gap Between Research and Field Applications for Multi-UAV Cooperative Missions
2013-09-01
BETWEEN RESEARCH AND FIELD APPLICATIONS FOR MULTI-UAV COOPERATIVE MISSIONS by Harn Chin Teo September 2013 Thesis Co-Advisors: Oleg...APPLICATIONS FOR MULTI-UAV COOPERATIVE MISSIONS 5. FUNDING NUMBERS 6. AUTHOR(S) Harn Chin Teo 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES...MISSIONS Harn Chin Teo Systems Engineer, ST Aerospace Ltd. B.E., Nanyang Technological University (Singapore), 2008 Submitted in partial
Experiment close out of lysimeter field testing of low-level radioactive waste forms
McConnell, J.W. Jr.; Rogers, R.D.; Jastrow, J.D.
1998-03-01
The Field Lysimeter Investigations: Low-Level Waste Data Base Development Program is obtaining information on the performance of radioactive waste forms. These experiments were recently shut down and the contents of the lysimeters have been examined in accordance with a detailed waste form and soil sampling plan. Ion-exchange resins from a commercial nuclear power station were solidified into waste forms using portland cement and vinyl ester-styrene. These waste forms were tested to (a) obtain information on performance of waste forms in typical disposal environments, (b) compare field results with bench leach studies, (c) develop a low-level waste data base for use in performance assessment source term calculations, and (d) apply the DUST computer code to compare predicted cumulative release to actual field data. The program, funded by the Nuclear Regulatory Commission (NRC), includes observed radio nuclide releases from waste forms in field lysimeters at two test sites over 10 years of successful operation. The purpose of this paper is to present the results of the examination of waste forms and soils of the two lysimeter arrays after shut down. During this examination, the waste forms were characterized after removal from the lysimeters and the results compared to the findings of the original characterizations. Vertical soil cores were taken from the soil columns and analyzed with radiochemistry to define movement of radionuclides in the soils after release from the waste forms. A comparison is made of the DUST and BLT code predictions of releases and movement, using recently developed partition coefficients and leachate measurements, to actual radio nuclide movement through the soil columns as determined from these core analyses.
NASA Astrophysics Data System (ADS)
Collinson, Glyn; Mitchell, David; Xu, Shaosui; Glocer, Alex; Grebowsky, Joseph; Hara, Takuya; Lillis, Robert; Espley, Jared; Mazelle, Christian; Sauvaud, Jean-André; Fedorov, Andrey; Liemohn, Mike; Andersson, Laila; Jakosky, Bruce
2017-02-01
Parallel electric fields and their associated electric potential structures play a crucial role in ionospheric-magnetospheric interactions at any planet. Although there is abundant evidence that parallel electric fields play key roles in Martian ionospheric outflow and auroral electron acceleration, the fields themselves are challenging to directly measure due to their relatively weak nature. Using measurements by the Solar Wind Electron Analyzer instrument aboard the NASA Mars Atmosphere and Volatile EvolutioN (MAVEN) Mars Scout, we present the discovery and measurement of a substantial (ΦMars=7.7 ± 0.6 V) parallel electric potential drop on closed magnetic field lines spanning the terminator from day to night above the great impact basin of Utopia Planitia, a region largely free of crustal magnetic fields. A survey of the previous 26 orbits passing over a range of longitudes revealed similar signatures on seven orbits, with a mean potential drop (ΦMars) of 10.9 ± 0.8 V, suggestive that although trans-terminator electric fields of comparable strength are not ubiquitous, they may be common, at least at these northerly latitudes.
NASA Astrophysics Data System (ADS)
Sati, Hisham; Schreiber, Urs
2017-03-01
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie ( p + 1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie ( p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.
Supersymmetry in physics: an algebraic overview
Ramond, P.
1983-01-01
In 1970, while attempting to generalize the Veneziano model (string model) to include fermions, I introduced a new algebraic structure which turned out to be a graded Lie algebra; it was used as a spectrum-generating algebra. This approach was soon after generalized to include interactions, yielding a complete model of fermions and boson (RNS model). In an unrelated work in the Soviet Union, it was shown how to generalize the Poincare group to include fermionic charges. However it was not until 1974 that an interacting field theory invariant under the Graded Poincare group in 3 + 1 dimensions was built (WZ model). Supersymmetric field theories turned out to have less divergent ultraviolet behavior than non-supersymmetric field theories. Gravity was generalized to include supersymmetry, to a theory called supergravity. By now many interacting local field theories exhibiting supersymmetry have been built and studied from 1 + 1 to 10 + 1 dimensions. Supersymmetric local field theories in less than 9 + 1 dimensions, can be understood as limits of multilocal (string) supersymmetric theories, in 9 + 1 dimensions. On the other hand, graded Lie algebras have been used in non-relativistic physics as approximate symmetries of Hamiltonians. The most striking such use so far helps comparing even and odd nuclei energy levels. It is believed that graded Lie algebras can be used whenever paired and unpaired fermions excitations can coexist. In this overview of a tremendously large field, I will only survey finite graded Lie algebras and their representations. For non-relativistic applications, all of GLA are potentially useful, while for relativistic applications, only these which include the Poincare group are to be considered.
Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
NASA Astrophysics Data System (ADS)
Anguelova, Iana I.
2013-12-01
The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two such correspondences are well known: the types A and B (and their super extensions). As a main result of this paper we present a new boson-fermion correspondence of type D-A. Further, we define a new concept of twisted vertex algebra of order N, which generalizes super vertex algebra. We develop the bicharacter construction which we use for constructing classes of examples of twisted vertex algebras, as well as for deriving formulas for the operator product expansions, analytic continuations, and normal ordered products. By using the underlying Hopf algebra structure we prove general bicharacter formulas for the vacuum expectation values for two important groups of examples. We show that the correspondences of types B, C, and D-A are isomorphisms of twisted vertex algebras.
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
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,…
Conformal manifolds in four dimensions and chiral algebras
NASA Astrophysics Data System (ADS)
Buican, Matthew; Nishinaka, Takahiro
2016-11-01
Any { N }=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral algebra is a Virasoro algebra. In this note, we consider the chiral algebras associated with interacting { N }=2 SCFTs possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these conformal manifolds, we argue that the associated chiral algebras possess at least three generators. In addition, we show that there are examples of SCFTs realizing such a minimal chiral algebra: they are certain points on the conformal manifold obtained by considering the low-energy limit of type IIB string theory on the three complex-dimensional hypersurface singularity {x}13+{x}23+{x}33+α {x}1{x}2{x}3+{w}2=0. The associated chiral algebra is the { A }(6) theory of Feigin, Feigin, and Tipunin. As byproducts of our work, we argue that (i) a collection of isolated theories can be conformally gauged only if there is a SUSY moduli space associated with the corresponding symmetry current moment maps in each sector, and (ii) { N }=2 SCFTs with a≥slant c have hidden fermionic symmetries (in the sense of fermionic chiral algebra generators).
Current algebra formulation of M-theory based on E11 Kac-Moody algebra
NASA Astrophysics Data System (ADS)
Sugawara, Hirotaka
2017-02-01
Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac-Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the E11 Kac-Moody algebra that was shown recently1‑5 to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside E11, so that, by constructing the current algebra of E11, I obtain both internal gauge theory and gravity theory. The energy-momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein-Hilbert action.
The dayside open/closed field line boundary as seen from space- and ground-based instrumentation
NASA Astrophysics Data System (ADS)
Johnsen, M. G.; Lorentzen, D. A.
2012-03-01
In this paper we validate the method of Johnsen et al. (2012) for obtaining the cusp open/closed field line boundary (OCB) by the means of a single meridian scanning photometer (MSP). Three cases of conjugate measurements between the Longyearbyen MSP and the NOAA-16 satellite are presented. The satellite OCB as obtained by the energetic particle detectors carried onboard the NOAA-16 satellite is well co-located with the OCB as obtained by the ground-based MSP and well within the calculated uncertainties. We conclude that the method presented by Johnsen et al. (2012) for deriving the cusp OCB using a single MSP produces conscientious results.
NASA Astrophysics Data System (ADS)
Paech, Martin; Apel, Walter; Kalinowski, Eva; Jeckelmann, Eric
2014-12-01
We present a large-scale combinatorial-diagrammatic computation of high-order contributions to the strong-coupling Kato-Takahashi perturbation series for the Hubbard model in high dimensions. The ground-state energy of the Mott-insulating phase is determined exactly up to the 15th order in 1 /U . The perturbation expansion is extrapolated to infinite order and the critical behavior is determined using the Domb-Sykes method. We compare the perturbative results with two dynamical mean-field theory (DMFT) calculations using a quantum Monte Carlo method and a density-matrix renormalization group method as impurity solvers. The comparison demonstrates the excellent agreement and accuracy of both extrapolated strong-coupling perturbation theory and quantum Monte Carlo based DMFT, even close to the critical coupling where the Mott insulator becomes unstable.
Pseudo-Riemannian Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2008-08-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
NASA Astrophysics Data System (ADS)
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Accounting Equals Applied Algebra.
ERIC Educational Resources Information Center
Roberts, Sondra
1997-01-01
Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)
Montgomery, S.L.
1996-09-01
Deep-water carbonate channel reservoirs form important oil reservoirs along the toe of the Eastern Shelf of the Permian basin in west Texas. In northwestern Glasscock County, these `Wolfcamp` reservoirs are Leonardian (Early Permian) in age and define high-energy channels incised into surrounding carbonate detritus and basinal shale. Porous grain-flow material filling these channels, along with encasing detritus, was derived from the shallow shelf located six miles to the east. Reservoirs are in packstone and grainstone facies and have significant interparticle and moldic porosity. Relevant exploration began in the 1960s, but expanded slowly thereafter due to lack of success caused by complex patterns of channel occurrence. Results of a three-dimensional (3-D) seismic survey conducted in 1990 have greatly enhanced the identification and mapping of productive channels in the Powell Ranch field complex. Wells in this complex are capable of flowing 400-1200 bbl of oil per day, and have reserves ranging from 0.2 to 1.3 MBO. The new 3-D data have improved the relevant geologic model and dramatically increased rates of drilling success. Application of such data to this setting offers a potential model for other parts of the Permian basin.
ADA interpretative system for image algebra
NASA Astrophysics Data System (ADS)
Murillo, Juan J.; Wilson, Joseph N.
1992-06-01
An important research problem in image processing is to find appropriate tools to support algorithm development. There have been efforts to build algorithm development support systems for image algebra in several languages, but these systems still have the disadvantage of the time consuming algorithm development style associated with compilation-oriented programming. This paper starts with a description of the Run-Time Support Library (RTSL), which serves as the base for executing programs on both the Image Algebra Ada Translator (IAAT) and Image Algebra Ada Interpreter (IAAI). A presentation on the current status of IAAT and its capabilities is followed by a brief introduction to the utilization of the Image Display Manager (IDM) for image manipulation and analysis. We then discuss in detail the current development stage of IAAI and its relation with RTSL and IDM. The last section describes the design of a syntax-directed graphical user interface for IAAI. We close with an analysis of the current performance of IAAI, and future trends are discussed. Appendix A gives a brief introduction to Image Algebra (IA), and in Appendix B the reader is presented to the Image Algebra Ada (IAA) grammar.
Galitski, Victor
2011-07-15
We propose a Lie-algebraic duality approach to analyze nonequilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the paper utilizes a geometric Hilbert-space-invariant formulation of unitary time evolution, where a quantum Hamiltonian is viewed as a trajectory in an abstract Lie algebra, while the sought-after evolution operator is a trajectory in a dynamic group, generated by the algebra via exponentiation. The evolution operator is uniquely determined by the time-dependent dual generators that satisfy a system of differential equations, dubbed here dual Schroedinger-Bloch equations, which represent a viable alternative to the conventional Schroedinger formulation. These dual Schroedinger-Bloch equations are derived and analyzed on a number of specific examples. It is shown that deterministic dynamics of a closed classical dynamical system occurs as action of a symmetry group on a classical manifold and is driven by the same dual generators as in the corresponding quantum problem. This represents quantum-to-classical correspondence. In the second part of the paper, we further extend the Lie-algebraic approach to a wide class of interacting many-particle lattice models. A generalized Hubbard-Stratonovich transform is proposed and it is used to show that the thermodynamic partition function of a generic many-body quantum lattice model can be expressed in terms of traces of single-particle evolution operators governed by the dynamic Hubbard-Stratonovich fields. The corresponding Hubbard-Stratonovich dynamical systems are generally nonunitary, which yields a number of notable complications, including breakdown of the global exponential representation. Finally, we derive Hubbard-Stratonovich dynamical systems for the Bose-Hubbard model and a quantum spin model and use the Lie-algebraic approach to obtain new nonperturbative dual
Pc 3-4 Pulsations Near the Cusp: Latitude dependence near the open-closed field line boundary
NASA Astrophysics Data System (ADS)
Yeoman, T. K.; Wright, D. M.; Clausen, L. B.; Engebretson, M.; Lu, F.; Posch, J.; Lessard, M.; Kim, H.
2008-12-01
Dayside ground magnetometer records at high latitudes frequently show evidence of Pc 3-4 pulsations (f ~ 10-100 mHz) which originate in the ion foreshock upstream of the Earth's bow shock due to the interaction between reflected ions and the solar wind. Previous studies have noted increased Pc 3-4 wave power in the vicinity of the dayside cusp and inferred that the upstream waves gained entry via the cusp, although more recent studies have revealed a more complex picture. Here, we examine Pc3-4 wave power near local noon observed by search coil magnetometers at three closely-spaced stations on Svalbard. Three intervals are chosen when the upstream conditions are favourable for Pc3-4 generation, clear band-limited Pc3-4 wave power is observed near local noon, and an extended interval of HF radar backscatter indicative of the cusp is detected by the Hankasalmi SuperDARN radar. A stereo mode of radar operation is employed, such that 3 s time resolution is available on one radar beam, whilst the high latitude convection is revealed with 1 min. resolution. The location of the equatorward edge of the HF radar cusp may then be directly compared with the Pc3-4 wave power measured at three latitudes as the cusp migrates across the stations. The radar data show clear evidence of transient ionospheric flows and high spectral widths associated with field lines newly- opened by dayside reconnection processes, but no evidence of oscillations in the Pc3-4 frequency range. In the ground magnetic field a peak in Pc3-4 power is generally observed in the equatormost magnetometer, except when the cusp is significantly poleward of the stations, consistent with a peak in wave power ~4 degrees equatorward of the cusp, but suggesting a modest dependence of wave power with latitude on closed field lines When the cusp does move equatorward of the magnetometer stations the Pc3-4 power drops rapidly, and does so earliest at the most poleward magnetometer station, suggesting a sharp drop in
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Aprepro - Algebraic Preprocessor
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Towards Cohomology of Renormalization: Bigrading the Combinatorial Hopf Algebra of Rooted Trees
NASA Astrophysics Data System (ADS)
Broadhurst, D. J.; Kreimer, D.
The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated by an infinite set of primitive divergences. The Hopf algebra of undecorated rooted trees, ℌR, generated by a single primitive divergence, solves a universal problem in Hochschild cohomology. It has two nontrivial closed Hopf subalgebras: the cocommutative subalgebra ℌladder of pure ladder diagrams and the Connes-Moscovici noncocommutative subalgebra ℌCM of noncommutative geometry. These three Hopf algebras admit a bigrading by n, the number of nodes, and an index k that specifies the degree of primitivity. In each case, we use iterations of the relevant coproduct to compute the dimensions of subspaces with modest values of n and k and infer a simple generating procedure for the remainder. The results for ℌladder are familiar from the theory of partitions, while those for ℌCM involve novel transforms of partitions. Most beautiful is the bigrading of ℌR, the largest of the three. Thanks to Sloane's superseeker, we discovered that it saturates all possible inequalities. We prove this by using the universal Hochschild-closed one-cocycle B+, which plugs one set of divergences into another, and by generalizing the concept of natural growth beyond that entailed by the Connes-Moscovici case. We emphasize the yet greater challenge of handling the infinite set of decorations of realistic quantum field theory.
Spinor representations of affine Lie algebras
Frenkel, I. B.
1980-01-01
Let [unk] be an infinite-dimensional Kac-Moody Lie algebra of one of the types Dl+1(2), Bl(1), or Dl(1). These algebras are characterized by the property that an elimination of any endpoint of their Dynkin diagrams gives diagrams of types Bl or Dl of classical orthogonal Lie algebras. We construct two representations of a Lie algebra [unk], which we call spinor representations, following the analogy with the classical case. We obtain that every spinor representation is either irreducible or has two irreducible components. This provides us with an explicit construction of fundamental representations of [unk], two for the type Dl+1(2), three for Bl(1), and four for Dl(1). We note the profound connection of our construction with quantum field theory—in particular, with fermion fields. Comparing the character formulas of our representations with another construction of the fundamental representations of Kac-Moody Lie algebras of types Al(1), Dl(1), El(1), we obtain classical Jacobi identities and addition formulas for elliptic θ-functions. PMID:16592912
NASA Astrophysics Data System (ADS)
Burgon, R. P., Jr.; Sargent, S.; Zha, T.; Jia, X.
