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.
Open-closed homotopy algebra in mathematical physics
Kajiura, Hiroshige; Stasheff, Jim
2006-02-15
In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A{sub {infinity}} algebras) by closed strings (L{sub {infinity}} algebras)
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Quantum field theories on algebraic curves. I. Additive bosons
NASA Astrophysics Data System (ADS)
Takhtajan, Leon A.
2013-04-01
Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.
Modular operads and the quantum open-closed homotopy algebra
NASA Astrophysics Data System (ADS)
Doubek, Martin; Jurčo, Branislav; Münster, Korbinian
2015-12-01
We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.
Vertex operator algebras and conformal field theory
Huang, Y.Z. )
1992-04-20
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics.
Multifractal vector fields and stochastic Clifford algebra
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
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.
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. PMID:26723166
Localization of Free Field Realizations of Affine Lie Algebras
NASA Astrophysics Data System (ADS)
Futorny, Vyacheslav; Grantcharov, Dimitar; Martins, Renato A.
2015-04-01
We use localization technique to construct new families of irreducible modules of affine Kac-Moody algebras. In particular, localization is applied to the first free field realization of the affine Lie algebra or, equivalently, to imaginary Verma modules.
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.
The spatial isomorphism problem for close separable nuclear C*-algebras
Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.; White, Stuart A.; Winter, Wilhelm
2010-01-01
The Kadison–Kastler problem asks whether close C*-algebras on a Hilbert space must be spatially isomorphic. We establish this when one of the algebras is separable and nuclear. We also apply our methods to the study of near inclusions of C*-algebras. PMID:20080723
The Universal C*-Algebra of the Electromagnetic Field
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio
2016-02-01
A universal C*-algebra of the electromagnetic field is constructed. It is represented in any quantum field theory which incorporates electromagnetism and expresses basic features of the field such as Maxwell's equations, Poincaré covariance and Einstein causality. Moreover, topological properties of the field resulting from Maxwell's equations are encoded in the algebra, leading to commutation relations with values in its center. The representation theory of the algebra is discussed with focus on vacuum representations, fixing the dynamics of the field.
On the Structure of Closed Right Ideals of a C*-Algebra
NASA Astrophysics Data System (ADS)
Kruml, David
2015-12-01
The lattice of closed right ideals is an important invariant of a C*-algebra and naturally generalizes the spectrum of a commutative C*-algebra. As the C*-algebra is a union of its commutative sub-C*-algebras, the lattice can be considered as a "piecewise frame". It is discussed here that there is no right residuated total operation extending the meet operation on compatible elements, no "Sasakian" product, and no active lattice structure.
Clifford Algebra Cℓ 3(ℂ) for Applications to Field Theories
NASA Astrophysics Data System (ADS)
Panicaud, B.
2011-10-01
The multivectorial algebras present yet both an academic and a technological interest. Difficulties can occur for their use. Indeed, in all applications care is taken to distinguish between polar and axial vectors and between scalars and pseudo scalars. Then a total of eight elements are often considered even if they are not given the correct name of multivectors. Eventually because of their simplicity, only the vectorial algebra or the quaternions algebra are explicitly used for physical applications. Nevertheless, it should be more convenient to use directly more complex algebras in order to have a wider range of application. The aim of this paper is to inquire into one particular Clifford algebra which could solve this problem. The present study is both didactic concerning its construction and pragmatic because of the introduced applications. The construction method is not an original one. But this latter allows to build up the associated real algebra as well as a peculiar formalism that enables a formal analogy with the classical vectorial algebra. Finally several fields of the theoretical physics will be described thanks to this algebra, as well as a more applied case in general relativity emphasizing simultaneously its relative validity in this particular domain and the easiness of modeling some physical problems.
Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory
NASA Astrophysics Data System (ADS)
Hoefel, Eduardo; Livernet, Muriel
2012-08-01
Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.
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.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
NASA Astrophysics Data System (ADS)
Abłamowicz, Rafał; Gonçalves, Icaro; da Rocha, Roldão
2014-10-01
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.
Adèlic formulas for string amplitudes in fields of algebraic numbers
NASA Astrophysics Data System (ADS)
Vladimirov, V. S.; Sapuzhak, T. M.
1996-06-01
On the basis of the analysis on adèle groups (Tate's formula) for any field of algebraic numbers, a regularization of infinite adèlic products of gamma and beta functions of local fields is proposed. The formulas obtained are applied to representations of the four-point crossing symmetric Veneziano and Virasoro-Shapiro amplitudes through regularized adèlic products of the corresponding string (open and closed, resp.) amplitudes.
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.
Dirac Field, Gravity, Inertial Effects, and Computer Algebra
NASA Astrophysics Data System (ADS)
Vulcanov, Dumitru N.; Cotăescu, Ion I.
The article presents some new results obtained for the non-relativistic approximation of the Dirac equation in a non-inertial reference frame — rotated and accelerated — and in Schwarzschild gravitational field. These results are obtained with new routines of algebraic programming in REDUCE + EXCALC language for the Dirac equation in a non-inertial reference frame and after three successive Foldy-Wouthuysen transformations.
NASA Astrophysics Data System (ADS)
Matone, Marco
2015-11-01
We show that there are {\\it 13 types} of commutator algebras leading to the new closed forms of the Baker-Campbell-Hausdorff (BCH) formula $$\\exp(X)\\exp(Y)\\exp(Z)=\\exp({AX+BZ+CY+DI}) \\ , $$ derived in arXiv:1502.06589, JHEP {\\bf 1505} (2015) 113. This includes, as a particular case, $\\exp(X) \\exp(Z)$, with $[X,Z]$ containing other elements in addition to $X$ and $Z$. The algorithm exploits the associativity of the BCH formula and is based on the decomposition $\\exp(X)\\exp(Y)\\exp(Z)=\\exp(X)\\exp({\\alpha Y}) \\exp({(1-\\alpha) Y}) \\exp(Z)$, with $\\alpha$ fixed in such a way that it reduces to $\\exp({\\tilde X})\\exp({\\tilde Y})$, with $\\tilde X$ and $\\tilde Y$ satisfying the Van-Brunt and Visser condition $[\\tilde X,\\tilde Y]=\\tilde u\\tilde X+\\tilde v\\tilde Y+\\tilde cI$. It turns out that $e^\\alpha$ satisfies, in the generic case, an algebraic equation whose exponents depend on the parameters defining the commutator algebra. In nine {\\it types} of commutator algebras, such an equation leads to rational solutions for $\\alpha$. We find all the equations that characterize the solution of the above decomposition problem by combining it with the Jacobi identity.
NASA Astrophysics Data System (ADS)
Hoppe, Jens
Over the past years, associative algebras have come to play a major role in several areas of theoretical physics. Firstly, it has been realized that Yang Baxter algebras [1] constitute the relevant structure underlying 1+1 dimensional integrable models; in addition, their relation to braid groups, the theory of knots and links, and the exchange algebras of 1+1 dimensional conformal field theories [2] has been quite well understood by now. Secondly, deformations of Poisson structures that appeared in 2+1 dimensional field theories as infinite dimensional symmetry algebras possess underlying associative structures, which have also been studied in some detail (concerning higher spin theories see, e.g., [3, 4] and references therein, concerning the enveloping algebra of sl(2, C) see, e.g., [5], concerning deformations of diffAT2 — the Lie algebra of infinitesimal area preserving diffeomorphisms of the Torus — see [6, 7, 8, 9]). Ideas on how both investigations could eventually converge (i.e., a relation between 2+1 and 1+1 dimensions) have, e.g., been expressed in [10]. As indicated by the two subtitles there will be two parts to my paper: the first one presents a view on something I met long ago [11], and recently got interested in again [5, 7, 9, 12], while the second part introduces some algebraic structures that seem to be interesting, and possibly new.
Algebraic and Dirac-Hestenes spinors and spinor fields
NASA Astrophysics Data System (ADS)
Rodrigues, Waldyr A.
2004-07-01
Almost all presentations of Dirac theory in first or second quantization in physics (and mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of nonhomogeneous even multivectors fields) is used. However, a careful analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski space-time as some equivalence classes of pairs (Ⅺu,ψⅪu), where Ⅺu is a spinorial frame field and ψⅪu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a careful analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the bilinear covariants (on Minkowski space-time) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary Riemann-Cartan space-times. The present paper contains also Appendixes A-E which exhibits a truly useful collection of results concerning the theory of Clifford algebras (including many tricks of the trade) necessary for the intelligibility of the text.
Mean-Field Dynamical Semigroups on C*-ALGEBRAS
NASA Astrophysics Data System (ADS)
Duffield, N. G.; Werner, R. F.
We study a notion of the mean-field limit of a sequence of dynamical semigroups on the n-fold tensor products of a C*-algebra { A} with itself. In analogy with the theory of semigroups on Banach spaces we give abstract conditions for the existence of these limits. These conditions are verified in the case of semigroups whose generators are determined by the successive resymmetrizations of a fixed operator, as well as generators which can be approximated by generators of this type. This includes the time evolutions of the mean-field versions of quantum lattice systems. In these cases the limiting dynamical semigroup is given by a continuous flow on the state space of { A}. For a class of such flows we show stability by constructing a Liapunov function. We also give examples where the limiting evolution is given by a diffusion, rather than a flow on the state space of { A}.
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.
Solutions in bosonic string field theory and higher spin algebras in AdS
NASA Astrophysics Data System (ADS)
Polyakov, Dimitri
2015-11-01
We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in AdS3. The solutions are expressed in terms of the generating function for the products of Bell polynomials in derivatives of bosonic space-time coordinates Xm(z ) of the open string, the form of which is determined in this work. The products of these polynomials form a natural operator algebra realizations of w∞ (area-preserving diffeomorphisms), enveloping algebra of SU(2) and higher spin algebra in AdS3. The class of string field theory solutions found can, in turn, be interpreted as the "enveloping of enveloping," or the enveloping of AdS3 higher spin algebra. We also discuss the extensions of this class of solutions to superstring theory and their relations to higher spin algebras in higher space-time dimensions.
The bundles of algebraic and Dirac-Hestenes spinor fields
NASA Astrophysics Data System (ADS)
Mosna, Ricardo A.; Rodrigues, Waldyr A.
2004-07-01
Our main objective in this paper is to clarify the ontology of Dirac-Hestenes spinor fields (DHSF) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M=(M,g,∇,τg,↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so-called Dirac-Hestenes equation (DHE) in the case where M is a Lorentzian spacetime (the general case when M is a RCST will be discussed in another publication). To this aim we introduce the Clifford bundle of multivector fields (Cl(M,g)) and the left (ClSpin1,3el(M)) and right (ClSpin1,3er(M)) spin-Clifford bundles on the spin manifold (M,g). The relation between left ideal algebraic spinor fields (LIASF) and Dirac-Hestenes spinor fields (both fields are sections of ClSpin1,3el(M)) is clarified. We study in detail the theory of covariant derivatives of Clifford fields as well as that of left and right spin-Clifford fields. A consistent Dirac equation for a DHSF Ψ∈sec ClSpin1,3el(M) (denoted DECll) on a Lorentzian spacetime is found. We also obtain a representation of the DECll in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by Clifford fields ψⅪ∈sec Cl(M,g). This means that to each DHSF Ψ∈sec ClSpin1,3el(M) and spin frame Ⅺ∈sec PSpin1,3e(M), there is a well-defined sum of even multivector fields ψⅪ∈sec Cl(M,g) (EMFS) associated with Ψ. Such an EMFS is called a representative of the DHSF on the given spin frame. And, of course, such a EMFS (the representative of the DHSF) is not a spinor field. With this crucial distinction between a DHSF and its representatives on the Clifford bundle, we provide a consistent theory for the covariant derivatives of Clifford and spinor fields of all kinds. We emphasize that the DECll and the DHE, although related, are equations of different mathematical natures. We study also the local Lorentz invariance and the electromagnetic gauge invariance and show that only for the DHE such
Putting Algebra Progress Monitoring into Practice: Insights from the Field
ERIC Educational Resources Information Center
Foegen, Anne; Morrison, Candee
2010-01-01
Algebra progress monitoring is a research-based practice that extends a long history of research in curriculum-based measurement (CBM). This article describes the theoretical foundations and research evidence for algebra progress monitoring, along with critical features of the practice. A detailed description of one practitioner's implementation…
Deformations of Poisson brackets and extensions of Lie algebras of contact vector fields
NASA Astrophysics Data System (ADS)
Ovsienko, V.; Roger, C.
1992-12-01
CONTENTSIntroduction § 1. Main theoremsChapter I. Algebra § 2. Moyal deformations of the Poisson bracket and *-product on \\mathbb R^{2n} § 3. Algebraic construction § 4. Central extensions § 5. ExamplesChapter II. Deformations of the Poisson bracket and *-product on an arbitrary symplectic manifold § 6. Formal deformations: definitions § 7. Graded Lie algebras as a means of describing deformations § 8. Cohomology computations and their consequences § 9. Existence of a *-productChapter III. Extensions of the Lie algebra of contact vector fields on an arbitrary contact manifold §10. Lagrange bracket §11. Extensions and modules of tensor fieldsAppendix 1. Extensions of the Lie algebra of differential operatorsAppendix 2. Examples of equations of Korteweg-de Vries typeReferences
Closed string field theory from polyhedra
NASA Astrophysics Data System (ADS)
Saadi, Maha; Zwiebach, Barton
1989-05-01
A fully nonpolynomial framework for closed string field theory is studied. All interactions are geometrical, the pattern of string overlaps gives polyhedra with equal perimeter faces and three edges at each vertex. All interactions are cubic in the sense that at most three strings can coincide at a point. The three point vertex used is that of Witten which is seen to be quite natural in the framework of quadratic differentials and to induce a very symmetric decomposition of moduli space.
NASA Astrophysics Data System (ADS)
Vladimirov, Vasilii S.
1996-02-01
On the basis of analysis on the adele group (the Tate formula) of an algebraic number field, a regularization is constructed for the divergent adelic products of the gamma and beta functions of all (non-isomorphic) completions of this field. The formulae obtained are applied to representations of the four-point crossing-symmetric Veneziano amplitudes and Virasoro-Shapiro amplitudes in terms of regularized adelic products of string amplitudes (for open or closed strings) corresponding to all non-Archimedean completions of the algebraic number field under consideration.
On \\delta-derivations of n-ary algebras
NASA Astrophysics Data System (ADS)
Kaygorodov, Ivan B.
2012-12-01
We give a description of \\delta-derivations of (n+1)-dimensional n-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial \\delta-derivations of Filippov algebras and show that there are no non-trivial \\delta-derivations of the simple ternary Mal'tsev algebra M_8.
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.
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.
Symmetric structure of field algebra of G-spin models determined by a normal subgroup
Xin, Qiaoling Jiang, Lining
2014-09-15
Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.
Quantum fields on closed timelike curves
Pienaar, J. L.; Myers, C. R.; Ralph, T. C.
2011-12-15
Recently, there has been much interest in the evolution of quantum particles on closed timelike curves (CTCs). However, such models typically assume pointlike particles with only two degrees of freedom; a very questionable assumption given the relativistic setting of the problem. We show that it is possible to generalize the Deutsch model of CTCs to fields using the equivalent circuit formalism. We give examples for coherent, squeezed, and single-photon states interacting with the CTC via a beamsplitter. The model is then generalized further to account for the smooth transition to normal quantum mechanics as the CTC becomes much smaller than the size of the modes interacting on it. In this limit, we find that the system behaves like a standard quantum-mechanical feedback loop.
Nilpotent orbits in classical Lie algebras over F2n and the Springer correspondence
Xue, Ting
2008-01-01
We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over F2n. Let G be an adjoint algebraic group of type B, C, or D defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of G. PMID:18202179
Finite-dimensional simple graded algebras
Bahturin, Yu A; Zaicev, M V; Sehgal, S K
2008-08-31
Let R be a finite-dimensional algebra over an algebraically closed field F graded by an arbitrary group G. In the paper it is proved that if the characteristic of F is zero or does not divide the order of any finite subgroup of G, then R is graded simple if and only if it is isomorphic to a matrix algebra over a finite-dimensional graded skew field. Bibliography: 24 titles.
Locally finite dimensional Lie algebras
NASA Astrophysics Data System (ADS)
Hennig, Johanna
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).
NASA Astrophysics Data System (ADS)
Ibarra-Sierra, V. G.; Sandoval-Santana, J. C.; Cardoso, J. L.; Kunold, A.