2015-12-01
Closed-path eddy covariance systems measure the flux of greenhouse gasses such as carbon dioxide, water vapor, and nitrous oxide. The challenge is to make accurate field measurements at sites around the world, even in extreme environmental conditions. Sites with dirty air present a particular challenge. Gas concentration measurements may be degraded as dust or debris is deposited on the optical windows in the sample cell. The traditional solution has been to add an in-line filter upstream of the sample cell to keep the windows clean. However, these filters clog over time and must be changed periodically. An in-line filter also acts as a mixing volume and in some cases limits the frequency response of the analyzer. A novel eddy-covariance system that includes a vortex air cleaner at the inlet has been developed and field tested. This new system eliminates the need for a traditional in-line filter to keep the sample cell windows clean. The new system reduces system maintenance and down time. Eddy covariance systems with the vortex intake were tested at several sites ranging from sites with extremely dirty urban air to sites with relatively clean mountain air, and in agricultural areas. These flux systems were monitoring either CO2 and H2O, or N2O. Results show that the closed-path eddy covariance systems with a vortex intake perform very well and require lower maintenance compared to similar systems with in-line filters.
Nagelmüller, Sebastian; Kirchgessner, Norbert; Yates, Steven; Hiltpold, Maya; Walter, Achim
2016-03-01
Leaf growth in monocot crops such as wheat and barley largely follows the daily temperature course, particularly under cold but humid springtime field conditions. Knowledge of the temperature response of leaf extension, particularly variations close to the thermal limit of growth, helps define physiological growth constraints and breeding-related genotypic differences among cultivars. Here, we present a novel method, called 'Leaf Length Tracker' (LLT), suitable for measuring leaf elongation rates (LERs) of cereals and other grasses with high precision and high temporal resolution under field conditions. The method is based on image sequence analysis, using a marker tracking approach to calculate LERs. We applied the LLT to several varieties of winter wheat (Triticum aestivum), summer barley (Hordeum vulgare), and ryegrass (Lolium perenne), grown in the field and in growth cabinets under controlled conditions. LLT is easy to use and we demonstrate its reliability and precision under changing weather conditions that include temperature, wind, and rain. We found that leaf growth stopped at a base temperature of 0°C for all studied species and we detected significant genotype-specific differences in LER with rising temperature. The data obtained were statistically robust and were reproducible in the tested environments. Using LLT, we were able to detect subtle differences (sub-millimeter) in leaf growth patterns. This method will allow the collection of leaf growth data in a wide range of future field experiments on different graminoid species or varieties under varying environmental or treatment conditions.
Kirchgessner, Norbert; Yates, Steven; Hiltpold, Maya; Walter, Achim
2016-01-01
Leaf growth in monocot crops such as wheat and barley largely follows the daily temperature course, particularly under cold but humid springtime field conditions. Knowledge of the temperature response of leaf extension, particularly variations close to the thermal limit of growth, helps define physiological growth constraints and breeding-related genotypic differences among cultivars. Here, we present a novel method, called ‘Leaf Length Tracker’ (LLT), suitable for measuring leaf elongation rates (LERs) of cereals and other grasses with high precision and high temporal resolution under field conditions. The method is based on image sequence analysis, using a marker tracking approach to calculate LERs. We applied the LLT to several varieties of winter wheat (Triticum aestivum), summer barley (Hordeum vulgare), and ryegrass (Lolium perenne), grown in the field and in growth cabinets under controlled conditions. LLT is easy to use and we demonstrate its reliability and precision under changing weather conditions that include temperature, wind, and rain. We found that leaf growth stopped at a base temperature of 0°C for all studied species and we detected significant genotype-specific differences in LER with rising temperature. The data obtained were statistically robust and were reproducible in the tested environments. Using LLT, we were able to detect subtle differences (sub-millimeter) in leaf growth patterns. This method will allow the collection of leaf growth data in a wide range of future field experiments on different graminoid species or varieties under varying environmental or treatment conditions. PMID:26818912
Iskra, S; McKenzie, R; Cosic, I
2011-11-01
Personal dosemeters can play an important role in epidemiological studies and in radiofrequency safety programmes. In this study, a Monte Carlo approach is used in conjunction with the finite difference time domain method to obtain distributions of the electric field strength close to a human body model in simulated realistic environments. The field is a proxy for the response of an ideal body-worn electric field dosemeter. A set of eight environments were modelled based on the statistics of Rayleigh, Rice and log-normal fading to simulate outdoor and indoor multipath exposures at 450, 900 and 2100 MHz. Results indicate that a dosemeter mounted randomly within 10-50 mm of the adult or child body model (torso region) will on average underestimate the spatially averaged value of the incident electric field strength by a factor of 0.52 to 0.74 over the frequencies of 450, 900 and 2100 MHz. The uncertainty in results, assessed at the 95 % confidence level (between the 2.5th and 97.5th percentiles) was largest at 2100 MHz and smallest at 450 MHz.
Constraint algebra for interacting quantum systems
NASA Astrophysics Data System (ADS)
Fubini, S.; Roncadelli, M.
1988-04-01
We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix. On leave from Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, I-27100 Pavia, Italy.
Weak Lie symmetry and extended Lie algebra
Goenner, Hubert
2013-04-15
The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).
Poisson and symplectic structures on Lie algebras. I
NASA Astrophysics Data System (ADS)
Alekseevsky, D. V.; Perelomov, A. M.
1997-06-01
The purpose of this paper is to describe a new class of Poisson and symplectic structures on Lie algebras. This gives a new class of solutions of the classical Yang-Baxter equation. The class of elementary Lie algebras is defined and the Poisson and symplectic structures for them are described. The algorithm is given for description of all closed 2-forms and of symplectic structures on any Lie algebra G, which is decomposed into semidirect sum of elementary subalgebras. Using these results we obtain the description of closed 2-forms and symplectic forms (if they exist) on the Borel subalgebra B(G) of semisimple Lie algebra G. As a byproduct, we get description of the second cohomology group H2( B( G)).
Algebraic mesh quality metrics
KNUPP,PATRICK
2000-04-24
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
A process algebra model of QED
NASA Astrophysics Data System (ADS)
Sulis, William
2016-03-01
The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.
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…
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
NASA Astrophysics Data System (ADS)
Dobrev, V. K.
2013-02-01
In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G ' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E 7(7) which is parabolically related to the CLA E 7(-25) , the parabolic subalgebras including E 6(6) and E 6(-26). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so( n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so( n - 1, 1) and its analogs so( p - 1, q - 1). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14) , the parabolic subalgebras including real forms of sl(6). We also give a formula for the number of representations in the main multiplets valid for CLAs and all algebras that are parabolically related to them. In all considered cases we give the main multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators. In the case of so( p, q) we give also the reduced multiplets. We should stress that the multiplets are given in the most economic way in pairs of shadow fields. Furthermore we should stress that the classification of all invariant differential operators includes as special cases all possible conservation laws and conserved currents, unitary or not.
NASA Astrophysics Data System (ADS)
Roytenberg, Dmitry
2007-11-01
A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.
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)
A Holistic Approach to Algebra.
ERIC Educational Resources Information Center
Barbeau, Edward J.
1991-01-01
Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)
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.
Wenzel, Jan; Wormit, Michael; Dreuw, Andreas
2014-10-05
Core-level excitations are generated by absorption of high-energy radiation such as X-rays. To describe these energetically high-lying excited states theoretically, we have implemented a variant of the algebraic-diagrammatic construction scheme of second-order ADC(2) by applying the core-valence separation (CVS) approximation to the ADC(2) working equations. Besides excitation energies, the CVS-ADC(2) method also provides access to properties of core-excited states, thereby allowing for the calculation of X-ray absorption spectra. To demonstrate the potential of our implementation of CVS-ADC(2), we have chosen medium-sized molecules as examples that have either biological importance or find application in organic electronics. The calculated results of CVS-ADC(2) are compared with standard TD-DFT/B3LYP values and experimental data. In particular, the extended variant, CVS-ADC(2)-x, provides the most accurate results, and the agreement between the calculated values and experiment is remarkable.
Comments on Higher-Spin Fields in Nontrivial Backgrounds
NASA Astrophysics Data System (ADS)
Rahman, Rakibur; Taronna, Massimo
We consider the free propagation of totally symmetric massive bosonic fields in nontrivial backgrounds. The mutual compatibility of the dynamical equations and constraints in flat space amounts to the existence of an Abelian algebra formed by the d'Alembertian, divergence and trace operators. The latter, along with the symmetrized gradient, symmetrized metric and spin operators, actually generate a bigger non-Abelian algebra, which we refer to as the "consistency" algebra. We argue that in nontrivial backgrounds, it is some deformed version of this algebra that governs the consistency of the system. This can be motivated, for example, from the theory of charged open strings in a background gauge field, where the Virasoro algebra ensures consistent propagation. For a gravitational background, we outline a systematic procedure of deforming the generators of the consistency algebra in order that their commutators close. We find that equalradii AdSp×Sq manifolds, for arbitrary p and q, admit consistent propagation of massive and massless fields, with deformations that include no higher-derivative terms but are non-analytic in the curvature. We argue that analyticity of the deformations for a generic manifold may call for the inclusion of mixed-symmetry tensor fields like in String Theory.
An algebra of reversible computation.
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.
NASA Astrophysics Data System (ADS)
Rath, N.; Onofri, M.; Barnes, D.; Romero, J.; the TAE Team
2015-11-01
The C-2U device has recently demonstrated sustainment of an advanced, beam-driven FRC over time scales longer than the characteristic times for confinement, fast ion slow-down, and wall current decay. In anticipation of further advances in plasma lifetime, we are developing feedback control techniques for major FRC parameters and resistive instabilities. The LamyRidge code solves the time-dependent extended MHD equations in axisymmetric geometry. In the Q2D code, LamyRidge is combined with a 3-D kinetic code that tracks fast ions and runs in parallel with LamyRidge. Periodically, the background fields in the kinetic code are updated from the MHD simulation and the averaged fast particle distribution is integrated into the fluid equations. Recently, we have added the capability to run Q2D simulations as subordinate processes in Simulink, giving us the ability to run non-linear, closed-loop simulations using control algorithms developed in Simulink. The same Simulink models can be exported to real-time targets (CPU or FPGA) to perform feedback control in experiments. We present closed-loop simulations of beam-driven FRCs under magnetically-actuated feedback control. Results for positionally unstable FRCs are compared with the predictions of a linearized rigid-plasma model. Plasmas predicted to be passively stabilized by the linear model are found to exhibit Alfvenic growth in several cases. Feedback gains predicted to be stabilizing in the linear model are generally found to be insufficient in non-linear simulations, and vice versa. Control of separatrix geometry is demonstrated.
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
Algebraic Thinking through Origami.
ERIC Educational Resources Information Center
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Spatial Operator Algebra for multibody system dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.
1992-01-01
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
NASA Astrophysics Data System (ADS)
Lai, Lifei; Wang, Jinxia; Wang, Hongtao; Bao, Mingdong
2017-01-01
The structures and properties of C-doped NiCr thin film as embedded thin film resistor (ETFR) materials were studied by closed-field, unbalanced magnetron sputtering method. The C-doped NiCr (NiCrC1) thin film had more stable electrical performance, better corrosion resistance, and higher hardness than NiCr thin film. The temperature coefficient of resistance (TCR) of NiCrC1 thin film deposited at room temperature (from 19.73 ppm/K to 173.7 ppm/K) was lower than that of NiCr thin film (from 157.8 ppm/K to 378.9 ppm/K), and the sheet resistor (154.25 Ω/Sq) was higher than that of NiCr thin film (62.84 Ω/Sq). The preferred orientations of C-doped NiCr thin film was Ni (111), while that of NiCr thin film was Ni (011). The carbon-doped NiCr thin film can reduce the defects and stress and change the preferred orientations. The dominant carbon in C-doped NiCr thin film had a graphite-like structure.
NASA Astrophysics Data System (ADS)
Parkinson, M. L.; Pinnock, M.; Dyson, P. L.; Devlin, J. C.
The comparatively low latitude of the Tasman International Geospace Environment Radar (TIGER) (147.2°E, 43.4°S, geographic; -54.6°Λ), a Southern Hemisphere HF SuperDARN radar, facilitates the observation of extensive backscatter from decametre-scale irregularities drifting in the auroral and polar cap ionosphere in the midnight sector. The radar often detects a persistent, sharp increase over ˜90 km of range in line-of-sight Doppler velocity spread, or spectral width, from <50 m s -1 at lower latitude to >200 m s -1 at higher latitude. It was previously shown that for moderately disturbed conditions in the pre-midnight sector, the location of the spectral width boundary (SWB) corresponds to the poleward edge of the auroral oval, as determined from energy spectra of precipitating particles measured on board Defense Meteorology Satellite Program satellites. This implies the radar SWB is a proxy for the open-closed magnetic field-line boundary (OCB) under these particular conditions. Here we investigate whether the radar SWB is aligned with the satellite OCB under a broader range of geomagnetic conditions including small to moderate substorms occurring in the pre- and post-magnetic midnight sectors. The behaviour of the SWB can be reconciled with the spatial and temporal variations of energetic particle precipitation throughout the substorm cycle.
A spatial operator algebra for manipulator modeling and control
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Kreutz, K.; Milman, M.
1988-01-01
A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.
Symmetric linear systems - An application of algebraic systems theory
NASA Technical Reports Server (NTRS)
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
Three-dimensional polarization algebra.
R Sheppard, Colin J; Castello, Marco; Diaspro, Alberto
2016-10-01
If light is focused or collected with a high numerical aperture lens, as may occur in imaging and optical encryption applications, polarization should be considered in three dimensions (3D). The matrix algebra of polarization behavior in 3D is discussed. It is useful to convert between the Mueller matrix and two different Hermitian matrices, representing an optical material or system, which are in the literature. Explicit transformation matrices for converting the column vector form of these different matrices are extended to the 3D case, where they are large (81×81) but can be generated using simple rules. It is found that there is some advantage in using a generalization of the Chandrasekhar phase matrix treatment, rather than that based on Gell-Mann matrices, as the resultant matrices are of simpler form and reduce to the two-dimensional case more easily. Explicit expressions are given for 3D complex field components in terms of Chandrasekhar-Stokes parameters.
Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.
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.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Said, R; Ahmed, W; Gracio, J
2010-04-01
In this study NiAl thin films have been deposited using closed field unbalanced magnetron sputtering Ion plating (CFUBMSIP). The influence of magnetron power has been investigated using dense and humongous NiAl compound targets onto stainless steel and glass substrates. Potential applications include tribological, electronic media and bond coatings in thermal barrier coatings system. Several techniques has been used to characterise the films including surface stylus profilometry, energy dispersive spectroscopy (EDAX), X-Ray diffraction (XRD) Composition analysis of the samples was carried out using VGTOF SIMS (IX23LS) and Atomic force microscopy (AFM). Scratch tester (CSM) combined with acoustic emission singles during loading in order to compare the coating adhesion. The acoustic emission signals emitted during the indentation process were used to determine the critical load, under which the film begins to crack and/or break off the substrate. The average thickness of the films was approximately 1 um. EDAX results of NiAl thin films coating with various magnetron power exhibited the near equal atomic% Ni:Al. The best result being obtained using 300 W and 400 W DC power for Ni and Al targets respectively. XRD revealed the presence of beta NiAl phase for all the films coatings. AFM analysis of the films deposited on glass substrates exhibited quite a smooth surface with surface roughness values in the nanometre range. CSM results indicate that best adhesion was achieved at 300 W for Ni, and 400 W for Al targets compared to sample other power values. SIMS depth profile showed a uniform distribution of the Ni and Al component from the surface of the film to the interface.
Oran, R.; Van der Holst, B.; Landi, E.; Jin, M.; Sokolov, I. V.; Gombosi, T. I.
2013-12-01
We describe, analyze, and validate the recently developed Alfvén Wave Solar Model, a three-dimensional global model starting from the top of the chromosphere and extending into interplanetary space (out to 1-2 AU). This model solves the extended, two-temperature magnetohydrodynamics equations coupled to a wave kinetic equation for low-frequency Alfvén waves. In this picture, heating and acceleration of the plasma are due to wave dissipation and to wave pressure gradients, respectively. The dissipation process is described by a fully developed turbulent cascade of counterpropagating waves. We adopt a unified approach for calculating the wave dissipation in both open and closed magnetic field lines, allowing for a self-consistent treatment in any magnetic topology. Wave dissipation is the only heating mechanism assumed in the model; no geometric heating functions are invoked. Electron heat conduction and radiative cooling are also included. We demonstrate that the large-scale, steady state (in the corotating frame) properties of the solar environment are reproduced, using three adjustable parameters: the Poynting flux of chromospheric Alfvén waves, the perpendicular correlation length of the turbulence, and a pseudoreflection coefficient. We compare model results for Carrington rotation 2063 (2007 November-December) with remote observations in the extreme-ultraviolet and X-ray ranges from the Solar Terrestrial Relations Observatory, Solar and Heliospheric Observatory, and Hinode spacecraft and with in situ measurements by Ulysses. The results are in good agreement with observations. This is the first global simulation that is simultaneously consistent with observations of both the thermal structure of the lower corona and the wind structure beyond Earth's orbit.
Absence of the Gribov ambiguity in a special algebraic gauge
NASA Astrophysics Data System (ADS)
Raval, Haresh
2016-11-01
The Gribov ambiguity exists in various gauges except algebraic gauges. However in general, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We show that nontrivial copies can not occur in this gauge. We then provide an example of spherically symmetric gauge field configuration and prove that with a proper boundary condition on the configuration, this gauge removes the ambiguity on a compact manifold S^3.
Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras
NASA Astrophysics Data System (ADS)
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.
2016-10-01
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
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.
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Beyond the Schwinger boson representation of the su(2)-algebra
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Providência, Constança; da Providência, João; Yamamura, Masatoshi
2015-04-01
With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors [Y. Tsue et al., Prog. Theor. Exp. Phys. 2013, 103D04 (2013)]. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra, which is also based on two kinds of bosons. It is proved that this new boson representation obeys the su(2)-algebra in a certain subspace in the whole boson space constructed by the Schwinger boson representation of the su(1,1)-algebra. This representation may be suitable for describing the time dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebras, various types of time evolution of a simple boson system are investigated.
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
Applications of algebraic grid generation
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
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…
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…
Zhai Hui; Zhou Fei
2005-07-01
We investigate the Zeeman-field-driven quantum phase transitions between singlet spin liquids and algebraically ordered O(2) nematic spin liquids of spin-one bosons in one-dimensional optical lattices. We find that the critical behavior is characterized by condensation of hardcore bosons instead of ideal magnons in high-dimensional lattices. Critical exponents are strongly renormalized by hardcore interactions and critical states are equivalent to the free Fermion model up to the Friedel oscillations. We also find that the algebraically ordered nematic spin liquids close to critical points are fully characterized by the Luttinger-liquid dynamics with Luttinger-liquid parameters magnetically tunable. The Bethe ansatz solution has been applied to determine the critical magnetization and nematic correlations.
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…
New infinite-dimensional algebras, sine brackets, and SU (infinity)
Zachos, C.K.; Fairlie, D.B.
1989-01-01
We investigate the infinite dimensional algebras we have previously introduced, which involve trigonometric functions in their structure constants. We find a realization for them which provides a basis-independent formulation, identified with the algebra of sine brackets. A special family of them, the cyclotomic ones, contain SU(N) as invariant subalgebras. In this basis, it is evident by inspection that the algebra of SU(infinity) is equivalent to the centerless algebra of SDiff/sub 0/ on two-dimensional manifolds. Gauge theories of SU(infinity) are thus simply reformulated in terms of surface (sheet) coordinates. Spacetime-independent configurations of their gauge fields describe strings through the quadratic Schild action. 11 refs.
Statecharts Via Process Algebra
NASA Technical Reports Server (NTRS)
Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance
1999-01-01
Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics
Algebraic isomorphism in two-dimensional anomalous gauge theories
Carvalhaes, C.G.; Natividade, C.P.
1997-08-01
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
Viterbi/algebraic hybrid decoder
NASA Technical Reports Server (NTRS)
Boyd, R. W.; Ingels, F. M.; Mo, C.
1980-01-01
Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.
Online Algebraic Tools for Teaching
ERIC Educational Resources Information Center
Kurz, Terri L.
2011-01-01
Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)
ERIC Educational Resources Information Center
1997
Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…
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.
Linear algebra and image processing
NASA Astrophysics Data System (ADS)
Allali, Mohamed
2010-09-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty.
Linear Algebra and Image Processing
ERIC Educational Resources Information Center
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…
ERIC Educational Resources Information Center
Buerman, Margaret
2007-01-01
Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
On the Lie Symmetry Algebras of the Stationary Schrödinger and Pauli Equations
NASA Astrophysics Data System (ADS)
Boldyreva, M. N.; Magazev, A. A.
2017-02-01
A general method for constructing first-order symmetry operators for the stationary Schrödinger and Pauli equations is proposed. It is proven that the Lie algebra of these symmetry operators is a one-dimensional extension of some subalgebra of an e(3) algebra. We also assemble a classification of stationary electromagnetic fields for which the Schrödinger (or Pauli) equation admits a Lie algebra of first-order symmetry operators.
Generalizing the Connes Moscovici Hopf algebra to contain all rooted trees
NASA Astrophysics Data System (ADS)
Agarwala, Susama; Delaney, Colleen
2015-04-01
This paper defines a generalization of the Connes-Moscovici Hopf algebra, H ( 1 ) , that contains the entire Hopf algebra of rooted trees. A relationship between the former, a much studied object in non-commutative geometry, and the latter, a much studied object in perturbative quantum field theory, has been established by Connes and Kreimer. The results of this paper open the door to study the cohomology of the Hopf algebra of rooted trees.
Applied Mathematical Modules for Use in a Linear Algebra Service Course
1990-05-01
are obsolete. SECURITY CLASSIFICATION O; THIS PAGE APPLIED MATHEMATICAL MODULES FOR USE IN A LINEAR ALGEBRA SERVICE COURSE SHIRLEY JO ZANDER A...MODULES FOR USE IN A LINEAR ALGEBRA SERVICE COURSE Shirley Jo Zander 272 Pages May. 1990 . The purpose of this study was to develop several applications...which could be used. to tupplemenfan undergradate course in linear algebra for non-mathematics majors. These applications were drawn from the fields
Generalizing the Connes Moscovici Hopf algebra to contain all rooted trees
Agarwala, Susama; Delaney, Colleen
2015-04-15
This paper defines a generalization of the Connes-Moscovici Hopf algebra, H(1), that contains the entire Hopf algebra of rooted trees. A relationship between the former, a much studied object in non-commutative geometry, and the latter, a much studied object in perturbative quantum field theory, has been established by Connes and Kreimer. The results of this paper open the door to study the cohomology of the Hopf algebra of rooted trees.
Boolean Operations with Prism Algebraic Patches
Bajaj, Chandrajit; Paoluzzi, Alberto; Portuesi, Simone; Lei, Na; Zhao, Wenqi
2009-01-01
In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C1-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation. PMID:21516262
Jarboe, T. R.; Nelson, B. A.; Sutherland, D. A.
2015-07-15
An analysis of imposed dynamo current drive (IDCD) [T.R. Jarboe et al., Nucl. Fusion 52 083017 (2012)] reveals: (a) current drive on closed flux surfaces seems possible without relaxation, reconnection, or other flux-surface-breaking large events; (b) the scale size of the key physics may be smaller than is often computationally resolved; (c) helicity can be sustained across closed flux; and (d) IDCD current drive is parallel to the current which crosses the magnetic field to produce the current driving force. In addition to agreeing with spheromak data, IDCD agrees with selected tokamak data.
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)
On central ideals of finitely generated binary (-1,1)-algebras
Pchelintsev, S V
2002-04-30
In 1975 the author proved that the centre of a free finitely generated (-1,1)-algebra contains a non-zero ideal of the whole algebra. Filippov proved that in a free alternative algebra of rank {>=}4 there exists a trivial ideal contained in the associative centre. Il'tyakov established that the associative nucleus of a free alternative algebra of rank 3 coincides with the ideal of identities of the Cayley-Dickson algebra. In the present paper the above-mentioned theorem of the author is extended to free finitely generated binary (-1,1)-algebras. Theorem. The centre of a free finitely generated binary (-1,1)-algebra of rank {>=}3 over a field of characteristic distinct from 2 and 3 contains a non-zero ideal of the whole algebra. As a by-product, we shall prove that the T-ideal generated by the function (z,x,(x,x,y)) in a free binary (-1,1)-algebra of finite rank is soluble. We deduce from this that the basis rank of the variety of binary (-1,1)-algebras is infinite.
NASA Astrophysics Data System (ADS)
Geng, J.; Zhang, H.; Li, C.; Zhang, X.; Shen, B.; Coombs, T. A.
2017-03-01
High T c superconducting (HTS) coils are ideal candidates in the use of high field magnets. HTS coils carrying a direct current, however, suffer a non-negligible loss when they are exposed to an external AC magnetic field. Although this phenomenon is well known, no study concerning AC magnetic field angular dependence of direct current decay has ever been shown. In this work, we experimentally investigate the direct current decay characteristics in a closed double pancake coil made of a YBCO coated conductor under external AC field. AC field of different angles with respect to the coil plane is applied. Results show that the current decay rate presents a strong angular dependence. The fastest decay occurs when the field is parallel to the coil plane, in which case the surface of the tape in the outermost layer experiences most flux variation. To reduce the decay rate, we propose wrapping superconducting tapes around the outermost layer of the coil to shield external AC field. This method significantly reduces direct current decay rate under parallel field, without affecting the perpendicular self-field of the coil.
A New Braid-like Algebra for Baxterisation
NASA Astrophysics Data System (ADS)
Crampe, N.; Frappat, L.; Ragoucy, E.; Vanicat, M.
2017-01-01
We introduce a new Baxterisation for R-matrices that depend separately on two spectral parameters. The Baxterisation is based on a new algebra, close to but different from the braid group. We study representations of this new algebra on the vector space {(C^m)^{⊗ n}}, when the generators act locally. The ones for {m=2} are completely classified. We also introduce some representations for generic m: they allow us to recover the R-matrix of the multi-species generalization of the totally asymmetric simple exclusion process with different hopping rates.
NASA Technical Reports Server (NTRS)
Wolf, S. A.; Gubser, D. U.; Cox, J. E.
1978-01-01
A general formula is given for the longitudinal shielding effectiveness of N closed concentric cylinders. The use of these equations is demonstrated by application to the design of magnetic shields for hydrogen maser atomic clocks. Examples of design tradeoffs such as size, weight, and material thickness are discussed. Experimental results on three sets of shields fabricated by three manufacturers are presented. Two of the sets were designed employing the techniques described. Agreement between the experimental results and the design calculations is then demonstrated.
Quantum algebra of N superspace
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-08-15
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Investigating Teacher Noticing of Student Algebraic Thinking
ERIC Educational Resources Information Center
Walkoe, Janet Dawn Kim
2013-01-01
Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…
Heiser, J.H.; Dwyer, B.
1997-09-01
The primary objective of this project was to develop and demonstrate the installation and measure the performance of a close-coupled barrier for the containment of subsurface waste or contaminant migration. A close-coupled barrier is produced by first installing a conventional, low-cost, cement-grout containment barrier followed by a thin lining of a polymer grout. The resultant barrier is a cement-polymer composite that has economic benefits derived from the cement and performance benefits from the durable and resistant polymer layer. The technology has matured from a regulatory investigation of the issues concerning the use of polymers to laboratory compatibility and performance measurements of various polymer systems to a pilot-scale, single column injection at Sandia to full-scale demonstration. The feasibility of the close-coupled barrier concept was proven in a full-scale cold demonstration at Hanford, Washington and then moved to the final stage with a full-scale demonstration at an actual remediation site at Brookhaven National Laboratory (BNL). At the Hanford demonstration the composite barrier was emplaced around and beneath a 20,000 liter tank. The secondary cement layer was constructed using conventional jet grouting techniques. Drilling was completed at a 45{degree} angle to the ground, forming a cone-shaped barrier. The primary barrier was placed by panel jet-grouting with a dual-wall drill stem using a two part polymer grout. The polymer chosen was a high molecular weight acrylic. At the BNL demonstration a V-trough barrier was installed using a conventional cement grout for the secondary layer and an acrylic-gel polymer for the primary layer. Construction techniques were identical to the Hanford installation. This report summarizes the technology development from pilot- to full-scale demonstrations and presents some of the performance and quality achievements attained.
Structured adaptive grid generation using algebraic methods
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.
1993-01-01
The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
Computing Matrix Representations of Filiform Lie Algebras
NASA Astrophysics Data System (ADS)
Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.
In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.
Cartooning in Algebra and Calculus
ERIC Educational Resources Information Center
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
GCD, LCM, and Boolean Algebra?
ERIC Educational Resources Information Center
Cohen, Martin P.; Juraschek, William A.
1976-01-01
This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Coherent States for Hopf Algebras
NASA Astrophysics Data System (ADS)
Škoda, Zoran
2007-07-01
Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.
Multiplier operator algebras and applications
Blecher, David P.; Zarikian, Vrej
2004-01-01
The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
Duval, B.; Cramez, C. ); Figuera, J. ); Lander, R. ); Hernandez, G. )
1993-02-01
About 10 billion bbl of recoverable oil have been found in these three fields for which the petroleum generating subsystem is very similar. The potential source rocks are the organic sediments associated with the major downlap surface of the post-Pangea continental encroachment sedimentary cycle, i.e., MFS 91, 5 Ma (La Luna formation). However, the concentrating physico-chemical petroleum subsystem is quite different. The El Furrial/Musipan field is associated with a Tertiary foredeep basin overlying a generating Atlantic type passive margin. On the other hand, Cusiana and Ceuta fields are associated with a Tertiary foredeep basin developed over a generating back-arc basin. The different stacking of sedimentary basins controls the migration/entrapment petroleum subsystem. In El Furrial/Musipan, decollement surfaces and their associated thrusts are predominant whereas, in Ceuta and Cusiana the majority of compressional structures are created by tectonic inversions. These tectonic settings create different petroleum systems: (a) supercharged with low impedance and lateral drainage in El Furrial/Musipan, (b) normally charged with high impedance and vertically drained in Ceuta and Cusiana area. Each case requires appropriated exploration approaches.
Bialgebra deformations and algebras of trees
NASA Technical Reports Server (NTRS)
Grossman, Robert; Radford, David
1991-01-01
Let A denote a bialgebra over a field k and let A sub t = A((t)) denote the ring of formal power series with coefficients in A. Assume that A is also isomorphic to a free, associative algebra over k. A simple construction is given which makes A sub t a bialgebra deformation of A. In typical applications, A sub t is neither commutative nor cocommutative. In the terminology of Drinfeld, (1987), A sub t is a quantum group. This construction yields quantum groups associated with families of trees.
Novikov algebras with associative bilinear forms
NASA Astrophysics Data System (ADS)
Zhu, Fuhai; Chen, Zhiqi
2007-11-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.
NASA Astrophysics Data System (ADS)
Peters, A. D.; Jaffé, C.; Gao, J.; Delos, J. B.
1997-07-01
In the preceding paper, we showed that the semiclassical approximation diverges at a bifurcation, and that this divergence coincides with the passage of a focused cusp through the origin. Here we obtain a wave function in the vicinity of this cusp, and we use that wave function to eliminate the divergences in the photodetachment cross section. To describe the focused cusp, we first discuss the wave function of an ordinary two-dimensional (nonfocused) cusp. This wave function is known as a Pearcey function, and it has been studied extensively. Then we show how the formulas that lead to the Pearcey function have to be modified to describe a cylindrically focused cusp. The resulting wave function turns out to be given by an integral of Fresnel type containing within it a cylindrical Bessel function. This wave function is used to derive a formula for the photodetachment cross section near a bifurcation. That formula is a simple closed-form expression containing a Fresnel integral. Comparison with exact quantum calculations shows that this corrected-semiclassical formula is quite accurate.