2015-11-01
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai-Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dappiaggi, Claudio; Nosari, Gabriele; Pinamonti, Nicola
2016-06-01
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
Some fundamental groups in the arithmetic of algebraic curves over finite fields
Ihara, Yasutaka
1975-01-01
Associated with some systems of unramified coverings of algebraic curves over finite fields there are spaces analogous to the universal covering transformation spaces. These spaces have also arithmetic features; they represent all the Frobeniuses in the systems. This theory can be applied to the reduction mod [unk] of the Shimura curves. PMID:16592274
A novel Lie algebra of the genetic code over the Galois field of four DNA bases.
Sánchez, Robersy; Grau, Ricardo; Morgado, Eberto
2006-07-01
Starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the main partitions of the genetic code table were obtained as equivalent classes of quotient spaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assignments and physicochemical properties of amino acids. Moreover, a distance defined between codons expresses a physicochemical meaning. It was also noticed that the distance between wild type and mutant codons tends to be small in mutational variants of four genes: human phenylalanine hydroxylase, human beta-globin, HIV-1 protease and HIV-1 reverse transcriptase. These results strongly suggest that deterministic rules in genetic code origin must be involved. PMID:16780898
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.
Role of division algebra in seven-dimensional gauge theory
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-03-01
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.
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.}
Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations
NASA Astrophysics Data System (ADS)
Gavrylenko, P.; Marshakov, A.
2016-02-01
We consider the conformal blocks in the theories with extended conformal W-symmetry for the integer Virasoro central charges. We show that these blocks for the generalized twist fields on sphere can be computed exactly in terms of the free field theory on the covering Riemann surface, even for a non-abelian monodromy group. The generalized twist fields are identified with particular primary fields of the W-algebra, and we propose a straightforward way to compute their W-charges. We demonstrate how these exact conformal blocks can be effectively computed using the technique arisen from the gauge theory/CFT correspondence. We discuss also their direct relation with the isomonodromic tau-function for the quasipermutation monodromy data, which can be an encouraging step on the way of definition of generic conformal blocks for W-algebra using the isomonodromy/CFT correspondence.
Classification of operator algebraic conformal field theories in dimensions one and two
NASA Astrophysics Data System (ADS)
Kawahigashi, Yasuyuki
2006-03-01
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of a two-dimensional theory into two chiral theories. We give the first classification result of such chiral theories with representation theoretic invariants. That is, we use the central charge as the first invariant, and if it is less than 1, we obtain a complete classification. Our classification list contains a new net which does not seem to arise from the known constructions such as the coset or orbifold constructions. We also present a classification of full two-dimensional conformal theories. These are joint works with Roberto Longo.
Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
NASA Astrophysics Data System (ADS)
Cirilo-Lombardo, Diego Julio
2015-10-01
Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in this UFT general context that the underlying basis of the single geometrical structure P( G, M) (the principal fiber bundle over the real spacetime manifold M with structural group G) reflecting the symmetries of the different fields carry naturally a biquaternionic structure instead of a complex one. This fact allows us to analyze algebraically and to interpret physically in a straighforward way the Majorana and Dirac representations and the relation of such structures with the spacetime signature and non-hermitian (CP) dynamic operators. Also, from the underlying structure of the tangent space, the existence of hidden (super) symmetries and the possibility of supersymmetric extensions of these UFT models are given showing that Rothstein's theorem is incomplete for that description. The importance of the Clifford algebras in the description of all symmetries, mainly the interaction of gravity with the other fields, is briefly discussed.
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
A Heisenberg Algebra Bundle of a Vector Field in Three-Space and its Weyl Quantization
Binz, Ernst; Pods, Sonja
2006-01-04
In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group H{sub X}{sup {infinity}}. A representation of the C*-group algebra of H{sub X}{sup {infinity}} is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.
The algebras of large N matrix mechanics
Halpern, M.B.; Schwartz, C.
1999-09-16
Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
Closed string cohomology in open string field theory
NASA Astrophysics Data System (ADS)
Moeller, Nicolas; Sachs, Ivo
2011-07-01
We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten's 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.
Magnetic field perturbartions in closed-field-line systems with zero toroidal magnetic field
Mauel, M; Ryutov, D; Kesner, J
2003-12-02
In some plasma confinement systems (e.g., field-reversed configurations and levitated dipoles) the confinement is provided by a closed-field-line poloidal magnetic field. We consider the influence of the magnetic field perturbations on the structure of the magnetic field in such systems and find that the effect of perturbations is quite different from that in the systems with a substantial toroidal field. In particular, even infinitesimal perturbations can, in principle, lead to large radial excursions of the field lines in FRCs and levitated dipoles. Under such circumstances, particle drifts and particle collisions may give rise to significant neoclassical transport. Introduction of a weak regular toroidal magnetic field reduces radial excursions of the field lines and neoclassical transport.
The genus zeta function of hereditary orders in central simple algebras over global fields
NASA Astrophysics Data System (ADS)
Denert, M.
1990-01-01
Louis Solomon introduced the notion of a zeta function {ζ_θ }(s) of an order θ in a finite-dimensional central simple K-algebra A, with K a number field or its completion {K_P} (P a non-Archimedean prime in K). In several papers, C. J. Bushnell and I. Reiner have developed the theory of zeta functions and they gave explicit formulae in some special cases. One important property of these zeta functions is the Euler product, which implies that in order to calculate {ζ_θ }(s) , it is sufficient to consider the zeta function of local orders {θ _P} . However, since these local orders {θ _P} are in general not principal ideal domains, their zeta function is a finite sum of so-called 'partial zeta functions'. The most complicated term is the 'genus zeta function', {Z_{{θ _P}}}(s) , which is related to the free {θ _P} -ideals. I. Reiner and C. J. Bushnell calculated the genus zeta function for hereditary orders in quaternion algebras (i.e., [A:K] = 4 ). The authors mention the general case but they remark that the calculations are cumbersome. In this paper we derive an explicit method to calculate the genus zeta function {Z_{{θ _P}}}(s) of any local hereditary order {θ _P} in a central simple algebra over a local field. We obtain {Z_{{θ _P}}}(s) as a finite sum of explicit terms which can be calculated with a computer. We make some remarks on the programming of the formula and give a short list of examples. The genus zeta function of the minimal hereditary orders (corresponding to the partition (1, 1, ... , 1) of n) seems to have a surprising property. In all examples, the nominator of this zeta function is a generating function for the q-Eulerian polynomials. We conclude with some remarks on a conjectured identity.
A Clifford Algebra Approach to the Classical Problem of a Charge in a Magnetic Monopole Field
NASA Astrophysics Data System (ADS)
Vaz, Jayme
2013-05-01
The motion of an electric charge in the field of a magnetic monopole is described by means of a Lagrangian model written in terms of the Clifford algebra of the physical space. The equations of motion are written in terms of a radial equation (involving r=| r|, where r( t) is the charge trajectory) and a rotor equation (written in terms of an unitary operator spinor R). The solution corresponding to the charge trajectory in the field of a magnetic monopole is given in parametric form. The model can be generalized in order to describe the motion of a charge in the field of a magnetic monopole and other additional central forces, and as an example, we discuss the classical ones involving linear and inverse square interactions.
NS-NS sector of closed superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2014-08-01
We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.
Classification of linearly compact simple Nambu-Poisson algebras
NASA Astrophysics Data System (ADS)
Cantarini, Nicoletta; Kac, Victor G.
2016-05-01
We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A, by generalizing a construction made in the work of De Sole and Kac [Jpn. J. Math. 8, 1-145 (2013)]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero.
Closed expressions for the magnetic field of toroidal multipole configurations
Sheffield, G.V.
1983-04-01
Closed analytic expressions for the vector potential and the magnetic field for the lower order toroidal multipoles are presented. These expressions can be applied in the study of tokamak plasma cross section shaping. An example of such an application is included. These expressions also allow the vacuum fields required for plasma equilibrium to be specified in a general form independent of a particular coil configuration.
Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields
NASA Technical Reports Server (NTRS)
Chen, C. P.; Shang, H. M.; Huang, J.
1993-01-01
Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.
Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields
NASA Astrophysics Data System (ADS)
Chen, C. P.; Shang, H. M.; Huang, J.
1993-07-01
Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.