Duquenne, Philippe; Simon, Xavier; Demange, Valérie; Harper, Martin; Wild, Pascal
2015-05-01
A set of 270 bioaerosol samples was taken from 15 composting facilities using polystyrene closed-face filter cassettes (CFCs). The objective was to measure the quantity of endotoxin deposits on the inner surfaces of the cassettes (sometimes referred to as 'wall deposits'). The results show that endotoxins are deposited on the inner surfaces of the CFCs through sampling and/or handling of samples. The quantity of endotoxins measured on inner surfaces range between 0.05 (the limit of detection of the method) and 3100 endotoxin units per cassette. The deposits can represent a large and variable percentage of the endotoxins sampled. More than a third of the samples presented a percentage of inner surface deposits >40% of the total quantity of endotoxins collected (filter + inner surfaces). Omitting these inner surface deposits in the analytical process lead to measurement errors relative to sampling all particles entering the CFC sampler, corresponding to a developing consensus on matching the inhalable particulate sampling convention. The result would be underestimated exposures and could affect the decision as to whether or not a result is acceptable in comparison to airborne concentration limits defined in terms of the inhalability convention. The results of this study suggest including the endotoxins deposited on the inner surfaces of CFCs during analysis. Further researches are necessary to investigate endotoxin deposits on the inner cassette surfaces in other working sectors.
NASA Astrophysics Data System (ADS)
Rubinstein, Marcos; Uman, Martin A.; Thomson, Ewen M.; Medelius, Pedro J.
1991-08-01
Measurements were characterized of simultaneous vertical electric fields and voltages induced at both ends of a 448 m overhead power line by artificially initiated lightning return strokes. The lightning discharges struck ground about 20 m from one end of the line. The measured line voltages could be grouped into two categories: those in which multiple, similarly shaped, evenly spaced pulses were observed, which are called oscillatory; and those dominated by a principal pulse with subsidiary oscillations of much smaller amplitude, which are called impulsive. Voltage amplitudes range from tens of kilovolts for oscillatory voltages to hundreds of kilovolts for impulsive voltages.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
Cube-Type Algebraic Attacks on Wireless Encryption Protocols
2009-09-01
15. NUMBER OF PAGES 99 14 . SUBJECT TERMS Wireless Security, Cryptanalysis, Boolean Functions, Algebraic Attacks, Correlation Attacks, Cube...Correspondence of the Finite Field....... 12 3. Boolean Function .................................................................. 14 4. Hamming...a a a a ; continue in that fashion up to the element where there is repetition ( 7a ). 14 3. Boolean Function Definition 2.6: A Boolean
Undergraduate Mathematics Students' Emotional Experiences in Linear Algebra Courses
ERIC Educational Resources Information Center
Martínez-Sierra, Gustavo; García-González, María del Socorro
2016-01-01
Little is known about students' emotions in the field of Mathematics Education that go beyond students' emotions in problem solving. To start filling this gap this qualitative research has the aim to identify emotional experiences of undergraduate mathematics students in Linear Algebra courses. In order to obtain data, retrospective focus group…
Kac-Moody Algebra for Two Dimensional Principal Chiral Models
NASA Astrophysics Data System (ADS)
Chou, Kuang-Chao; Song, Xing-Chang
A Darboux transformation depending on single continuous parameter t is constructed for a principal chiral field. The transformation forms a nonlinear representation of the group for any fixed value of t. Part of the kernel in the Riemann-Hilbert transform is shown to be related to the Darboux transformation with its generators forming a Kac-Moody algebra. Conserved currents associated with the Kac-Moody algebra of the linearized equations and the Nöether current for the group transformations with fixed value of t are obtained.
Surface charge algebra in gauge theories and thermodynamic integrability
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Compère, Geoffrey
2008-04-01
Surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius' theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Comparison with Hamiltonian and covariant phase space methods is made. All approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context.
NASA Astrophysics Data System (ADS)
Wogau-Chong, K.; Bohnel, H.; Aranda Gomez, J.
2009-05-01
The Sierra the Aguachile is a Miocene volcanic sequence located in the SE of Chihuahua State NW of the Camargo volcanic field and belongs to the Agua Mayo Group, which unconformably overlays Mesozoic calcareous units. The Sierra de Aguachile sequence defines a structure that may be interpreted as a plunging fold, which could be the result of a reactivation of the San Marcos Fault. This major fault is well known more to the east but may extend into the study area where it would be covered by the younger volcanic sequences; its main activity has been reported to be during the the Neocomian with reactivation phases in the Paleogene and Miocene. To test if the observed structure is the result of a tectonic deformation that happened after the emplacement of the volcanic sequence, a paleomagnetic study was carried out. A total of 14 sites were sampled from different parts of the structure, all in the capping ignimbrite layers. Site mean directions were determined using AF demagnetization. The fold test was applied to analyze if the remanence was acquired in situ or before the proposed folding. Precision parameters k before and after application of the tectonic corrections are 25.38 and 31.43, respectively. This indicates that the Sierra de Aguachile indeed was folded after emplacement of the ignimbrites, which restricts the age of the corresponding tectonic event to be younger than 31.3 +/- 0.7 Ma. Due to the gentle folding though, the difference in precision parameters is not significant at the 95% probability level.
Longman, M.W.
1996-10-01
The Lower Mississippian Lodgepole carbonate buildup reservoir at Dickinson Field in Stark County, North Dakota, has been widely reported as being a Waulsortian (or Waulsortian-like) mound. The term {open_quotes}Waulsortian mound{close_quotes} is used for a variety of Early Mississippian carbonate buildups that share a number of features including an abundance of carbonate mud, a {open_quotes}framework{close_quotes} of organisms such as fenestrate bryozoans and crinoids that tended to trap or baffle sediment, and a general absence of marine-cemented reef framework. Although the age of the Lodgepole mound at Dickinson Field qualifies it to be a Waulsortian mound, petrographic study of cores reveals that the reservoir rocks are quite unlike those in true Waulsortian mounds. Instead of being dominated by carbonate mud, the Lodgepole mound core is dominated by marine cement. Furthermore, ostracods and microbial limestones are common in the mound core where they occur with crinoid debris and small amounts of bryozoan, coral, and brachiopod debris. The abundant microbial limestones and marine cement indicate that the Dickinson mound formed as a lithified reef on the sea floor rather than as a Waulsortian mud mound. The microbial limestones, marine cement, and common ostracods in the mount core, and the fact that the mound nucleated almost directly o top of the Bakken Shale, suggest that the Dickinson Lodgepole mound formed at the site of a submarine spring and gas seep.
Colored Quantum Algebra and Its Bethe State
NASA Astrophysics Data System (ADS)
Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun
2014-12-01
We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.
Using Number Theory to Reinforce Elementary Algebra.
ERIC Educational Resources Information Center
Covillion, Jane D.
1995-01-01
Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
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.
Symmetry algebras of linear differential equations
NASA Astrophysics Data System (ADS)
Shapovalov, A. V.; Shirokov, I. V.
1992-07-01
The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.
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.
Applications of Algebraic Logic and Universal Algebra to Computer Science
1989-06-21
conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords
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…
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…
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…
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…
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…
Embedding Algebraic Thinking throughout the Mathematics Curriculum
ERIC Educational Resources Information Center
Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph
2005-01-01
This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…
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"…
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…
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…
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…
Cyclic homology for Hom-associative algebras
NASA Astrophysics Data System (ADS)
Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan
2015-12-01
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.
Mastering algebra retrains the visual system to perceive hierarchical structure in equations.
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.
Aspects of QCD current algebra on a null plane
NASA Astrophysics Data System (ADS)
Beane, S. R.; Hobbs, T. J.
2016-09-01
Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabibbo-Radicati and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.
Carry Groups: Abstract Algebra Projects
ERIC Educational Resources Information Center
Miller, Cheryl Chute; Madore, Blair F.
2004-01-01
Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.
Algebra, Home Mortgages, and Recessions
ERIC Educational Resources Information Center
Mariner, Jean A. Miller; Miller, Richard A.
2009-01-01
The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…
Exploring Algebraic Misconceptions with Technology
ERIC Educational Resources Information Center
Sakow, Matthew; Karaman, Ruveyda
2015-01-01
Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…
Easing Students' Transition to Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2006-01-01
Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…
Algebra for All. Research Brief
ERIC Educational Resources Information Center
Bleyaert, Barbara
2009-01-01
The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless…
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
Inequalities, Assessment and Computer Algebra
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…
Adventures in Flipping College Algebra
ERIC Educational Resources Information Center
Van Sickle, Jenna
2015-01-01
This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…
Elementary Algebra Connections to Precalculus
ERIC Educational Resources Information Center
Lopez-Boada, Roberto; Daire, Sandra Arguelles
2013-01-01
This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
Weaving Geometry and Algebra Together
ERIC Educational Resources Information Center
Cetner, Michelle
2015-01-01
When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…
Algebraic Activities Aid Discovery Lessons
ERIC Educational Resources Information Center
Wallace-Gomez, Patricia
2013-01-01
After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…
Teachers' Understanding of Algebraic Generalization
NASA Astrophysics Data System (ADS)
Hawthorne, Casey Wayne
Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive
Lie algebraic methods for particle tracking calculations
Douglas, D.R.; Dragt, A.J.
1983-08-01
A study of the nonlinear stability of an accelerator or storage ring lattice typically includes particle tracking simulations. Such simulations trace rays through linear and nonlinear lattice elements by numerically evaluating linear matrix or impulsive nonlinear transformations. Using the mathematical tools of Lie groups and algebras, one may construct a formalism which makes explicit use of Hamilton's equations and which allows the description of groups of linear and nonlinear lattice elements by a single transformation. Such a transformation will be exactly canonical and will describe finite length linear and nonlinear elements through third (octupole) order. It is presently possible to include effects such as fringing fields and potentially possible to extend the formalism to include nonlinearities of higher order, multipole errors, and magnet misalignments. We outline this Lie algebraic formalism and its use in particle tracking calculations. A computer code, MARYLIE, has been constructed on the basis of this formalism. We describe the use of this program for tracking and provide examples of its application. 6 references, 3 figures.
On special classes of n-algebras
NASA Astrophysics Data System (ADS)
Vainerman, L.; Kerner, R.
1996-05-01
We define n-algebras as linear spaces on which the internal composition law involves n elements: m:V⊗n■V. It is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics. Using the notion of a commutant of two subalgebras of an n-algebra, we distinguish certain classes of n-algebras with reasonable properties: semisimple, Abelian, nilpotent, solvable. We also consider a few examples of n-algebras of different types, and show their properties.
Detorakis, Georgios Is.; Chaillet, Antoine; Palfi, Stéphane; Senova, Suhan
2015-01-01
Several disorders are related to pathological brain oscillations. In the case of Parkinson's disease, sustained low-frequency oscillations (especially in the β-band, 13–30 Hz) correlate with motor symptoms. It is still under debate whether these oscillations are the cause of parkinsonian motor symptoms. The development of techniques enabling selective disruption of these β-oscillations could contribute to the understanding of the underlying mechanisms, and could be exploited for treatments. A particularly appealing technique is Deep Brain Stimulation (DBS). With clinical electrical DBS, electrical currents are delivered at high frequency to a region made of potentially heterogeneous neurons (the subthalamic nucleus (STN) in the case of Parkinson's disease). Even more appealing is DBS with optogenetics, which is until now a preclinical method using both gene transfer and deep brain light delivery and enabling neuromodulation at the scale of one given neural network. In this work, we rely on delayed neural fields models of STN and the external Globus Pallidus (GPe) to develop, theoretically validate and test in silico a closed-loop stimulation strategy to disrupt these sustained oscillations with optogenetics. First, we rely on tools from control theory to provide theoretical conditions under which sustained oscillations can be attenuated by a closed-loop stimulation proportional to the measured activity of STN. Second, based on this theoretical framework, we show numerically that the proposed closed-loop stimulation efficiently attenuates sustained oscillations, even in the case when the photosensitization effectively affects only 50% of STN neurons. We also show through simulations that oscillations disruption can be achieved when the same light source is used for the whole STN population. We finally test the robustness of the proposed strategy to possible acquisition and processing delays, as well as parameters uncertainty. PMID:26217171
Chen Famin; Wu Yongshi
2010-11-15
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
A geometric formulation of exceptional field theory
NASA Astrophysics Data System (ADS)
du Bosque, Pascal; Hassler, Falk; Lüst, Dieter; Malek, Emanuel
2017-03-01
We formulate the full bosonic SL(5) exceptional field theory in a coordinateinvariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with SL(5) × ℝ +-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the SL(5) × ℝ +-structure is not locally flat.
Deformed Kac Moody and Virasoro algebras
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.
2007-07-01
Whenever the group {\\bb R}^n acts on an algebra {\\cal A} , there is a method to twist \\cal A to a new algebra {\\cal A}_\\theta which depends on an antisymmetric matrix θ (θμν = -θνμ = constant). The Groenewold-Moyal plane {\\cal A}_\\theta({\\bb R}^{d+1}) is an example of such a twisted algebra. We give a general construction to realize this twist in terms of {\\cal A} itself and certain 'charge' operators Qμ. For {\\cal A}_\\theta({\\bb R}^{d+1}), Q_\\mu are translation generators. This construction is then applied to twist the oscillators realizing the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have an implication for statistics as well.
Spatial operator algebra framework for multibody system dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Jain, Abhinandan; Kreutz, K.
1989-01-01
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
ERIC Educational Resources Information Center
Boyles, Nancy
2013-01-01
"A significant body of research links the close reading of complex text--whether the student is a struggling reader or advanced--to significant gains in reading proficiency and finds close reading to be a key component of college and career readiness" (Partnership for Assessment of Readiness for College and Careers, 2011, p. 7). When the author…
NASA Astrophysics Data System (ADS)
Shi, Yongjing; Long, Siyuan; Yang, Shicai; Pan, Fusheng
2008-09-01
In this paper, a series of multi-layer hard coating system of CrTiAlN has been prepared by closed-field unbalanced magnetron sputtering ion plating (CFUBMSIP) technique in a gas mixture of Ar + N 2. The coatings were deposited onto AZ31 Mg alloy substrates. During deposition step, technological temperature and metallic atom concentration of coatings were controlled by adjusting the currents of different metal magnetron targets. The nitrogen level was varied by using the feedback control of plasma optical emission monitor (OEM). The structural, mechanical and tribological properties of coatings were characterized by means of X-ray photoelectron spectrometry, high-resolution transmission electron microscope, field emission scanning electron microscope (FESEM), micro-hardness tester, and scratch and ball-on-disc tester. The experimental results show that the N atomic concentration increases and the oxide on the top of coatings decreases; furthermore the modulation period and the friction coefficient decrease with the N 2 level increasing. The outstanding mechanical property can be acquired at medium N 2 level, and the CrTiAlN coatings on AZ31 Mg alloy substrates outperform the uncoated M42 high speed steel (HSS) and the uncoated 316 stainless steel (SS).
The elliptic quantum algebra Aq,p(sln∧) and its bosonization at level one
NASA Astrophysics Data System (ADS)
Fan, Heng; Hou, Bo-yu; Shi, Kang-jie; Yang, Wen-li
1998-09-01
We extend the work of Foda et al. and propose an elliptic quantum algebra Aq,p(sln∧). Similar to the case of Aq,p(sl2∧), our presentation of the algebra is based on the relation RLL=LLR*, where R and R* are Zn symmetric R matrices with the elliptic moduli chosen differently, and a scalar factor is also involved. With the help of the results obtained by Asai et al., we realize type I and type II vertex operators in terms of bosonic free fields for the Zn symmetric Belavin model. We also give a bosonization for the elliptic quantum algebra Aq,p(sln∧) at level one.
NASA Astrophysics Data System (ADS)
Dixon, P.; MacDonald, E. A.; Funsten, H. O.; Glocer, A.; Grande, M.; Kletzing, C.; Larsen, B. A.; Reeves, G.; Skoug, R. M.; Spence, H.; Thomsen, M. F.
2015-08-01
The twin Van Allen Probes spacecraft witnessed a series of lobe encounters between 0200 and 0515 UT on 14 November 2012. Although lobe entry had been observed previously by other spacecraft, the two Van Allen Probe spacecraft allow us to observe the motion of the boundary for the first time. Moreover, this event is unique in that it consists of a series of six quasi-periodic lobe entries. The events occurred on the dawn flank between 4 and 6.6 local time and at altitudes between 5.6 and 6.2 RE. During the events Dst dropped to less than -100nT with the IMF being strongly southward (Bz = -15nT) and eastward (By = 20 nT). Observations by LANL-GEO spacecraft at geosynchronous orbit also show lobe encounters on the dawn and dusk flanks. The two spacecraft configuration provides strong evidence that these periodic entries into the lobe are the result of local expansions of the OCB propagating from the tail and passing over the Van Allen Probes. Examination of pitch angle binned data from the HOPE instrument shows spatially large, accelerated ion structures occurring near simultaneously at both spacecraft, with the presence of oxygen indicating that they have an ionospheric source. The outflows are dispersed in energy and are detected when the spacecraft are on both open and closed field lines. These events provide a chance to examine the global magnetic field topology in detail, as well as smaller-scale spatial and temporal characteristics of the OCB, allowing us to constrain the position of the open/closed field line boundary and compare it to a global MHD model using a novel method. This technique shows that the model can reproduce a periodic approach and retreat of the OCB from the spacecraft but can overestimate its distance by as much as 3 RE. The model appears to simulate the dynamic processes that cause the spacecraft to encounter the lobe but incorrectly maps the overall topology of the magnetosphere during these extreme conditions.