Clifford algebra-based structure filtering analysis for geophysical vector fields
NASA Astrophysics Data System (ADS)
Yu, Z.; Luo, W.; Yi, L.; Hu, Y.; Yuan, L.
2013-07-01
A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002-2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.
Hamiltonian description of closed configurations of the vacuum magnetic field
NASA Astrophysics Data System (ADS)
Skovoroda, A. A.
2015-05-01
Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.
Hamiltonian description of closed configurations of the vacuum magnetic field
Skovoroda, A. A.
2015-05-15
Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.
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.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
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…
Stoked nondynamos: sustaining field in magnetically non-closed systems
NASA Astrophysics Data System (ADS)
Byington, B. M.; Brummell, N. H.; Stone, J. M.; Gough, D. O.
2014-08-01
Much effort has gone into identifying and classifying systems that might be capable of dynamo action, i.e. capable of generating and sustaining magnetic field indefinitely against dissipative effects in a conducting fluid. However, it is difficult, if not almost technically impossible, to derive a method of determining in both an absolutely conclusive and a pragmatic manner whether a system is a dynamo or not in the nonlinear regime. This problem has generally been examined only for closed systems, despite the fact that most realistic situations of interest are not strictly closed. Here we examine the even more complex problem of whether a known nondynamo closed system can be distinguished pragmatically from a true dynamo when a small input of magnetic field to the system is allowed. We call such systems ‘stoked nondynamos’ owing to the ‘stoking’ or augmentation of the magnetic field in the system. It may seem obvious that magnetic energy can be sustained in such systems since there is an external source, but crucial questions remain regarding what level is maintained and whether such nondynamo systems can be distinguished from a true dynamo. In this paper, we perform 3D nonlinear numerical simulations with time-dependent ABC forcing possessing known dynamo properties. We find that magnetic field can indeed be maintained at a significant stationary level when stoking a system that is a nondynamo when not stoked. The maintained state results generally from an eventual rough balance of the rates of input and decay of magnetic field. We find that the relevance of this state is dictated by a parameter κ representing the correlation of the resultant field with the stoking forcing function. The interesting regime is where κ is small but non-zero, as this represents a middle ground between a state where the stoking has no effect on the pre-existing nondynamo properties and a state where the effect of stoking is easily detectable. We find that in this regime, (a
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.
Electrons on closed field lines of lunar crustal fields in the solar wind wake
NASA Astrophysics Data System (ADS)
Nishino, Masaki N.; Saito, Yoshifumi; Tsunakawa, Hideo; Takahashi, Futoshi; Fujimoto, Masaki; Harada, Yuki; Yokota, Shoichiro; Matsushima, Masaki; Shibuya, Hidetoshi; Shimizu, Hisayoshi
2015-04-01
Plasma signature around crustal magnetic fields is one of the most important topics of the lunar plasma sciences. Although recent spacecraft measurements are revealing solar-wind interaction with the lunar crustal fields on the dayside, plasma signatures around crustal fields on the night side have not been fully studied yet. Here we show evidence of plasma trapping on the closed field lines of the lunar crustal fields in the solar-wind wake, using SELENE (Kaguya) plasma and magnetic field data obtained at 14-15 km altitude from the lunar surface. In contrast to expectation on plasma cavity formation at the strong crustal fields, electron flux is enhanced above Crisium Antipode (CA) anomaly which is one of the strongest lunar crustal fields. The enhanced electron fluxes above CA are characterised by (1) occasional bi-directional field-aligned beams in the lower energy range (<150 eV) and (2) a medium energy component (150-300 eV) that has a double loss-cone distribution representing bounce motion between the two footprints of the crustal magnetic fields. The low-energy electrons on the closed field lines may come from the lunar night side surface, while supply mechanism of medium-energy electrons on the closed field line remains to be solved. We also report that a density cavity in the wake is observed not above the strongest magnetic field but in its vicinity.
Electrons on closed field lines of lunar crustal fields in the solar wind wake
NASA Astrophysics Data System (ADS)
Nishino, Masaki N.; Saito, Yoshifumi; Tsunakawa, Hideo; Takahashi, Futoshi; Fujimoto, Masaki; Harada, Yuki; Yokota, Shoichiro; Matsushima, Masaki; Shibuya, Hidetoshi; Shimizu, Hisayoshi
2015-04-01
Plasma signature around crustal magnetic fields is one of the most important topics of the lunar plasma sciences. Although recent spacecraft measurements are revealing solar-wind interaction with the lunar crustal fields on the dayside, plasma signatures around crustal fields on the night side have not been fully studied yet. Here we show evidence of plasma trapping on the closed field lines of the lunar crustal fields in the solar-wind wake, using SELENE (Kaguya) plasma and magnetic field data obtained at 14-15 km altitude from the lunar surface. In contrast to expectation on plasma cavity formation at the strong crustal fields, electron flux is enhanced above Crisium Antipode (CA) anomaly which is one of the strongest lunar crustal fields. The enhanced electron fluxes above CA are characterised by (1) occasional bi-directional field-aligned beams in the lower energy range (< 150 eV) and (2) a medium energy component (150-300 eV) that has a double loss-cone distribution representing bounce motion between the two footprints of the crustal magnetic fields. The low-energy electrons on the closed field lines may come from the lunar night side surface, while supply mechanism of medium-energy electrons on the closed field line remains to be solved. We also report that a density cavity in the wake is observed not above the strongest magnetic field but in its vicinity.
Electrons on closed field lines of lunar crustal fields in the solar wind wake
NASA Astrophysics Data System (ADS)
Nishino, M. N.; Saito, Y.; Tsunakawa, H.; Takahashi, F.; Fujimoto, M.; Yokota, S.; Harada, Y.; Matsushima, M.; Shibuya, H.; Shimizu, H.
2014-12-01
Plasma signature around crustal magnetic fields is one of the most important topics of the lunar plasma sciences. Although recent spacecraft measurements are revealing solar-wind interaction with the lunar crustal fields on the dayside, plasma signatures around crustal fields on the night side have not been fully studied yet. Here we show evidence of plasma trapping on the closed field lines of the lunar crustal fields in the solar-wind wake, using SELENE (Kaguya) plasma and magnetic field data obtained at 14-15 km altitude from the lunar surface. In contrast to expectation on plasma cavity formation at the strong crustal fields, electron flux is enhanced over Crisium Antipode (CA) anomaly which is one of the strongest lunar crustal fields. The enhanced electron fluxes over the CA anomaly are characterised by (1) occasional bi-directional field-aligned beams in the lower energy range (< 150 eV) and (2) a medium energy component (150-300 eV) that has a double loss-cone distribution that represents bounce motion between the two footprints of the crustal magnetic fields. The low-energy electrons on the closed field lines may come from the lunar night side surface, while supply mechanism of medium-energy electrons on the closed field line remains to be solved. We also report that a density cavity in the wake is observed not above the strongest magnetic field but in its vicinity.
Anomalies in non-polynomial closed string field theory
NASA Astrophysics Data System (ADS)
Kaku, Michio
1990-11-01
The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.
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.
Closed Field Coronal Heating Models Inspired by Wave Turbulence
NASA Astrophysics Data System (ADS)
Downs, C.; Lionello, R.; Mikic, Z.; Linker, J.; Velli, M. M.
2013-12-01
To simulate the energy balance of coronal plasmas on macroscopic scales, we often require the specification of the coronal heating mechanism in some functional form. To go beyond empirical formulations and to build a more physically motivated heating function, we investigate the wave-turbulence dissipation (WTD) phenomenology for the heating of closed coronal loops. To do so, we employ an implementation of non-WKB equations designed to capture the large-scale propagation, reflection, and dissipation of wave turbulence along a loop. The parameter space of this model is explored by solving the coupled WTD and hydrodynamic equations in 1D for an idealized loop, and the relevance to a range of solar conditions is established by computing solutions for several hundred loops extracted from a realistic 3D coronal field. Due to the implicit dependence of the WTD heating model on loop geometry and plasma properties along the loop and at the footpoints, we find that this model can significantly reduce the number of free parameters when compared to traditional empirical heating models, and still robustly describe a broad range of quiet-sun and active region conditions. The importance of the self-reflection term in producing realistic heating scale heights and thermal non-equilibrium cycles is discussed, and preliminary 3D thermodynamic MHD simulations using this formulation are presented. Research supported by NASA and NSF.
THE INTERSTELLAR MAGNETIC FIELD CLOSE TO THE SUN. II
Frisch, P. C.; Andersson, B-G; Berdyugin, A.; Piirola, V.; DeMajistre, R.; Funsten, H. O.; Magalhaes, A. M.; Seriacopi, D. B.; McComas, D. J.; Schwadron, N. A.; Slavin, J. D.; Wiktorowicz, S. J.
2012-12-01
The magnetic field in the local interstellar medium (ISM) provides a key indicator of the galactic environment of the Sun and influences the shape of the heliosphere. We have studied the interstellar magnetic field (ISMF) in the solar vicinity using polarized starlight for stars within 40 pc of the Sun and 90 Degree-Sign of the heliosphere nose. In Frisch et al. (Paper I), we developed a method for determining the local ISMF direction by finding the best match to a group of interstellar polarization position angles obtained toward nearby stars, based on the assumption that the polarization is parallel to the ISMF. In this paper, we extend the analysis by utilizing weighted fits to the position angles and by including new observations acquired for this study. We find that the local ISMF is pointed toward the galactic coordinates l, b =47 Degree-Sign {+-} 20 Degree-Sign , 25 Degree-Sign {+-} 20 Degree-Sign . This direction is close to the direction of the ISMF that shapes the heliosphere, l, b =33 Degree-Sign {+-} 4 Degree-Sign , 55 Degree-Sign {+-} 4 Degree-Sign , as traced by the center of the 'Ribbon' of energetic neutral atoms discovered by the Interstellar Boundary Explorer (IBEX) mission. Both the magnetic field direction and the kinematics of the local ISM are consistent with a scenario where the local ISM is a fragment of the Loop I superbubble. A nearby ordered component of the local ISMF has been identified in the region l Almost-Equal-To 0 Degree-Sign {yields} 80 Degree-Sign and b Almost-Equal-To 0 Degree-Sign {yields} 30 Degree-Sign , where PlanetPol data show a distance-dependent increase of polarization strength. The ordered component extends to within 8 pc of the Sun and implies a weak curvature in the nearby ISMF of {approx}0.{sup 0}25 pc{sup -1}. This conclusion is conditioned on the small sample of stars available for defining this rotation. Variations from the ordered component suggest a turbulent component of {approx}23 Degree-Sign . The ordered
NASA Astrophysics Data System (ADS)
Moayedi, S. K.; Setare, M. R.; Khosropour, B.
2013-11-01
In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β‧)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (\\triangle Xi)\\min = \\hbar √ {Dβ +β '}, \\forall i\\in \\{1, 2, ..., D\\}. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β‧ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.
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.
Homotopy Classification of Bosonic String Field Theory
NASA Astrophysics Data System (ADS)
Münster, Korbinian; Sachs, Ivo
2014-09-01
We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.
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.
Influence of strike object grounding on close lightning electric fields
NASA Astrophysics Data System (ADS)
Baba, Yoshihiro; Rakov, Vladimir A.
2008-06-01
Using the finite difference time domain (FDTD) method, we have calculated vertical electric field Ez, horizontal (radial) electric field Eh, and azimuthal magnetic field Hϕ produced on the ground surface by lightning strikes to 160-m- and a 553-m-high conical strike objects representing the Peissenberg tower (Germany) and the CN Tower (Canada), respectively. The fields were computed for a typical subsequent stroke at distances d' from the bottom of the object ranging from 5 to 100 m for the 160-m tower and from 10 to 300 m for the 553-m tower. Grounding of the 160-m object was assumed to be accomplished by its underground basement represented by a 10-m-radius and 8-m-long perfectly conducting cylinder with or without a reference ground plane located 2 m below. The reference ground plane simulates, to some extent, a higher-conducting ground layer that is expected to exist below the water table. The configuration without reference ground plane actually means that this plane is present, but is located at an infinitely large depth. Grounding of the 553-m object was modeled in a similar manner but in the absence of reference ground plane only. In all cases considered, waveforms of Eh and Hϕ are not much influenced by the presence of strike object, while waveforms of Ez are. Waveforms of Ez are essentially unipolar (as they are in the absence of strike object) when the ground conductivity σ is 10 mS/m (the equivalent transient grounding impedance is several ohms) or greater. Thus, for the CN Tower, for which σ ≥ 10 mS/m, the occurrence of Ez polarity change is highly unlikely. For the 160-m tower and for σ = 1 and 0.1 mS/m, waveforms of Ez become bipolar (exhibit polarity change) at d' ≤ 10 m and d' ≤ 50 m, respectively, regardless of the presence of the reference ground plane. The corresponding equivalent transient grounding impedances are about 30 and 50 Ω in the absence of the reference ground plane and smaller than 10 Ω in the presence of the reference
New family of Maxwell like algebras
NASA Astrophysics Data System (ADS)
Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.
2016-08-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration
NASA Astrophysics Data System (ADS)
Breev, A. I.; Shapovalov, A. V.
2016-01-01
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
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.…
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Song, Yang; Zhang, Bin; He, Anzhi
2006-11-01
A novel algebraic iterative algorithm based on deflection tomography is presented. This algorithm is derived from the essentials of deflection tomography with a linear expansion of the local basis functions. By use of this algorithm the tomographic problem is finally reduced to the solution of a set of linear equations. The algorithm is demonstrated by mapping a three-peak Gaussian simulative temperature field. Compared with reconstruction results obtained by other traditional deflection algorithms, its reconstruction results provide a significant improvement in reconstruction accuracy, especially in cases with noisy data added. In the density diagnosis of a hypersonic wind tunnel, this algorithm is adopted to reconstruct density distributions of an axial symmetry flow field. One cross section of the reconstruction results is selected to be compared with the inverse Abel transform algorithm. Results show that the novel algorithm can achieve an accuracy equivalent to the inverse Abel transform algorithm. However, the novel algorithm is more versatile because it is applicable to arbitrary kinds of distribution. PMID:17068552
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.
Vertex Algebras, Kac-Moody Algebras, and the Monster
NASA Astrophysics Data System (ADS)
Borcherds, Richard E.
1986-05-01
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.
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.
NASA Astrophysics Data System (ADS)
Zhang, He
2013-01-01
The space charge effect is one of the most important collective effects in beam dynamic studies. In many cases, numerical simulations are inevitable in order to get a clear understanding of this effect. The particle-particle interaction algorithms and the article-in-cell algorithms are widely used in space charge effect simulations. But they both have difficulties in dealing with highly correlated beams with abnormal distributions or complicated geometries. We developed a new algorithm to calculate the three dimensional self-field between charged particles by combining the differential algebra (DA) techniques with the fast multi-pole method (FMM). The FMM hierarchically decomposes the whole charged domain into many small regions. For each region it uses multipole expansions to represent the potential/field contributions from the particles far away from the region and then converts the multipole expansions into a local expansion inside the region. The potential/field due to the far away particles is calculated from the expansions and the potential/field due to the nearby particles is calculated from the Coulomb force law. The DA techniques are used in the calculation, translation and converting of the expansions. The new algorithm scales linearly with the total number of particles and it is suitable for any arbitrary charge distribution. Using the DA techniques, we can calculate both the potential/field and its high order derivatives, which will be useful for the purpose of including the space charge effect into transfer maps in the future. We first present the single level FMM, which decomposes the whole domain into boxes of the same size. It works best for charge distributions that are not overly non-uniform. Then we present the multilevel fast multipole algorithm (MLFMA), which decomposes the whole domain into different sized boxes according to the charge density. Finer boxes are generated where the higher charge density exists; thus the algorithm works for any
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
Higher level twisted Zhu algebras
Ekeren, Jethro van
2011-05-15
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
NASA Astrophysics Data System (ADS)
Bouwknegt, Peter
1988-06-01
We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.
Electric-field effects on the closed orbits of the diamagnetic Kepler problem
NASA Astrophysics Data System (ADS)
Bleasdale, C.; Bruno-Alfonso, A.; Lewis, R. A.
2016-02-01
The nonrelativistic closed orbits of an electron interacting with a unit positive charge in the presence of homogeneous magnetic and electric fields are investigated. A simplified theoretical model is proposed utilizing appropriate initial conditions in semiparabolic coordinates for arbitrary magnetic- and electric-field alignments. The evolution of both the angular spectrum of orbits and the shape and duration of individual orbits, as the electric-field intensity and scaled energy are increased, is shown for the cases of both parallel and crossed fields. Orbit mixing in the high-field regime is investigated in the case of parallel fields, giving an indication of the system moving from the quasi-Landau chaotic regime to the electric-field-induced (Stark effect) regular regime. For crossed fields, it is shown that the Garton-Tomkins orbits lead to a pair of orbits that have opposite behaviors as a function of the electric-field intensity.