Lie{endash}Poisson deformation of the Poincar{acute e} algebra
Stern, A. |
1996-04-01
We find a one-parameter family of quadratic Poisson structures on {bold R}{sup 4}{times}SL(2,{ital C}) which satisfies the properties: (a) that it reduces to the standard Poincar{acute e} algebra for a particular limiting value of the parameter (which we associate with the {open_quote}{open_quote}canonical limit{close_quote}{close_quote}), as well as, (b) that it is preserved under the Lie{endash}Poisson action of the Lorentz group (and the Lie{endash}Poisson transformations reduce to canonical ones in the canonical limit). As with the Poincar{acute e} algebra, our deformed Poincar{acute e} algebra has two Casimir functions which correspond to {open_quote}{open_quote}mass{close_quote}{close_quote} and {open_quote}{open_quote}spin.{close_quote}{close_quote} The constant mass and spin surfaces in {bold R}{sup 4}{times}SL(2,{ital C}) define symplectic leaves which we parametrize with space{endash}time coordinates, momenta, and spin. We thereby obtain realizations of the deformed Poincar{acute e} algebra for both spinning and spinless particles. The formalism can be applied for finding a one-parameter family of canonically inequivalent descriptions of the photon. {copyright} {ital 1996 American Institute of Physics.}
Disjointness preserving operators between little Lipschitz algebras
NASA Astrophysics Data System (ADS)
Jiménez-Vargas, A.
2008-01-01
Given a real number [alpha][set membership, variant](0,1) and a metric space (X,d), let Lip[alpha](X) be the algebra of all scalar-valued bounded functions f on X such that endowed with any one of the norms ||f||=max{p[alpha](f),||f||[infinity]} or ||f||=p[alpha](f)+||f||[infinity]. The little Lipschitz algebra lip[alpha](X) is the closed subalgebra of Lip[alpha](X) formed by all those functions f such that f(x)-f(y)/d(x,y)[alpha]->0 as d(x,y)->0. A linear mapping is called disjointness preserving if f[dot operator]g=0 in lip[alpha](X) implies (Tf)[dot operator](Tg)=0 in lip[alpha](Y). In this paper we study the representation and the automatic continuity of such maps T in the case in which X and Y are compact. We prove that T is essentially a weighted composition operator Tf=h[dot operator](f[circle, open][phi]) for some nonvanishing little Lipschitz function h and some continuous map [phi]. If, in addition, T is bijective, we deduce that h is a nonvanishing function in lip[alpha](Y) and [phi] is a Lipschitz homeomorphism from Y onto X and, in particular, we obtain that T is automatically continuous and T-1 is disjointness preserving. Moreover we show that there exists always a discontinuous disjointness preserving linear functional on lip[alpha](X), provided X is an infinite compact metric space.
Alternative algebraic approaches in quantum chemistry
Mezey, Paul G.
2015-01-22
Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.
Algebraic Methods to Design Signals
2015-08-27
group theory are employed to investigate the theory of their construction methods leading to new families of these arrays and some generalizations...sequences and arrays with desirable correlation properties. The methods used are very algebraic and number theoretic. Many new families of sequences...context of optical quantum computing, we prove that infinite families of anticirculant block weighing matrices can be obtained from generic weighing
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
Introduction to Image Algebra Ada
NASA Astrophysics Data System (ADS)
Wilson, Joseph N.
1991-07-01
Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.
Algebraic approach to form factors in the complex sinh-Gordon theory
NASA Astrophysics Data System (ADS)
Lashkevich, Michael; Pugai, Yaroslav
2017-01-01
We study form factors of the quantum complex sinh-Gordon theory in the algebraic approach. In the case of exponential fields the form factors can be obtained from the known form factors of the ZN-symmetric Ising model. The algebraic construction also provides an Ansatz for form factors of descendant operators. We obtain generating functions of such form factors and establish their main properties: the cluster factorization and reflection equations.
New phases of D ge 2 current and diffeomorphism algebras in particle physics
Tze, Chia-Hsiung.
1990-09-01
We survey some global results and open issues of current algebras and their canonical field theoretical realization in D {ge} 2 dimensional spacetime. We assess the status of the representation theory of their generalized Kac-Moody and diffeomorphism algebras. Particular emphasis is put on higher dimensional analogs of fermi-bose correspondence, complex analyticity and the phase entanglements of anyonic solitons with exotic spin and statistics. 101 refs.
Computations and generation of elements on the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2015-05-01
Two programs, feyngen and feyncop, were developed. feyngen is designed to generate high loop order Feynman graphs for Yang-Mills, QED and ϕk theories. feyncop can compute the coproduct of these graphs on the underlying Hopf algebra of Feynman graphs. The programs can be validated by exploiting zero dimensional field theory combinatorics and identities on the Hopf algebra which follow from the renormalizability of the theories. A benchmark for both programs was made.
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.…
Bilinear forms on fermionic Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2007-05-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian super-operator in a super-variable. In this paper, we show that there is a remarkable geometry on fermionic Novikov algebras with non-degenerate invariant symmetric bilinear forms, which we call pseudo-Riemannian fermionic Novikov algebras. They are related to pseudo-Riemannian Lie algebras. Furthermore, we obtain a procedure to classify pseudo-Riemannian fermionic Novikov algebras. As an application, we give the classification in dimension <=4. Motivated by the one in dimension 4, we construct some examples in high dimensions.
Cotangent bundle quantization: entangling of metric and magnetic field
NASA Astrophysics Data System (ADS)
Karasev, M. V.; Osborn, T. A.
2005-10-01
For manifolds \\mathcal{M} of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field), we define a Hilbert algebra structure in the space L^2(T^*\\!{\\mathcal{M}}) and construct an irreducible representation of this algebra in L^2(\\mathcal{M}) . This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions, this algebra is unique. The non-commutative product over T^*\\!{\\mathcal{M}} is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals that this product has a front, which is described in terms of geodesic triangles in \\mathcal{M} . The quantization of δ-functions induces a family of symplectic reflections in T^*\\!{\\mathcal{M}} and generates a magneto-geodesic connection Γ on T^*\\mathcal{M} . This symplectic connection entangles, on the phase space level, the original affine structure on \\mathcal{M} and the magnetic field. In the classical approximation, the planck2-part of the quantum product contains the Ricci curvature of Γ and a magneto-geodesic coupling tensor.
Coherent States for Landau Levels: Algebraic and Thermodynamical Properties
NASA Astrophysics Data System (ADS)
Aremua, Isiaka; Hounkonnou, Mahouton Norbert; Baloïtcha, Ezinvi
2015-10-01
This work describes coherent states for a physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The underlying su(1 , 1) Lie algebra and Barut-Girardello coherent states are constructed and discussed. Then, the Berezin-Klauder-Toeplitz quantization, also known as coherent state (or anti-Wick) quantization, is discussed. The thermodynamics of such a quantum gas system is elaborated and analyzed.
Numerical linear algebra algorithms and software
NASA Astrophysics Data System (ADS)
Dongarra, Jack J.; Eijkhout, Victor
2000-11-01
The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.
Symbolic Lie algebras manipulations using COMMON LISP
NASA Astrophysics Data System (ADS)
Cecchini, R.; Tarlini, M.
1989-01-01
We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie algebra. Using the general definitions of vector space Lie algebra and enveloping algebra, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula. All the computations are exact, including numerical coefficients. For the interactive user an optional menu facility and online help are available. LISP knowledge is unnecessary.
Lie algebras of classical and stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Neto, J. J. Soares; Vianna, J. D. M.
1994-03-01
The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.
NASA Astrophysics Data System (ADS)
Manerowska, Anna; Nieznański, Edward; Mulawka, Jan
2013-10-01
Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.
Dispersion Operators Algebra and Linear Canonical Transformations
NASA Astrophysics Data System (ADS)
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-04-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Dispersion Operators Algebra and Linear Canonical Transformations
NASA Astrophysics Data System (ADS)
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-02-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Banach Algebras Associated to Lax Pairs
NASA Astrophysics Data System (ADS)
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
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.
Multicloning and Multibroadcasting in Operator Algebras
NASA Astrophysics Data System (ADS)
Kaniowski, Krzysztof; Lubnauer, Katarzyna; Łuczak, Andrzej
2015-12-01
We investigate multicloning and multibroadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained in this framework for simple cloning and broadcasting.
NASA Astrophysics Data System (ADS)
Parkinson, M.; Pinnock, M.; Dyson, P.; Devlin, J.
The comparatively low latitude of the Tasman International Geospace Environment Radar (147.2°E, 43.4°S, geographic; -54.6°) a Southern Hemisphere HF SuperDARN radar, facilitates the observation of extensive backscatter from decametre-scale irregularities drifting in the auroral and polar cap ionosphere in the pre-midnight sector. The radar often detects a persistent, sharp latitudinal decrease (~90 km) in line-of-sight Doppler velocity spread, or spectral width, from >200 m s-1 in the polar cap ionosphere, to <50 m s-1 in the auroral ionosphere. The location of this spectral width boundary (SWB) matches the poleward edge of the auroral oval determined using energy spectra of precipitating particles measured on board Defence Meteorology Satellite Program satellites. This implies the radar SWB is a reasonable proxy for the open-closed magnetic field-line boundary (OCB). The location of the SWB fluctuates on a spread of time scales, expanding equatorward or contracting poleward, much as would be expected when dayside or nightside reconnection dominate the nightside flows, respectively. Here we investigate how accurately the radar SWB is aligned with the satellite OCB during moderately disturbed geomagnetic conditions, and a substorm. For example, does the alignment of the radar SWB with the OCB change with magnetic local time and geomagnetic activity? Down to what spatial and temporal scales is the radar SWB an accurate proxy for the satellite OCB?
Leroch, Michaela; Plesken, Cecilia; Weber, Roland W S; Kauff, Frank; Scalliet, Gabriel; Hahn, Matthias
2013-01-01
The gray mold fungus Botrytis cinerea is a major threat to fruit and vegetable production. Strawberry fields usually receive several fungicide treatments against Botrytis per season. Gray mold isolates from several German strawberry-growing regions were analyzed to determine their sensitivity against botryticides. Fungicide resistance was commonly observed, with many isolates possessing resistance to multiple (up to six) fungicides. A stronger variant of the previously described multidrug resistance (MDR) phenotype MDR1, called MDR1h, was found to be widely distributed, conferring increased partial resistance to two important botryticides, cyprodinil and fludioxonil. A 3-bp deletion mutation in a transcription factor-encoding gene, mrr1, was found to be correlated with MDR1h. All MDR1h isolates and the majority of isolates with resistance to multiple fungicides were found to be genetically distinct. Multiple-gene sequencing confirmed that they belong to a novel clade, called Botrytis group S, which is closely related to B. cinerea and the host-specific species B. fabae. Isolates of Botrytis group S genotypes were found to be widespread in all German strawberry-growing regions but almost absent from vineyards. Our data indicate a clear subdivision of gray mold populations, which are differentially distributed according to their host preference and adaptation to chemical treatments.
Yi, Peiyun; Peng, Linfa; Huang, Jiaqiang
2016-02-01
Ti6Al4V alloy has been widely used as a suitable material for surgical implants such as artificial hip joints. In this study, a series of multilayered gradient TiAlN coatings were deposited on Ti6Al4V substrate using closed field unbalanced magnetron sputter ion plating (CFUBMSIP) process. Taguchi design of experiment approach was used to reveal the influence of depositing parameters to the film composition and performance of TiAlN coatings. The phase structure and chemical composition of the TiAlN films were characterized by X-ray diffractometry (XRD) and X-ray photoelectron spectroscopy (XPS). Mechanical properties, including hardness, Young's modulus, friction coefficient, wear rate and adhesion strength were systematically evaluated. Potentiodynamic tests were conducted to evaluate the corrosion resistance of the coated samples in Ringer's solution at 37°C to simulate human body environment. Comprehensive performance of TiAlN films was evaluated by assigning different weight according to the application environment. S8, deposited by Ti target current of 8A, Al target current of 6A, bias voltage of -60V and nitrogen content with OEM (optical emission monitor) value of 45%, was found to achieve best performance in orthogonal experiments. Depositing parameters of S8 might be practically applied for commercialization of surgical implants.
Tropospheric wet refractivity tomography using multiplicative algebraic reconstruction technique
NASA Astrophysics Data System (ADS)
Xiaoying, Wang; Ziqiang, Dai; Enhong, Zhang; Fuyang, K. E.; Yunchang, Cao; Lianchun, Song
2014-01-01
Algebraic reconstruction techniques (ART) have been successfully used to reconstruct the total electron content (TEC) of the ionosphere and in recent years be tentatively used in tropospheric wet refractivity and water vapor tomography in the ground-based GNSS technology. The previous research on ART used in tropospheric water vapor tomography focused on the convergence and relaxation parameters for various algebraic reconstruction techniques and rarely discussed the impact of Gaussian constraints and initial field on the iteration results. The existing accuracy evaluation parameters calculated from slant wet delay can only evaluate the resultant precision of the voxels penetrated by slant paths and cannot evaluate that of the voxels not penetrated by any slant path. The paper proposes two new statistical parameters Bias and RMS, calculated from wet refractivity of the total voxels, to improve the deficiencies of existing evaluation parameters and then discusses the effect of the Gaussian constraints and initial field on the convergence and tomography results in multiplicative algebraic reconstruction technique (MART) to reconstruct the 4D tropospheric wet refractivity field using simulation method.
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…
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…
Correlates of gender and achievement in introductory algebra based physics
NASA Astrophysics Data System (ADS)
Smith, Rachel Clara
The field of physics is heavily male dominated in America. Thus, half of the population of our country is underrepresented and underserved. The identification of factors that contribute to gender disparity in physics is necessary for educators to address the individual needs of students, and, in particular, the separate and specific needs of female students. In an effort to determine if any correlations could be established or strengthened between sex, gender identity, social network, algebra skill, scientific reasoning ability, and/or student attitude, a study was performed on a group of 82 students in an introductory algebra based physics course. The subjects each filled out a survey at the beginning of the semester of their first semester of algebra based physics. They filled out another survey at the end of that same semester. These surveys included physics content pretests and posttests, as well as questions about the students' habits, attitudes, and social networks. Correlates of posttest score were identified, in order of significance, as pretest score, emphasis on conceptual learning, preference for male friends, number of siblings (negatively correlated), motivation in physics, algebra score, and parents' combined education level. Number of siblings was also found to negatively correlate with, in order of significance, gender identity, preference for male friends, emphasis on conceptual learning, and motivation in physics. Preference for male friends was found to correlate with, in order of significance, emphasis on conceptual learning, gender identity, and algebra score. Also, gender identity was found to correlate with emphasis on conceptual learning, the strongest predictor of posttest score other than pretest score.
Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
Boulanger, Nicolas
2007-06-29
Conformally invariant systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to the Weyl invariance of classical massless field systems in interaction with gravity. In the quantum theory, the latter symmetry no longer survives: A Weyl anomaly appears. Anomalies are a cornerstone of quantum field theory, and, for the first time, a general, purely algebraic understanding of the universal structure of the Weyl anomalies is obtained, in arbitrary dimensions and independently of any regularization scheme.
NASA Astrophysics Data System (ADS)
Schreiber, P.; Forbrich, I.; Kutzbach, L.; Hormann, A.; Wolf, U.; Miglovec, M.; Pihlatie, M.; Christiansen, J. R.; Wilmking, M.
2009-04-01
Closed chambers are the most common method to determine methane (CH4) fluxes in peatlands. The concentration change over time is monitored, and the flux is usually calculated by the slope of a linear regression function. However, chambers tend to slow down the gas diffusion by changing the concentration gradient between soil and atmosphere. Theoretically, this would result in a near-exponential concentration change in the chamber headspace. Here, we present data from a laboratory experiment and from two field campaigns on the basis of which we evaluate flux calculation approaches based either on linear or exponential regression models. To compare the fit performances of the two models, we used the Akaike Information Criterion with small sample second order bias correction (AICc). For checking the quality of flux data, we used the standard deviation of residuals. The calibration system in the laboratory experiment used during the chamber calibration campaign at Hyytiälä Forestry Field Station in August 2008 has been described by Pumpanen et al. (2004). Five different flux levels on two different soil porosities where tested. Preliminary results show that most concentration-over-time datasets were best described by the exponential model as evaluated by the AICc. It appeared that the flux calculation using the exponential model was better suited to determine the preset fluxes than that using the linear model. In the dataset of the first field campaign (April to October 2007) from Salmisuo (Finland, 62.46Ë N, 30.58Ë E), however, the majority of fluxes was best fitted with a linear regression on all microsite types. Those fluxes which are best fitted exponentially are most probable due to chamber artefacts. They occurred mostly during a drought period in August 2007, which seemed to increase the artificial impact of the chamber. However, these results might be site-specific: In Ust-Pojeg (Russia, 61.56Ë N, 50.13Ë E), where CH4 emissions are supposed to be
NASA Astrophysics Data System (ADS)
Kundu, Anjan
2016-12-01
Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang-Baxter integrability is proved for the model by finding a new kind of commutation rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau-Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras.