Tushev, A V
2006-10-31
In the present paper certain methods are developed that enable one to study the properties of the controller of a prime faithful ideal I of the group algebra kA of an Abelian torsion-free group A of finite rank over a field k. The main idea is that the quotient ring kA/I by the given ideal I can be embedded as an integral domain k[A] into some field F and the group A becomes a subgroup of the multiplicative group of the field F. This allows one to apply certain results of field theory, such as Kummer's theory and the properties of the multiplicative groups of fields, to the study of the integral domain k[A]. In turn, the properties of the integral domain k[A]{approx_equal}kA/I depend essentially on the properties of the ideal I. In particular, by using these methods, an independent proof of the new version of Brookes's theorem on the controllers of prime ideals of the group algebra kA of an Abelian torsion-free group A of finite rank is obtained in the case where the field k has positive characteristic.
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
Alternative algebras admitting derivations with invertible values and invertible derivations
NASA Astrophysics Data System (ADS)
Kaygorodov, I. B.; Popov, Yu S.
2014-10-01
We prove an analogue of the Bergen-Herstein-Lanski theorem for alternative algebras: describe all alternative algebras that admit derivations with invertible values. We also prove an analogue of Moens' theorem for alternative algebras (a finite-dimensional alternative algebra over a field of characteristic zero is nilpotent if and only if it admits an invertible Leibniz derivation).
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.
On the third cohomology of algebraic groups of rank two in positive characteristic
NASA Astrophysics Data System (ADS)
Dzhumadil'daev, A. S.; Ibraev, Sh Sh
2014-03-01
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 \\operatorname{SL}_3, greater than 5 for \\operatorname{Sp}_4, and greater than 11 for G_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.
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.
78 FR 24765 - Notice of Intent To Close 16 Field Offices
Federal Register 2010, 2011, 2012, 2013, 2014
2013-04-26
... Memorandum 2010-07--Disposing of Unneeded Federal Real Estate (75 FR 33987, June 16, 2010), HUD is publishing... following 16 field offices: Camden, NJ; Syracuse, NY; Orlando, FL; Tampa, FL; Springfield, IL; Cincinnati... closed are: Camden, NJ; Syracuse, NY; Orlando, FL; Tampa, FL; Springfield, IL; Cincinnati, OH; Flint,...
Cassini Multi-instrument Assessment of the Open-closed Field Line Boundary of Saturn's Magnetosphere
NASA Astrophysics Data System (ADS)
Jinks, S. L.; Bunce, E. J.; Provan, G.; Yeoman, T. K.; Cowley, S. W. H.; Arridge, C. S.; Krupp, N.; Kurth, W. S.; Mitchell, D. G.; Wahlund, J. E.; Morooka, M.; Dougherty, M. K.
2013-09-01
In gas giant magnetospheres the balance between external solar wind driving and internal driving due to the planet's rotation is a critical issue which needs to be addressed. Following the high-latitude orbits of Cassini during 2006/7, 2008 and 2009 a region where magnetic field lines are "open" to the solar wind has been tentatively identified at Saturn. However, precisely where and how the open-closed field line boundary is determined from the various in situ instrument data sets has not yet been systematically investigated. Here we present a Cassini multi-instrument assessment (using magnetic field analysis, CAPS-ELS electrons, MIMI-LEMMS electrons, Langmuir Probe electron density, and RPWS measurements of the auroral hiss) of the location between "open" and "closed" magnetic field lines for the high-latitude orbits. We discuss the extent to which the different instruments can locate a common boundary and identify the average co-latitude of the boundary region in each hemisphere. The average co-latitude of the upward field-aligned current region is identified equatorward of the open-closed field line boundary in each hemisphere. There is possible evidence of displacement of the boundary equatorward towards midnight in both hemispheres indicating a local time dependence of the boundary location. Variation in southern co-latitude of the open-closed field line boundary with respect to the southern magnetic oscillation phase is shown to follow a sine relationship with an amplitude of ~2.4° co-latitude. Initial investigation shows no clear relationship in ordering the data by the northern magnetic oscillation phase.
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.
NASA Technical Reports Server (NTRS)
Sproul, William D.; Rudnik, Paul J.; Graham, Michael E.; Rohde, Suzanne L.
1990-01-01
Attention is given to an opposed cathode sputtering system constructed with the ability to coat parts with a size up to 15 cm in diameter and 30 cm in length. Initial trials with this system revealed very low substrate bias currents. When the AlNiCo magnets in the two opposed cathodes were arranged in a mirrored configuration, the plasma density at the substrate was low, and the substrate bias current density was less than 1 mA/sq cm. If the magnets were arranged in a closed-field configuration where the field lines from one set of magnets were coupled with the other set, the substrate bias current density was as high as 5.7 mA/sq cm when NdFeB magnets were used. In the closed-field configuration, the substrate bias current density was related to the magnetic field strength between the two cathodes and to the sputtering pressure. Hard well-adhered TiN coatings were reactively sputtered in the opposed cathode system in the closed-field configuration, but the mirrored configuration produced films with poor adhesion because of etching problems and low plasma density at the substrate.
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.
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.
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. [Gott space
Boulware, D.G.
1992-01-01
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 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.
Quantum field theory in spaces with closed time-like curves
Boulware, D.G.
1992-12-31
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.
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.
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.
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.
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®,…
On Realization of Generalized Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan
2012-12-01
A well-known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G(H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G(H) possesses an order determining set of generalized states.
Future missions for observing Earth's changing gravity field: a closed-loop simulation tool
NASA Astrophysics Data System (ADS)
Visser, P. N.
2008-12-01
The GRACE mission has successfully demonstrated the observation from space of the changing Earth's gravity field at length and time scales of typically 1000 km and 10-30 days, respectively. Many scientific communities strongly advertise the need for continuity of observing Earth's gravity field from space. Moreover, a strong interest is being expressed to have gravity missions that allow a more detailed sampling of the Earth's gravity field both in time and in space. Designing a gravity field mission for the future is a complicated process that involves making many trade-offs, such as trade-offs between spatial, temporal resolution and financial budget. Moreover, it involves the optimization of many parameters, such as orbital parameters (height, inclination), distinction between which gravity sources to observe or correct for (for example are gravity changes due to ocean currents a nuisance or a signal to be retrieved?), observation techniques (low-low satellite-to-satellite tracking, satellite gravity gradiometry, accelerometers), and satellite control systems (drag-free?). A comprehensive tool has been developed and implemented that allows the closed-loop simulation of gravity field retrievals for different satellite mission scenarios. This paper provides a description of this tool. Moreover, its capabilities are demonstrated by a few case studies. Acknowledgments. The research that is being done with the closed-loop simulation tool is partially funded by the European Space Agency (ESA). An important component of the tool is the GEODYN software, kindly provided by NASA Goddard Space Flight Center in Greenbelt, Maryland.
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
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}
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. PMID:23053737
Impact of close habitat on the entomological diversity and abundance in carrot open fields.
Colignon, P; Gaspar, C; Haubruge, E; Francis, F
2002-01-01
Vegetable open fields areas have been increasing for the last decade in Wallonia (South part of Belgium), mainly in Hesbaye. To be in accordance with quality standards, especially in terms of agrochemical residues (R.M.L.), biological pest control was developed and reduces the insecticide use, leading to have safer fresh products. Carrot represents an important cultivated species in Wallonia. To asses the impact of close habitat on both pest (mainly aphids) and beneficial insects, carrot fields were investigated during all the production duration in 2000. Twelve fields between Waremme and Hannut were visited weekly from June to October. Insects were caught using yellow traps and determined to the family level. Approximately 90,000 insects belonging to 109 families were identified. Significant differences linked to field closed habitat were observed on 31 families. An increase of biodiversity in term of family number near set-asides and woody borders was observed. Evaluation of pest and beneficial diversity and density in vegetable crops was discussed to promote future IPM program. PMID:12696415
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
Lie algebra of conformal Killing–Yano forms
NASA Astrophysics Data System (ADS)
Ertem, Ümit
2016-06-01
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing–Yano forms. A new Lie bracket for conformal Killing–Yano forms that corresponds to slightly modified Schouten–Nijenhuis bracket of differential forms is proposed. We show that conformal Killing–Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing–Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing–Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases.