Application of symbolic and algebraic manipulation software in solving applied mechanics problems
NASA Technical Reports Server (NTRS)
Tsai, Wen-Lang; Kikuchi, Noboru
1993-01-01
As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.
ERIC Educational Resources Information Center
Saccomano, Doreen
2014-01-01
Close Reading is a strategy that can be used when reading challenging text. This strategy requires teachers to provide scaffolding, and create opportunities for think-alouds and rereading of text in order to help students become active readers who focus on finding text-based support for their answers. In addition, teachers must also be aware of…
Classification of filiform Lie algebras of order 3
NASA Astrophysics Data System (ADS)
Navarro, Rosa María
2016-12-01
Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.
A comparison of three algebraic stress closures for combustor flow calculations
NASA Technical Reports Server (NTRS)
Nikjooy, M.; So, R. M. C.; Hwang, B. C.
1985-01-01
A comparison is made of the performance of two locally nonequilibrium and one equilibrium algebraic stress closures in calculating combustor flows. Effects of four different pressure-strain models on these closure models are also analyzed. The results show that the pressure-strain models have a much greater influence on the calculated mean velocity and turbulence field than the algebraic stress closures, and that the best mean strain model for the pressure-strain terms is that proposed by Launder, Reece and Rodi (1975). However, the equilibrium algebraic stress closure with the Rotta return-to-isotropy model (1951) for the pressure-strain terms gives as good a correlation with measurements as when the Launder et al. mean strain model is included in the pressure-strain model. Finally, comparison of the calculations with the standard k-epsilon closure results show that the algebraic stress closures are better suited for simple turbulent flow calculations.
The Algebra of Lexical Semantics
NASA Astrophysics Data System (ADS)
Kornai, András
The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.
Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras
NASA Astrophysics Data System (ADS)
Konig, Martinvaldo
2014-10-01
Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem.
Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2014-12-01
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.
NASA Astrophysics Data System (ADS)
Chen, X.-C.; Lorentzen, D. A.; Moen, J. I.; Oksavik, K.; Baddeley, L. J.
2015-11-01
Previous studies have confirmed that the equatorward boundaries of OI 630.0 nm auroral emissions and broad Doppler spectral widths in Super Dual Auroral Radar Network (SuperDARN) data, the so-called spectral width boundary (SWB), are good empirical proxies for the dayside open/closed field line boundary (OCB) in the ionosphere. However, both observational techniques are associated with mapping errors. SuperDARN uses a virtual height model for mapping, but it is not well known how the mapping error responds to a changing background ionosphere or transient reconnection events. Optical instruments, such as the meridian-scanning photometers, have high spatial resolution near zenith, where the mapping error due to the assumed OI 630.0 nm auroral emission height becomes small by comparison. In this work, an adjusted method is introduced to identify the SWB, which does not require temporal smoothing across several scans. The difference in latitude between the SWB, as identified using this method, and the simultaneously observed OI 630.0 nm auroral emission boundary along a common line of sight is compared. Utilizing the OI 630.0 nm boundary as a reference location, we present two case studies observed at different levels of solar activity. In both instances the latitude offset of SWB from the reference location is discussed in relation to the background ionospheric electron density. The compared results indicate that the intake of high-density solar extreme ultraviolet ionized plasma from subauroral latitudes causes a refraction of the HF radar beam path, which results in an overestimation of range mapping. The adjusted method would thus be a useful tool for identifying the OCB under changing ionospheric conditions in the cusp region.
Evolution of the Frequency of Luminous (>=L*V) Close Galaxy Pairs at z < 1.2 in the COSMOS Field
NASA Astrophysics Data System (ADS)
Kartaltepe, J. S.; Sanders, D. B.; Scoville, N. Z.; Calzetti, D.; Capak, P.; Koekemoer, A.; Mobasher, B.; Murayama, T.; Salvato, M.; Sasaki, S. S.; Taniguchi, Y.
2007-09-01
We measure the fraction of luminous galaxies in pairs at projected separations of 5-20 kpc out to z=1.2 in the Cosmic Evolution Survey (COSMOS) field using ACS images and photometric redshifts derived from an extensive multiwavelength data set. Analysis of a complete sample of 106,188 galaxies more luminous than MV=-19.8 (~L*V) in the redshift range 0.1
Chevron Energy Solutions; Matt Rush; Scott Shulda
2011-01-03
Colorado Northwestern Community College (CNCC) is working collaboratively with recipient vendor Chevron Energy Solutions, an energy services company (ESCO), to develop an innovative GHP project at the new CNCC Campus constructed in 2010/2011 in Craig, Colorado. The purpose of the CNCC Craig Campus Geothermal Program scope was to utilize an energy performance contracting approach to develop a geothermal system with a shared closed-loop field providing geothermal energy to each building's GHP mechanical system. Additional benefits to the project include promoting good jobs and clean energy while reducing operating costs for the college. The project has demonstrated that GHP technology is viable for new construction using the energy performance contracting model. The project also enabled the project team to evaluate several options to give the College a best value proposition for not only the initial design and construction costs but build high performance facilities that will save the College for many years to come. The design involved comparing the economic feasibility of GHP by comparing its cost to that of traditional HVAC systems via energy model, financial life cycle cost analysis of energy savings and capital cost, and finally by evaluating the compatibility of the mechanical design for GHP compared to traditional HVAC design. The project shows that GHP system design can be incorporated into the design of new commercial buildings if the design teams, architect, contractor, and owner coordinate carefully during the early phases of design. The public also benefits because the new CNCC campus is a center of education for the much of Northwestern Colorado, and students in K-12 programs (Science Spree 2010) through the CNCC two-year degree programs are already integrating geothermal and GHP technology. One of the greatest challenges met during this program was coordination of multiple engineering and development stakeholders. The leadership of Principle Investigator
Algebraic Thinking: A Problem Solving Approach
ERIC Educational Resources Information Center
Windsor, Will
2010-01-01
Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…
Learning from Student Approaches to Algebraic Proofs
ERIC Educational Resources Information Center
D'Ambrosio, Beatriz S.; Kastberg, Signe E.; Viola dos Santos, Joao Ricardo
2010-01-01
Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand…
A Technology-Intensive Approach to Algebra.
ERIC Educational Resources Information Center
Heid, M. Kathleen; Zbiek, Rose Mary
1995-01-01
Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)
Focus on Fractions to Scaffold Algebra
ERIC Educational Resources Information Center
Ooten, Cheryl Thomas
2013-01-01
Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…
Post-Lie Algebras and Isospectral Flows
NASA Astrophysics Data System (ADS)
Ebrahimi-Fard, Kurusch; Lundervold, Alexander; Mencattini, Igor; Munthe-Kaas, Hans Z.
2015-11-01
In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical R-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation.
Teaching Modeling and Axiomatization with Boolean Algebra.
ERIC Educational Resources Information Center
De Villiers, Michael D.
1987-01-01
Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)
Arithmetic and Cognitive Contributions to Algebra
ERIC Educational Resources Information Center
Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.
2013-01-01
Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…
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…
Calif. Laws Shift Gears on Algebra, Textbooks
ERIC Educational Resources Information Center
Robelen, Erik W.
2012-01-01
New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…
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…
An algebraic approach to the scattering equations
NASA Astrophysics Data System (ADS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-12-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
THE RADICAL OF A JORDAN ALGEBRA
McCrimmon, Kevin
1969-01-01
In this paper we define a Jacobson radical for Jordan algebras analogous to that for associative algebras and show that it enjoys many of the properties of the associative radical. We then relate the corresponding notion of “semisimplicity” to the previously defined notion of “nondegeneracy” (Jacobson, N., these Proceedings, 55, 243-251 (1966)). PMID:16591736
The operator algebra approach to quantum groups
Kustermans, Johan; Vaes, Stefaan
2000-01-01
A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
Using the Internet To Investigate Algebra.
ERIC Educational Resources Information Center
Sherwood, Walter
The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…
Teaching Algebra to Students with Learning Disabilities
ERIC Educational Resources Information Center
Impecoven-Lind, Linda S.; Foegen, Anne
2010-01-01
Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…
Gary M. Klingler Algebra Teacher Assistance Packages
ERIC Educational Resources Information Center
Klingler, Gary
2005-01-01
Several packages designed by Elizabeth Marquez for mathematics teachers of grades 6-12, officially entitled the Teacher Assistance Package in Support of Better Algebra Assessment, is a series of resources developed to accompany ET's End-of-Course Algebra Assessment. It is designed to enhance teachers classroom assessment by providing examples of…
Just Say Yes to Early Algebra!
ERIC Educational Resources Information Center
Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy
2015-01-01
Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…
Symbolic Notations and Students' Achievements in Algebra
ERIC Educational Resources Information Center
Peter, Ebiendele E.; Olaoye, Adetunji A.
2013-01-01
This study focuses on symbolic notations and its impact on students' achievement in Algebra. The main reason for this study rests on the observation from personal and professional experiences on students' increasing hatred for Algebra. One hundred and fifty (150) Senior Secondary School Students (SSS) from Ojo Local Education District, Ojo, Lagos,…
Algebraic Formulas for Areas between Curves.
ERIC Educational Resources Information Center
Gabai, Hyman
1982-01-01
Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…
An Inquiry-Based Linear Algebra Class
ERIC Educational Resources Information Center
Wang, Haohao; Posey, Lisa
2011-01-01
Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…
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,…
Success in Algebra among Community College Students
ERIC Educational Resources Information Center
Reyes, Czarina
2010-01-01
College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…
Is Algebra Really Difficult for All Students?
ERIC Educational Resources Information Center
Egodawatte, Gunawardena
2009-01-01
Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…
Assessment of an Explicit Algebraic Reynolds Stress Model
NASA Technical Reports Server (NTRS)
Carlson, Jan-Renee
2005-01-01
This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-07
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.
LINPACK. Simultaneous Linear Algebraic Equations
Miller, M.A.
1990-05-01
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
LINPACK. Simultaneous Linear Algebraic Equations
Dongarra, J.J.
1982-05-02
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
Hexagonal tessellations in image algebra
NASA Astrophysics Data System (ADS)
Eberly, David H.; Wenzel, Dennis J.; Longbotham, Harold G.
1990-11-01
In image algebra '' the concept of a coordinate set X is general in that such a set is simply a subset of ndimensional Euclidean space . The standard applications in 2-dimensional image processing use coordinate sets which are rectangular arrays X 72 x ZZm. However some applications may require other geometries for the coordinate set. We look at three such related applications in the context of image algebra. The first application is the modeling of photoreceptors in primate retinas. These receptors are inhomogeneously distributed on the retina. The largest receptor density occurs in the center of the fovea and decreases radially outwards. One can construct a hexagonal tessellation of the retina such that each hexagon contains approximately the same number of receptors. The resulting tessellation called a sunflower heart2 consists of concentric rings of hexagons whose sizes increase as the radius of the ring increases. The second application is the modeling of the primary visual . The neurons are assumed to be uniformly distributed as a regular hexagonal lattice. Cortical neural image coding is modeled by a recursive convolution of the retinal neural image using a special set of filters. The third application involves analysis of a hexagonally-tessellated image where the pixel resolution is variable .
Primordial fluctuations from deformed quantum algebras
Day, Andrew C.; Brown, Iain A.; Seahra, Sanjeev S. E-mail: ibrown@astro.uio.no
2014-03-01
We study the implications of deformed quantum algebras for the generation of primordial perturbations from slow-roll inflation. Specifically, we assume that the quantum commutator of the inflaton's amplitude and momentum in Fourier space gets modified at energies above some threshold M{sub *}. We show that when the commutator is modified to be a function of the momentum only, the problem of solving for the post-inflationary spectrum of fluctuations is formally equivalent to solving a one-dimensional Schr and quot;odinger equation with a time dependent potential. Depending on the class of modification, we find results either close to or significantly different from nearly scale invariant spectra. For the former case, the power spectrum is characterized by step-like behaviour at some pivot scale, where the magnitude of the jump is O(H{sup 2}/M{sub *}{sup 2}). (H is the inflationary Hubble parameter.) We use our calculated power spectra to generate predictions for the cosmic microwave background and baryon acoustic oscillations, hence demonstrating that certain types of deformations are incompatible with current observations.
Quantum integrable systems related to lie algebras
NASA Astrophysics Data System (ADS)
Olshanetsky, M. A.; Perelomov, A. M.
1983-03-01
Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g2v( q) of the following 5 types: vI( q) = q-2, vII( q) = sinh-2q, vIII( q) = sin-2q, v IV(q) = P(q) , vV( q) = q-2 + ω2q2. Here P(q) is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp( qjqj+ 1 ) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.
NASA Astrophysics Data System (ADS)
Pramanik, Souvik; Ghosh, Subir
2013-08-01
We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.
NASA Astrophysics Data System (ADS)
Pramanik, Souvik; Ghosh, Subir
2013-10-01
We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.
Effective Lagrangians and Current Algebra in Three Dimensions
NASA Astrophysics Data System (ADS)
Ferretti, Gabriele
In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.
Generalization of n-ary Nambu algebras and beyond
Ataguema, H.; Makhlouf, A.; Silvestrov, S.
2009-08-15
The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.
Muehlhoff, Rainer
2011-02-15
Existence and uniqueness of advanced and retarded fundamental solutions (Green's functions) and of global solutions to the Cauchy problem is proved for a general class of first order linear differential operators on vector bundles over globally hyperbolic Lorentzian manifolds. This is a core ingredient to CAR-/CCR-algebraic constructions of quantum field theories on curved spacetimes, particularly for higher spin field equations.
The Hom-Yang-Baxter equation and Hom-Lie algebras
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.
Full Regularity for a C*-ALGEBRA of the Canonical Commutation Relations
NASA Astrophysics Data System (ADS)
Grundling, Hendrik; Neeb, Karl-Hermann
The Weyl algebra — the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect, in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S, B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a generalized group algebra, explained below) for the σ-representation theory of the Abelian group S where σ(·,·) ≔ eiB(·,·)/2. As an easy application, it then follows that for every regular representation of /line{Δ (S, B)} on a separable Hilbert space, there is a direct integral decomposition of it into irreducible regular representations (a known result).
Light polarization: A geometric-algebra approach
NASA Astrophysics Data System (ADS)
Baylis, W. E.; Bonenfant, J.; Derbyshire, J.; Huschilt, J.
1993-06-01
The geometric algebra of three-dimensional space (the ``Pauli algebra'') is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the three-dimensional Stokes subspace to describe the polarization of an approximately monochromatic collimated beam of electromagnetic radiation. The coherency density ρ is a real element of the algebra whose components are the four Stokes parameters: a scalar representing the total photon flux density plus a three-dimensional vector whose direction and length in the Poincaré sphere give the type and degree of polarization. The detection of the radiation and the incoherent and coherent modification of the polarization by various optical elements are calculated by algebraic multiplication which has faithful representations in 2×2 matrices. One matrix representation of ρ is the coherency matrix with which Jones and Mueller matrices are related whereas another representation is the spin density matrix. However, the calculations are simplest to perform and interpret in the algebraic form independent of any particular matrix representation. It is shown that any possible change in the Stokes parameters can be treated algebraically by a combination of attenuation, depolarization, polarization, and rotation transformations of ρ. The geometric algebra thus unifies Stokes parameters, the Poincaré sphere, Jones and Mueller matrices, and the coherency and density matrices in a single, simple formalism.
Working memory, worry, and algebraic ability.
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.
Jucys-Murphy elements for Birman-Murakami-Wenzl algebras
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2011-05-01
The Burman-Wenzl-Murakami algebra, considered as the quotient of the braid group algebra, possesses the commutative set of Jucys-Murphy elements. We show that the set of Jucys-Murphy elements is maximal commutative for the generic Birman-Wenzl-Murakami algebra and reconstruct the representation theory of the tower of Birman-Wenzl-Murakami algebras.
Kinematical superalgebras and Lie algebras of order 3
Campoamor-Stursberg, R.; Rausch de Traubenberg, M.