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.
Pastukhov, V.P.; Ilgisonis, V.I.; Subbotin, A.A.
1994-05-01
General formalism is developed to analyze the equilibrium and stability of low beta anisotropic pressure plasmas confined in closed field line magnetic systems. The formalism allows one to consider rather general magnetic systems with nonuniform axis curvature and longitudinal profiles of toroidal and multipole poloidal field. It also allows having a strong pressure anisotropy corresponding to enhanced plasma pressure in mirror cells of the system. As an example of such a system the authors consider the recently proposed linked mirror neutron source (LMNS). Application of the above formalism to the LMNS analysis confirms most of the preliminary results, however, they obtain a considerable reduction of mirror cell axis curvature and an appreciable ellipticity of plasma cross-section in the mirror cell midplane. They have also optimized the longitudinal pressure and magnetic field distribution.
Closed star product on noncommutative ℝ 3 and scalar field dynamics
NASA Astrophysics Data System (ADS)
Jurić, Tajron; Poulain, Timothé; Wallet, Jean-Christophe
2016-05-01
We consider the noncommutative space ℝ θ 3 , a deformation of ℝ 3 for which the star product is closed for the trace functional. We study one-loop IR and UV properties of the 2-point function for real and complex noncommutative scalar field theories with quartic interactions and Laplacian on ℝ 3 as kinetic operator. We find that the 2-point functions for these noncommutative scalar field theories have no IR singularities in the external momenta, indicating the absence of UV/IR mixing. We also find that the 2-point functions are UV finite with the deformation parameter θ playing the role of a natural UV cut-off. The possible origin of the absence of UV/IR mixing in noncommutative scalar field theories on ℝ θ 3 as well as on ℝ λ 3 , another deformation of ℝ 3, is discussed.
Formation of accretion disks in close-binary systems with magnetic fields
NASA Astrophysics Data System (ADS)
Zhilkin, A. G.; Bisikalo, D. V.
2010-12-01
We have developed a three-dimensional numerical model and applied it to simulate plasma flows in semi-detached binary systems whose accretor possesses a strong intrinsic magnetic field. The model is based on the assumption that the plasma dynamics are determined by the slow mean flow, which forms a backdrop for the rapid propagation of MHD waves. The equations describing the slow motion of matter were obtained by averaging over rapidly propagating pulsations. The numerical model includes the diffusion of magnetic field by current dissipation in turbulent vortices, magnetic buoyancy, and wave MHD turbulence. A modified three-dimensional, parallel, numerical code was used to simulate the flow structure in close binary systems with various accretor magnetic fields, from 105 to 108 G. The conditions for the formation of the accretion disk and the criteria distinguishing the two types of flow corresponding to intermediate polars and polars are discussed.
The close classical T Tauri binary V4046 Sgr: complex magnetic fields and distributed mass accretion
NASA Astrophysics Data System (ADS)
Donati, J.-F.; Gregory, S. G.; Montmerle, T.; Maggio, A.; Argiroffi, C.; Sacco, G.; Hussain, G.; Kastner, J.; Alencar, S. H. P.; Audard, M.; Bouvier, J.; Damiani, F.; Güdel, M.; Huenemoerder, D.; Wade, G. A.
2011-11-01
We report here the first results of a multi-wavelength campaign focusing on magnetospheric accretion processes within the close binary system V4046 Sgr, hosting two partly convective classical T Tauri stars of masses ≃0.9 M⊙ and age ≃12 Myr. In this paper, we present time-resolved spectropolarimetric observations collected in 2009 September with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT) and covering a full span of 7 d or ≃2.5 orbital/rotational cycles of V4046 Sgr. Small circularly polarized Zeeman signatures are detected in the photospheric absorption lines but not in the accretion-powered emission lines of V4046 Sgr, thereby demonstrating that both system components host large-scale magnetic fields weaker and more complex than those of younger, fully convective classical T Tauri stars (cTTSs) of only a few Myr and similar masses. Applying our tomographic imaging tools to the collected data set, we reconstruct maps of the large-scale magnetic field, photospheric brightness and accretion-powered emission at the surfaces of both stars of V4046 Sgr. We find that these fields include significant toroidal components, and that their poloidal components are mostly non-axisymmetric with a dipolar component of 50-100 G strongly tilted with respect to the rotation axis; given the similarity with fields of partly convective main-sequence stars of similar masses and rotation periods, we conclude that these fields are most likely generated by dynamo processes. We also find that both stars in the system show cool spots close to the pole and extended regions of low-contrast, accretion-powered emission; it suggests that mass accretion is likely distributed rather than confined in well-defined high-contrast accretion spots, in agreement with the derived magnetic field complexity.
The {open_quotes}INVERSE PROBLEM{close_quotes} to the evaluation of the magnetic fields
Caspi, S.; Helm, M.; Laslett, L.J.
1995-06-01
In the design of superconducting magnet elements, such as may be required to guide and focus ions in a particle accelerator, one frequently premises some particular current distribution and then proceeds to compute the consequent magnetic field through use of the laws of Blot and Savart or of Ampere. When working in this manner one of course may need to revise frequently the postulated current distribution before arriving at a resulting magnetic field of acceptable field quality. It therefore is of interest to consider an alternative ({open_quotes}inverse{close_quotes}) procedure in which one specifies a desired character for the field required in the region interior to the winding and undertakes then to evaluate the current distribution on the specified winding surface that would provide this desired field. By evaluating the specified potential in the region interior to the winding along the interface, the authors have determined that a relaxation solution to the potential in the region outside the winding can be converged and used to calculate wire location. They have demonstrated this method by applying a slightly modified version of the program POISSON to a periodic alternating sinusoidal quadrupole field.
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.
Nonequilibrium problems in quantum field theory and Schwinger`s closed time path formalism
Cooper, F.
1995-05-01
We review the closed time path formalism of Schwinger using a path integral approach. We apply this formalism to the study of pair production from strong external fields as well as the time evolution of a nonequilibrium chiral phase transition. In 1961 in his classic paper ``Brownian Motion of a Quantum Particle,`` Schwinger solved the formidable technical problem of how to use the action principle to study initial value problems. Previously, the action principle was formulated to study only transition matrix elements from an earlier time to a later time. The elegant solution of this problem was the invention of the closed time path (CTP) formalism. This formalism was first used to study field theory problems by Mahanthappa and Bakshi. With the advent of supercomputers, it has now become possible to use this formalism to numerically solve important field theory questions which are presented as initial value problems. Two of these problems we shall review here. They are (1) The time evolution of the quark- gluon plasma. (2) Dynamical evolution of a non-equilibrium chiral phase transition following a relativistic heavy ion collision.
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Complex Kumjian-Pask algebras of 2-graphs
NASA Astrophysics Data System (ADS)
Yusnitha, Isnie; Rosjanuardi, Rizky
2016-02-01
Let Λ be a row-finitek-graph without sources and R be any field. The Kumjian-Pask algebras KPR(Λ) is an algebraic analog of k-graph algebrasC*(Λ). When the field R is the complex field ℂ, there is a special relationship between the complex Kumjian-Pask algebras KP𝕔(Λ) and k-graph algebrasC*(Λ). We examine this relationship particularly to the case 2-graph 𝔽θ+, 2-graph on single vertex generated by m blue edges and n red edges with θ respect to some commutation relations, by analyzing the associated C*-algebras of 𝔽θ+ . As the presence of cycles on 2-graph 𝔽θ+, we can imply that 2-graph algebras C*(𝔽F+ ) is infinite-dimensional. Hence, the complex Kumjian-Pask algebras KP𝕔 (𝔽θ+ ) is also infinite dimensional.
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
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.``
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
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.
Algebras of Measurements: The Logical Structure of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lehmann, Daniel; Engesser, Kurt; Gabbay, Dov M.
2006-04-01
In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.
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.
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.
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.
A closed cycle-cryostat for high-field Mössbauer spectroscopy
NASA Astrophysics Data System (ADS)
Janoschka, A.; Svenconis, G.; Schünemann, V.