2008-06-15
We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order 3. All these algebras are related through generalized Inonue-Wigner contractions from either the orthosymplectic superalgebra or the de Sitter Lie algebra of order 3.
Becchi-Rouet-Stora-Tyutin operators for W algebras
Isaev, A. P.; Krivonos, S. O.; Ogievetsky, O. V.
2008-07-15
The study of quantum Lie algebras motivates a use of noncanonical ghosts and antighosts for nonlinear algebras, such as W-algebras. This leads, for the W{sub 3} and W{sub 3}{sup (2)} algebras, to the Becchi-Rouet-Stora-Tyutin operator having the conventional cubic form.
Lie algebra lattices and strings on T-folds
NASA Astrophysics Data System (ADS)
Satoh, Yuji; Sugawara, Yuji
2017-02-01
We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, A 1 , D 2 r , E 7 , E 8, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the E 8 × E 8 heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.
On computational complexity of Clifford algebra
NASA Astrophysics Data System (ADS)
Budinich, Marco
2009-05-01
After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last part we apply these results to the Clifford algebra formulation of the NP-complete problem of the maximum clique of a graph introduced by Budinich and Budinich ["A spinorial formulation of the maximum clique problem of a graph," J. Math. Phys. 47, 043502 (2006)].
Homomorphisms between C*-algebras and linear derivations on C*-algebras
NASA Astrophysics Data System (ADS)
Park, Choonkil; Boo, Deok-Hoon; An, Jong Su
2008-01-01
It is shown that every almost unital almost linear mapping of a unital C*-algebra to a unital C*-algebra is a homomorphism when h(3nuy)=h(3nu)h(y) holds for all unitaries , all , and all , and that every almost unital almost linear continuous mapping of a unital C*-algebra of real rank zero to a unital C*-algebra is a homomorphism when h(3nuy)=h(3nu)h(y) holds for all , and v is invertible}, all , and all . Furthermore, we prove the Hyers-Ulam-Rassias stability of *-homomorphisms between unital C*-algebras, and -linear *-derivations on unital C*-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300.
Lie algebra type noncommutative phase spaces are Hopf algebroids
NASA Astrophysics Data System (ADS)
Meljanac, Stjepan; Škoda, Zoran; Stojić, Martina
2016-11-01
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.
A note on derivations of Murray–von Neumann algebras
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
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
Highest-weight representations of Brocherd`s algebras
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.
BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
NASA Astrophysics Data System (ADS)
Graziani, Giacomo; Makhlouf, Abdenacer; Menini, Claudia; Panaite, Florin
2015-10-01
A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β\\colon A→ A such that α (a)(bc)=(ab)β (c), for all a, b, cin A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new structures by presenting some basic properties and constructions (representations, twisted tensor products, smash products etc).
Using Schemas to Develop Algebraic Thinking
ERIC Educational Resources Information Center
Steele, Diana F.
2005-01-01
This article describes ways in which students develop schemas as they generalize and formalize patterns when solving related algebraic problems that involve size, shape, growth, and change. (Contains 7 figures and 3 tables.)
Cohomological invariants of central simple algebras
NASA Astrophysics Data System (ADS)
Merkurjev, A. S.
2016-10-01
We determine the indecomposable degree 3 cohomological invariants of tuples of central simple algebras with linear relations. Equivalently, we determine the degree 3 reductive cohomological invariants of all split semisimple groups of type A.
Cyclic Cocycles on Twisted Convolution Algebras
NASA Astrophysics Data System (ADS)
Angel, Eitan
2013-01-01
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper étale groupoids, Tu and Xu (Adv Math 207(2):455-483, 2006) provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to the construction of Mathai and Stevenson (Adv Math 200(2):303-335, 2006). When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras.
ALGEBRAIC DEPENDENCE THEOREMS ON COMPLEX PSEUDOCONCAVE SPACES
The notion of pseudoconcave space is introduced and classical theorems on algebraic dependence of meromorphic functions are extended for this new class of spaces and for sections in a coherent sheaf. (Author)
Lisa's Lemonade Stand: Exploring Algebraic Ideas.
ERIC Educational Resources Information Center
Billings, Esther M. H.; Lakatos, Tracy
2003-01-01
Presents an activity, "Lisa's Lemonade Stand," that actively engages students in algebraic thinking as they analyze change by investigating relationships between variables and gain experience describing and representing these relationships graphically. (YDS)
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 operator approach to gas kinetic models
NASA Astrophysics Data System (ADS)
Il'ichov, L. V.
1997-02-01
Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - Â†Âϕ with the operators ÂandÂ† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.
Dynamical systems and quantum bicrossproduct algebras
NASA Astrophysics Data System (ADS)
Arratia, Oscar; del Olmo, Mariano A.
2002-06-01
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, such as Poincaré, Galilei and Euclidean in N dimensions. The action associated with the bicrossproduct structure allows us to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system with each generator which is the object of our study.
Vague Congruences and Quotient Lattice Implication Algebras
Qin, Xiaoyan; Xu, Yang
2014-01-01
The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given. PMID:25133207
Edge covers and independence: Algebraic approach
NASA Astrophysics Data System (ADS)
Kalinina, E. A.; Khitrov, G. M.; Pogozhev, S. V.
2016-06-01
In this paper, linear algebra methods are applied to solve some problems of graph theory. For ordinary connected graphs, edge coverings and independent sets are considered. Some results concerning minimum edge covers and maximum matchings are proved with the help of linear algebraic approach. The problem of finding a maximum matching of a graph is fundamental both practically and theoretically, and has numerous applications, e.g., in computational chemistry and mathematical chemistry.
Algebraic Sub-Structuring for Electromagnetic Applications
Yang, C.; Gao, W.G.; Bai, Z.J.; Li, X.Y.S.; Lee, L.Q.; Husbands, P.; Ng, E.G.; /LBL, Berkeley /UC, Davis /SLAC
2006-06-30
Algebraic sub-structuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem. In this paper, they show that algebraic sub-structuring can be effectively used to solve generalized eigenvalue problems arising from the finite element analysis of an accelerator structure.
Algebraic sub-structuring for electromagnetic applications
Yang, Chao; Gao, Weiguo; Bai, Zhaojun; Li, Xiaoye; Lee, Lie-Quan; Husbands, Parry; Ng, Esmond G.
2004-09-14
Algebraic sub-structuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem. In this paper, we show that algebraic sub-structuring can be effectively used to solve generalized eigenvalue problems arising from the finite element analysis of an accelerator structure.
Integral-valued polynomials over sets of algebraic integers of bounded degree.
Peruginelli, Giulio
2014-04-01
Let K be a number field of degree n with ring of integers [Formula: see text]. By means of a criterion of Gilmer for polynomially dense subsets of the ring of integers of a number field, we show that, if [Formula: see text] maps every element of [Formula: see text] of degree n to an algebraic integer, then [Formula: see text] is integral-valued over [Formula: see text], that is, [Formula: see text]. A similar property holds if we consider the set of all algebraic integers of degree n and a polynomial [Formula: see text]: if [Formula: see text] is integral over [Formula: see text] for every algebraic integer α of degree n, then [Formula: see text] is integral over [Formula: see text] for every algebraic integer β of degree smaller than n. This second result is established by proving that the integral closure of the ring of polynomials in [Formula: see text] which are integer-valued over the set of matrices [Formula: see text] is equal to the ring of integral-valued polynomials over the set of algebraic integers of degree equal to n.
New phases of D greater than or equal to 2 current and diffeomorphism algebras in particle physics
NASA Astrophysics Data System (ADS)
Tze, Chia-Hsiung
1990-09-01
We survey some global results and open issues of current algebras and their canonical field theoretical realization in D greater than or equal to 2 dimensional spacetime. We assess the status of the representation theory of their generalized Kac-Moody and diffeomorphism algebras. Particular emphasis is put on higher dimensional analogs of fermi-bose correspondence, complex analyticity and the phase entanglements of anyonic solitons with exotic spin and statistics.
Solving the generalized Langevin equation with the algebraically correlated noise
NASA Astrophysics Data System (ADS)
Srokowski, T.; Płoszajczak, M.
1998-04-01
We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.
Flux-driven algebraic damping of m=2 diocotron mode
NASA Astrophysics Data System (ADS)
Chim, C. Y.; O'Neil, T. M.
2016-10-01
Recent experiments with pure electron plasmas in a Malmberg-Penning trap have observed the algebraic damping of m = 2 diocotron modes. Due to small field asymmetries a low density halo of electrons is transported radially outward from the plasma core, and the mode damping begins when the halo reaches the resonant radius rres, where f = mfE × B (rres) . The damping rate is proportional to the flux of halo particles through the resonant layer. The damping is related to, but distinct from the exponential spatial Landau damping in a linear wave-particle resonance. This poster uses analytic theory and simulations to explain the new flux-driven algebraic damping of the mode. As electrons are swept around the nonlinear ``cat's eye'' orbits of the resonant wave-particle interaction, they form a quadrupole (m = 2) density distribution, which sets up an electric field that acts back on the plasma core. The field causes an E × B drift motion that symmetrizes the core, i.e. damps the m = 2 mode. Supported by NSF Grant PHY-1414570, and DOE Grants DE-SC0002451.
I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2007
2007-01-01
The "I CAN Learn[R] Pre-Algebra" and "Algebra" computerized curricula are designed to cover mathematics and problem-solving skills for ethnically diverse, inner-city students in grades 6-12. The curricula are designed to equip students with the skills they need to meet district, state, and national math objectives through an…
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…
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…
The Application of a Computer Algebra System as a Tool in College Algebra.
ERIC Educational Resources Information Center
Mayes, Robert L.
1995-01-01
Students (n=61) in an experimental course stressing active student involvement and the use of a computer algebra system scored higher than students (n=76) in a traditional college algebra course on final measures of inductive reasoning, visualization, and problem solving while maintaining equivalent manipulation and computation skills. (Author/MLB)
ERIC Educational Resources Information Center
Davies Gomez, Lisa
2012-01-01
Algebra is the gatekeeper of access to higher-level math and science courses, higher education and future earning opportunities. Unequal numbers of African-American males drop out of Algebra and mathematics courses and underperform on tests of mathematical competency and are thus denied both essential skills and a particularly important pathway to…
Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Makhlouf, Abdenacer; Silvestrov, Sergei
2010-04-01
The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction.
NASA Astrophysics Data System (ADS)
Peräntie, J.; Hagberg, J.; Uusimäki, A.; Tian, J.; Han, P.
2012-08-01
The special characteristics of polarization rotation and accompanying electric-field-induced ferroelectric-ferroelectric phase transitions in <001>-poled Pb(Mg1/3Nb2/3)1-xTixO3 (x = 27.4, 28.8, and 30.7 mol. %) single crystals close to the morphotropic phase boundary region were studied by means of dielectric and thermal measurements as a function of a unipolar electric field at various temperatures. Discontinuous first-order-type phase transition behavior was evidenced by distinct and sharp changes in polarization and thermal responses with accompanying hysteresis as a function of the electric field. All compositions of crystals showed either one or two reversible discontinuities along the polarization rotation paths, which can be understood by electric-field-induced phase transition sequences to the tetragonal phase through different monoclinic phases previously observed along the polarization rotation path. Together with increasing polarization, a field-induced reversible decrease in temperature was observed with increasing electric field, indicating increased dipolar entropy during the electric-field-induced phase transitions. Constructed electric field-temperature phase diagrams based on the polarization and thermal data suggest that the complex polarization rotation path extends to a wider composition range than previously observed. The measured thermal response showed that a transition from the monoclinic to the tetragonal phase produced a greater thermal change in comparison with a transition within two monoclinic phases.
Classification of central extensions of Lax operator algebras
Schlichenmaier, Martin
2008-11-18
Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever's theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost-graded central extensions. It turns out that in case that the finite-dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost-graded central extension up to equivalence and rescaling of the central element.
Linearizing W2,4 and WB2 algebras
NASA Astrophysics Data System (ADS)
Bellucci, S.; Krivonos, S.; Sorin, A.
1995-02-01
It has recently been shown that the W3 and W3(2) algebras can be considered as subalgebras in some linear conformal algebras. In this paper we show that the nonlinear algebras W2,4 and WB2 as well as Zamolodchikov's spin {5}/{2} superalgebra also can be embedded as subalgebras into some linear conformal algebras with a finite set of currents. These linear algebras give rise to new realizations of the nonlinear algebras which could be suitable in the construction of W-string theories.
Classification of central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, Martin
2008-11-01
Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever's theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost-graded central extensions. It turns out that in case that the finite-dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost-graded central extension up to equivalence and rescaling of the central element.
Principal Component Analysis: Resources for an Essential Application of Linear Algebra
ERIC Educational Resources Information Center
Pankavich, Stephen; Swanson, Rebecca
2015-01-01
Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…
A Practical Approach to Inquiry-Based Learning in Linear Algebra
ERIC Educational Resources Information Center
Chang, J.-M.
2011-01-01
Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…
Student Connections of Linear Algebra Concepts: An Analysis of Concept Maps
ERIC Educational Resources Information Center
Lapp, Douglas A.; Nyman, Melvin A.; Berry, John S.
2010-01-01
This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…
Algebraic grid adaptation method using non-uniform rational B-spline surface modeling
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, B. K.
1992-01-01
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course
ERIC Educational Resources Information Center
Cook, John Paul
2015-01-01
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION
NASA Technical Reports Server (NTRS)
Smith, R. E.
1994-01-01
TBGG, Two-Boundary Grid Generation, applies an interactive algebraic grid generation technique in two dimensions. The program incorporates mathematical equations that relate the computational domain to the physical domain. TBGG has application to a variety of problems using finite difference techniques, such as computational fluid dynamics. Examples include the creation of a C-type grid about an airfoil and a nozzle configuration in which no left or right boundaries are specified. The underlying two-boundary technique of grid generation is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are defined by two ordered sets of points, referred to as the top and bottom. Left and right side boundaries may also be specified, and call upon linear blending functions to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly spaced computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth cubic spline functions is also presented. The TBGG program is written in FORTRAN 77. It works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. The program has been implemented on a CDC Cyber 170 series computer using NOS 2.4 operating system, with a central memory requirement of 151,700 (octal) 60 bit words. TBGG requires a Tektronix 4015 terminal and the DI-3000 Graphics Library of Precision Visuals, Inc. TBGG was developed in 1986.
Polarization ellipse and Stokes parameters in geometric algebra.
Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J
2012-01-01
In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.
EDITORIAL: Close contact Close contact
NASA Astrophysics Data System (ADS)
Demming, Anna
2010-07-01
means to produce nanoscale device elements, such as carbon nanotube transistors [5] and high-density memory crossbar circuits [6]. Recently, the use of scanning tunnelling microscopes has broached a new field of research, which is currently attracting enormous interest—single molecule detection. In issue 25 of Nanotechnology researchers in Houston reported unprecedented sensitivities using localized surface plasmon resonance shifts of gold bipyramids to detect concentrations of substances down to the single molecule level [7]. In issue 26 a collaboration of researchers from the US and Czech Republic describe a different approach, namely tunnelling recognition. In their topical review they describe hydrogen-bond mediated tunnelling and the associated experimental methods that facilitate the detection of single molecules in a tunnel junction using chemically functionalized electrodes [8]. The nanoworld depicted by scanning probe microgaphs over 20 years ago may have looked as extraterrestrial as any science fiction generated alien terrain, but though study and analysis these nano-landscapes have become significantly less alien territory. The work so far to unveil the intricacies of electronic contact has been a story of progress in investigating this new territory and manipulating the mechanisms that govern it to formulate new devices and delve deeper into phenomena at the nanoscale. References [1] Binning G, Rohrer H, Gerber Ch and Weibel E 1982 Phys. Rev. Lett. 49 57-61 [2] X D Cui, X Zarate, J Tomfohr, O F Sankey, A Primak, A L Moore, T A Moore, D Gust, G~Harris and S M Lindsay 2002 Nanotechnology 13 5-14 [3] Martin C A, van Ruitenbeek J M and van der Zant S J H 2010 Nanotechnology 21 265201 [4] Davis J J and Hanyu Y 2010 Nanotechnology 21 265302 [5] Tans S J, Verschueren A R M and Dekker C 1998 Nature 393 49-52 [6] Chen Y, Jung G-Y, Ohlberg D A A, Li X, Stewart D R, Jeppesen J O, Nielsen K A, Stoddart J F and Williams R S 2003 Nanotechnology 14 462-8 [7] Mayer K M
Permutation centralizer algebras and multimatrix invariants
NASA Astrophysics Data System (ADS)
Mattioli, Paolo; Ramgoolam, Sanjaye
2016-03-01
We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.
TRACER version 1.1 A mathematica package for γ-algebra in arbitrary dimensions
NASA Astrophysics Data System (ADS)
Jamin, Matthias; Lautenbacher, Markus E.
1993-02-01
This paper describes the first MATHEMATICA implementation of γ-algebra in arbitrary space-time dimensions according to the 't Hooft-Veltman scheme. It is the only system based on a general purpose computer algebra system treating the γ 5-problem mathematically consistently in arbitrary dimensions. The TRACER package is capable of doing just purely algebraic manipulations as well as trace operations on strings of γ-algebra objects. In addition, it provides a set of utility functions for reordering, simplifying and improving the readability of the output. Optionally the output can be obtained in a form suitable to be fed into a T EX system for high quality text processing. As a whole, the TRACER package is intended as a computerized aid to a researcher working on higher order corrections in Relativistic Quantum Field Theories. A short comparison of procedural versus rule-based programming approaches is given and the discussion is supplemented by a toy implementation of the γ-algebra in rule-based style. The paper describes in detail the usage of the TRACER package and for further illustration a correlation function of two weak currents is calculated with the aid of TRACER. Finally, data on the performance of TRACER on some common platforms are given.
Hearing Math: Algebra Supported eText for Students With Visual Impairments.
Bouck, Emily C; Weng, Pei-Lin
2014-01-01
Supported eText for students with visual impairments in mathematics has a promising, emerging literature base, although little of the existing research focuses on implementation within a classroom setting. This qualitative study sought to understand the use of supported eText to deliver algebra to students with visual impairments enrolled in algebra mathematics courses. The study also sought to explore supported eText in contrast to students' traditional means of accessing an algebra text. The main results suggest supported eText holds potential in terms of delivering mathematics content; however, more research and more reflection on the field is needed regarding this approach as a sole means of presenting text. Implications for teacher professional development and implementation practices are discussed.
Guionet, Alexis; David, Fabienne; Zaepffel, Clément; Coustets, Mathilde; Helmi, Karim; Cheype, Cyril; Packan, Denis; Garnier, Jean-Pierre; Blanckaert, Vincent; Teissié, Justin
2015-06-01
One of the different ways to eradicate microorganisms, and particularly bacteria that might have an impact on health consists in the delivery of pulsed electric fields (PEFs). The technologies of millisecond (ms) or microsecond (μs) PEF are still well known and used for instance in the process of fruit juice sterilization. However, this concept is costly in terms of delivered energy which might be too expensive for some other industrial processes. Nanosecond pulsed electric fields (nsPEFs) might be an alternative at least for lower energetic cost. However, only few insights were available and stipulate a gain in cost and in efficiency as well. Using Escherichia coli, the impact of frequency and low rate on eradication and energy consumption by msPEF, μsPEF and nsPEF have been studied and compared. While a 1 log10 was reached with an energy cost of 100 and 158 kJ/L with micro- and millisecond PEFs respectively, nsPEF reached the reduction for similar energy consumption. The best condition was obtained for a 1 log10 deactivation in 0.5h, for energy consumption of 143 kJ/L corresponding to 0.04 W · h when the field was around 100 kV/cm. Improvement can also be expected by producing a generator capable to increase the electric field.
Close range fault tolerant noncontacting position sensor
Bingham, D.N.; Anderson, A.A.
1996-02-20
A method and system are disclosed for locating the three dimensional coordinates of a moving or stationary object in real time. The three dimensional coordinates of an object in half space or full space are determined based upon the time of arrival or phase of the wave front measured by a plurality of receiver elements and an established vector magnitudes proportional to the measured time of arrival or phase at each receiver element. The coordinates of the object are calculated by solving a matrix equation or a set of closed form algebraic equations. 3 figs.
Close range fault tolerant noncontacting position sensor
Bingham, Dennis N.; Anderson, Allen A.
1996-01-01
A method and system for locating the three dimensional coordinates of a moving or stationary object in real time. The three dimensional coordinates of an object in half space or full space are determined based upon the time of arrival or phase of the wave front measured by a plurality of receiver elements and an established vector magnitudes proportional to the measured time of arrival or phase at each receiver element. The coordinates of the object are calculated by solving a matrix equation or a set of closed form algebraic equations.
Finite-Dimensional Lie Algebras for Fast Diffeomorphic Image Registration.
Zhang, Miaomiao; Fletcher, P Thomas
2015-01-01
This paper presents a fast geodesic shooting algorithm for diffeomorphic image registration. We first introduce a novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields. We then show that this space can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registration accuracy. We then leverage the fact that the geodesic evolution equations, as well as the adjoint Jacobi field equations needed for gradient descent methods, can be computed entirely in this finite-dimensional Lie algebra. The result is a geodesic shooting method for large deformation metric mapping (LDDMM) that is dramatically faster and less memory intensive than state-of-the-art methods. We demonstrate the effectiveness of our model to register 3D brain images and compare its registration accuracy, run-time, and memory consumption with leading LDDMM methods. We also show how our algorithm breaks through the prohibitive time and memory requirements of diffeomorphic atlas building.
Flux-driven algebraic damping of m = 1 diocotron mode
NASA Astrophysics Data System (ADS)
Chim, Chi Yung; O'Neil, Thomas M.
2016-07-01
Recent experiments with pure electron plasmas in a Malmberg-Penning trap have observed the algebraic damping of m = 1 diocotron modes. Transport due to small field asymmetries produces a low density halo of electrons moving radially outward from the plasma core, and the mode damping begins when the halo reaches the resonant radius r = Rw at the wall of the trap. The damping rate is proportional to the flux of halo particles through the resonant layer. The damping is related to, but distinct from, spatial Landau damping, in which a linear wave-particle resonance produces exponential damping. This paper explains with analytic theory the new algebraic damping due to particle transport by both mobility and diffusion. As electrons are swept around the "cat's eye" orbits of the resonant wave-particle interaction, they form a dipole (m = 1) density distribution. From this distribution, the electric field component perpendicular to the core displacement produces E × B-drift of the core back to the axis, that is, damps the m = 1 mode. The parallel component produces drift in the azimuthal direction, that is, causes a shift in the mode frequency.
Flux-driven algebraic damping of m = 1 diocotron mode
NASA Astrophysics Data System (ADS)
Chim, Chi Yung; O'Neil, Thomas
2015-11-01
Recent experiments with pure electron plasmas in a Malmberg-Penning trap have observed the algebraic damping of m = 1 diocotron modes. Transport due to small field asymmetries produce a low density halo of electrons moving radially outward from the plasma core, and the mode damping begins when the halo reaches the resonant radius rres, where f = mfE × B (rres) . The damping rate is proportional to the flux of halo particles through the resonant layer. The damping is related to, but distinct from spatial Landau damping, in which a linear wave-particle resonance produces exponential damping. This poster explains with analytic theory and simulations the new algebraic damping due to both mobility and diffusive fluxes. As electrons are swept around the ``cat's eye'' orbits of resonant wave-particle interaction, they form a dipole (m = 1) density distribution, and the electric field from this distribution produces an E × B drift of the core back to the axis, i.e. damps the m = 1 mode. Supported by National Science Foundation Grant PHY-1414570.
An algebra of discrete event processes
NASA Technical Reports Server (NTRS)
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Algebraic quantum gravity (AQG): II. Semiclassical analysis
NASA Astrophysics Data System (ADS)
Giesel, K.; Thiemann, T.
2007-05-01
In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity (AQG), was introduced. In the framework of AQG, existing semiclassical tools can be applied to operators that encode the dynamics of AQG such as the master constraint operator. In this paper, we will analyse the semiclassical limit of the (extended) algebraic master constraint operator and show that it reproduces the correct infinitesimal generators of general relativity. Therefore, the question of whether general relativity is included in the semiclassical sector of the theory, which is still an open problem in LQG, can be significantly improved in the framework of AQG. For the calculations, we will substitute SU(2) with U(1)3. That this substitution is justified will be demonstrated in the third paper (Giesel and Thiemann 2006 Semiclassical perturbation theory Preprint gr-qc/0607101) of this series.
Computational algebraic geometry of epidemic models
NASA Astrophysics Data System (ADS)
Rodríguez Vega, Martín.
2014-06-01
Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.
Sound Off! A Dialogue between Calculator and Algebra
ERIC Educational Resources Information Center
Wade, William R.
2006-01-01
This article illustrates the fact that unless tempered by algebraic reasoning, a graphing calculator can lead one to erroneous conclusions. It also demonstrates that some problems can be solved by combining technology with algebra.
A new algebra core for the minimal form' problem
Purtill, M.R. . Center for Communications Research); Oliveira, J.S.; Cook, G.O. Jr. )
1991-12-20
The demands of large-scale algebraic computation have led to the development of many new algorithms for manipulating algebraic objects in computer algebra systems. For instance, parallel versions of many important algorithms have been discovered. Simultaneously, more effective symbolic representations of algebraic objects have been sought. Also, while some clever techniques have been found for improving the speed of the algebraic simplification process, little attention has been given to the issue of restructuring expressions, or transforming them into minimal forms.'' By minimal form,'' we mean that form of an expression that involves a minimum number of operations. In a companion paper, we introduce some new algorithms that are very effective at finding minimal forms of expressions. These algorithms require algebraic and combinatorial machinery that is not readily available in most algebra systems. In this paper we describe a new algebra core that begins to provide the necessary capabilities.
Infinitesimal deformations of naturally graded filiform Leibniz algebras
NASA Astrophysics Data System (ADS)
Khudoyberdiyev, A. Kh.; Omirov, B. A.
2014-12-01
In the present paper we describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any n-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra Fn3(0) . We establish that in the same way any n-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras Fn1,Fn2and Fn3(α) . Moreover, we describe the linear integrable deformations of the above-mentioned algebras with a fixed basis of HL2 in the set of all n-dimensional Leibniz algebras. Among these deformations one new rigid algebra has been found.
Kac-Moody algebra and nonlinear sigma model
NASA Astrophysics Data System (ADS)
Ogura, Waichi; Hosoya, Akio
1985-12-01
We investigate the nonlinear sigma model over an arbitrary homogeneous space. Then it is shown that the sigma model realizes the Kac-Moody algebra as current algebra only if the homogeneous space is restricted to the group manifold.
Rees algebras, Monomial Subrings and Linear Optimization Problems
NASA Astrophysics Data System (ADS)
Dupont, Luis A.
2010-06-01
In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.
NASA Technical Reports Server (NTRS)
Traver, D. P.; Mitchell, D. G.; Williams, D. J.; Frank, L. A.; Huang, C. Y.
1991-01-01
The structure of the flank low-latitude boundary layer (LLBL) is examined through differential energy spectra and particle angular anisotropies for traversals of the dawn flank (December 19, 1977) and dusk flank (July 7, 1978) during periods of predominantly northward magnetosheath field orientation. Spectra are presented that were obtained from combined ISEE 1 low-energy-proton and electron-differential-energy-analyzer and medium-energy-particle-instrument data extending over the 200-eV/q to 2-MeV energy range for the plasma sheet, stagnation region, outer LLBL, and magnetosheath regions. The stagnation region and the outer LLBL are each a mixture of plasma-sheet and magnetosheath populations, but the stagnation region contains a relatively higher fraction of plasma sheet particles, consistent with its placement earthward of the outer LLBL. Evidence for energization of thermal electrons appears during the dusk flank crossing. Bidirectional field-aligned ion distributions are observed with typically 5-to-1 enhancement of the flux along the magnetic field during certain portions of the dusk flank crossing.
Double conformal space-time algebra
NASA Astrophysics Data System (ADS)
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G 4,8that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G 8,2 with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G 1,3. Two Conformal Space-Time subalgebras (CSTA) G 2,4 provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G 4,8 is a doubling product of two G 2,4 CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
Fréchet-algebraic deformation quantizations
NASA Astrophysics Data System (ADS)
Waldmann, S.
2014-09-01
In this review I present some recent results on the convergence properties of formal star products. Based on a general construction of a Fréchet topology for an algebra with countable vector space basis I discuss several examples from deformation quantization: the Wick star product on the flat phase space m2n gives a first example of a Fréchet algebraic framework for the canonical commutation relations. More interesting, the star product on the Poincare disk can be treated along the same lines, leading to a non-trivial example of a convergent star product on a curved Kahler manifold.
Shapes and stability of algebraic nuclear models
NASA Technical Reports Server (NTRS)
Lopez-Moreno, Enrique; Castanos, Octavio
1995-01-01
A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.
Bohr model as an algebraic collective model
Rowe, D. J.; Welsh, T. A.; Caprio, M. A.
2009-05-15
Developments and applications are presented of an algebraic version of Bohr's collective model. Illustrative examples show that fully converged calculations can be performed quickly and easily for a large range of Hamiltonians. As a result, the Bohr model becomes an effective tool in the analysis of experimental data. The examples are chosen both to confirm the reliability of the algebraic collective model and to show the diversity of results that can be obtained by its use. The focus of the paper is to facilitate identification of the limitations of the Bohr model with a view to developing more realistic, computationally tractable models.
Riemannian manifolds as Lie-Rinehart algebras
NASA Astrophysics Data System (ADS)
Pessers, Victor; van der Veken, Joeri
2016-07-01
In this paper, we show how Lie-Rinehart algebras can be applied to unify and generalize the elementary theory of Riemannian geometry. We will first review some necessary theory on a.o. modules, bilinear forms and derivations. We will then translate some classical theory on Riemannian geometry to the setting of Rinehart spaces, a special kind of Lie-Rinehart algebras. Some generalized versions of classical results will be obtained, such as the existence of a unique Levi-Civita connection, inducing a Levi-Civita connection on a submanifold, and the construction of spaces with constant sectional curvature.
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.
Dynamical algebras for Poeschl-Teller Hamiltonian hierarchies
Kuru, S.; Negro, J.
2009-12-15
The dynamical algebras of the trigonometric and hyperbolic symmetric Poeschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.
Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups
NASA Astrophysics Data System (ADS)
Batat, W.; Onda, K.
2017-04-01
We study algebraic Ricci solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are solvsolitons. In particular, we obtain new solitons on G2, G5, and G6, and we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not be algebraic Ricci solitons.
Capability and Schur multiplier of a pair of Lie algebras
NASA Astrophysics Data System (ADS)
Johari, Farangis; Parvizi, Mohsen; Niroomand, Peyman
2017-04-01
The aim of this work is to find some criteria for detecting the capability of a pair of Lie algebras. We characterize the exact structure of all pairs of capable Lie algebras in the class of abelian and Heisenberg ones. Among the other results, we also give some exact sequences on the Schur multiplier and exterior product of Lie algebras.
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…
The Impact of Early Algebra: Results from a Longitudinal Intervention
ERIC Educational Resources Information Center
Brizuela, Bárbara M.; Martinez, Mara V.; Cayton-Hodges, Gabrielle A.
2013-01-01
In this paper, we provide evidence of the impact of early algebra (EA) over time. We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an…
Changing Pre-Service Elementary Teachers' Attitudes to Algebra.
ERIC Educational Resources Information Center
McGowen, Mercedes A.; Davis, Gary E.
This article addresses the question: "What are the implications for the preparation of prospective elementary teachers of 'early algebra' in the elementary grades curriculum?" Part of the answer involves language aspects of algebra: in particular, how a change in pre-service teachers' attitudes to algebra, from instrumental to relational, is…
A Research Base Supporting Long Term Algebra Reform?
ERIC Educational Resources Information Center
Kaput, James J.
This paper discusses three dimensions of algebra reform: breadth, integration, and pedagogy. Breadth of algebra includes algebra as: generalizing and formalizing patterns and constraints; syntactically-guided manipulation of formalisms; study of structures abstracted from computations and relations; study of functions, relations, and joint…
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…
Processes Used by College Students in Understanding Basic Algebra.
ERIC Educational Resources Information Center
Rachlin, Sidney Lee
The purpose of this study was to uncover information about and gain a greater insight into the extent to which students who are successful in a basic algebra course: l) demonstrate a reversibility of reasoning processes when solving algebraic problems; 2) demonstrate a flexibility of reasoning processes when solving algebraic problems; 3)…
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…
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,…
Static friction, differential algebraic systems and numerical stability
NASA Astrophysics Data System (ADS)
Chen, Jian; Schinner, Alexander; Matuttis, Hans-Georg
We show how Differential Algebraic Systems (Ordinary Differential Equations with algebraic constraints) in mechanics are affected by stability issues and we implement Lubich's projection method to reduce the error to practically zero. Then, we explain how the "numerically exact" implementation for static friction by Differential Algebraic Systems can be stabilized. We conclude by comparing the corresponding steps in the "Contact mechanics" introduced by Moreau.