2010-03-01
A closed cycle-cryostat coupled to a Mössbauer spectrometer has been installed at the University of Kaiserslautern and is in full operation since march 2007. The setup is equipped with a low vibrating two-stage pulse tube cooler and has a cool down time of 48 h. The sample can be top loaded without the need to shut off the refrigerator. With the static helium exchange gas in the variable temperature insert the sample may be cooled down from room temperature to 50 K within several hours. Dynamic exchange gas with external supply of gaseous helium is used to cool the sample down to 2 K. The superconducting self-shielding split-coil generates a magnetic field of up to 5 Tesla and a stray field of ca. 60 mT at the outer cryostat walls. Mössbauer measurements can be performed in perpendicular or parallel field orientations. The sample holder and the Mössbauer drive are rigidly connected to the cryostat. In this way a line width of the two inner α-Fe lines of 0.32 mm/s has been currently achieved.
Upper bound for the length of commutative algebras
Markova, Ol'ga V
2009-12-31
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.
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…
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.
Wide field adaptive optics laboratory demonstration with closed-loop tomographic control.
Costille, Anne; Petit, Cyril; Conan, Jean-Marc; Kulcsár, Caroline; Raynaud, Henri-François; Fusco, Thierry
2010-03-01
HOMER, the new bench developed at ONERA devoted to wide field adaptive optics (WFAO) laboratory research, has allowed the first experimental validations of multi-conjugate adaptive optics (MCAO) and laser tomography adaptive optics (LTAO) concepts with a linear quadratic Gaussian (LQG) control approach. Results obtained in LTAO in closed loop show the significant gain in performance brought by LQG control, which allows tomographic reconstruction. We present a calibration and model identification strategy. Experimental results are shown to be consistent with end-to-end simulations. These results are very encouraging and demonstrate robustness of performance with respect to inevitable experimental uncertainties. They represent a first step for the study of very large telescope (VLT) and extremely large telescopes (ELT) instruments. PMID:20208937
Derivation of clones close to met by preparative field inversion gel electrophoresis
Michiels, F.; Burmeister, M.; Lehrach, H.
1987-06-05
The molecular analysis of genes identified by mutations is a major problems in mammalian genetics. As a step toward this goal, preparative field inversion gel electrophoresis (FIGE) was used to selectively isolate clones from the environment of genetically linked markers, and to select a subset of these clones containing sequences next to specific restriction sites rare in mammalian DNA. This approach has been used to generate a library highly enriched in sequences closely linked to the cystic fibrosis marker met. One clone derived from the end of a Not I restriction fragment containing the met sequence was analyzed in detail and localized within a long range map to a position of 300 kilobase pairs 5' of the metD sequence.
The quest for conformal geometric algebra Fourier transformations
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
Conformal geometric algebra is preferred in many applications. Clifford Fourier transforms (CFT) allow holistic signal processing of (multi) vector fields, different from marginal (channel wise) processing: Flow fields, color fields, electro-magnetic fields, ... The Clifford algebra sets (manifolds) of √-1 lead to continuous manifolds of CFTs. A frequently asked question is: What does a Clifford Fourier transform of conformal geometric algebra look like? We try to give a first answer.
Entropy algebras and Birkhoff factorization
NASA Astrophysics Data System (ADS)
Marcolli, Matilde; Tedeschi, Nicolas
2015-11-01
We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.
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
NASA Astrophysics Data System (ADS)
Kimura, Yusuke
2015-07-01
It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
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.
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.
NASA Astrophysics Data System (ADS)
Gainutdinov, A. M.; Read, N.; Saleur, H.
2016-01-01
We develop in this paper the principles of an associative algebraic approach to bulk logarithmic conformal field theories (LCFTs). We concentrate on the closed {gl(1|1)} spin-chain and its continuum limit—the {c=-2} symplectic fermions theory—and rely on two technical companion papers, Gainutdinov et al. (Nucl Phys B 871:245-288, 2013) and Gainutdinov et al. (Nucl Phys B 871:289-329, 2013). Our main result is that the algebra of local Hamiltonians, the Jones-Temperley-Lieb algebra JTL N , goes over in the continuum limit to a bigger algebra than {V}, the product of the left and right Virasoro algebras. This algebra, {S}—which we call interchiral, mixes the left and right moving sectors, and is generated, in the symplectic fermions case, by the additional field {S(z,bar{z})≡ S_{αβ} ψ^α(z)bar{ψ}^β(bar{z})}, with a symmetric form {S_{αβ}} and conformal weights (1,1). We discuss in detail how the space of states of the LCFT (technically, a Krein space) decomposes onto representations of this algebra, and how this decomposition is related with properties of the finite spin-chain. We show that there is a complete correspondence between algebraic properties of finite periodic spin chains and the continuum limit. An important technical aspect of our analysis involves the fundamental new observation that the action of JTL N in the {gl(1|1)} spin chain is in fact isomorphic to an enveloping algebra of a certain Lie algebra, itself a non semi-simple version of {sp_{N-2}}. The semi-simple part of JTL N is represented by {U sp_{N-2}}, providing a beautiful example of a classical Howe duality, for which we have a non semi-simple version in the full JTL N image represented in the spin-chain. On the continuum side, simple modules over {S} are identified with "fundamental" representations of {sp_∞}.
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.
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
NASA Astrophysics Data System (ADS)
Jackson, Bernard; Tokumaru, Munetoshi; Gonzalez-Esparza, Americo; Hick, P.; Buffington, Andrew; Hong, Sunhak; Bisi, Mario M.; Kim, Jaehun; Yu, Hsiu-Shan
2016-07-01
We find that a portion of the interplanetary magnetic field measured in situ near Earth is present from a direct outward mapping of closed fields from the low solar corona. The Current-Sheet Source Surface (CSSS) model (Zhao & Hoeksema, 1995 JGR 100, 19), extrapolate magnetogram-derived fields upward from near the solar surface. Global velocities and densities inferred from a combination of observations of interplanetary scintillation (IPS), matched to in-situ velocities and densities measured by spacecraft instrumentation, then provide an accurate outward timing to 1 AU using the UCSD tomography model that assumes conservation of mass and mass flux. All three field components at 1 AU are present including the north-south (or Bn) component field, and are compared with the appropriate ACE magnetometer in-situ (RTN) field coordinate. A significant positive daily correlation variation sometimes as high as 0.8 exists between these closed loop components and those determined by in-situ measurement over the last ten years for individual Carrington rotations. We determine that a consistent small fraction of the static low-coronal component flux (˜2%), that includes the Bn component, regularly escapes from closed-field regions. However, this percentage of closed projected fields relative to those measured in situ at Earth varies somewhat, indicating that a more efficient process for this flux propagation exists at the peak of the solar cycle than at its minimum. 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 of using this technique for space weather predictions are being actively developed.
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)
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.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
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…
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…
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…
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.
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.
Twisted Logarithmic Modules of Vertex Algebras
NASA Astrophysics Data System (ADS)
Bakalov, Bojko
2016-07-01
Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted fields involve the logarithm of the formal variable. We develop the theory of such twisted modules and, in particular, derive a Borcherds identity and commutator formula for them. We investigate in detail the examples of affine and Heisenberg vertex algebras.
Basic characterization of TORPEX electrostatic modes in closed field line configurations
Avino, F. Fasoli, A.; Furno, I.; Jolliet, S.; Ricci, P.
2014-12-15
Electrostatic coherent modes are studied in the TORPEX device [Fasoli et al., Plasma Phys. Controlled Fusion 52, 124020 (2010)], in closed flux surfaces. The accessibility to this magnetic geometry is provided by a current-carrying in-vessel toroidal conductor developed to generate a poloidal magnetic field [Avino et al., Rev. Sci. Instrum. 85, 033506 (2014)]. The background plasma parameters are measured, and the ion saturation current fluctuations are characterized in terms of power spectral density to identify the dominant coherent modes and their spatial localization. A statistical approach is implemented to determine the mode spectral properties by computing the statistical dispersion relation. The poloidal wave number k{sub θ} and the toroidal wave number k{sub ϕ} are obtained, as well as the corresponding mode numbers. A three-dimensional linear code based on the drift-reduced Braginskii equations is used to investigate the nature of the instabilities. The linear analysis suggests a dominant ballooning character of the modes.
Optical coatings and thin films for display technologies using closed-field magnetron sputtering
NASA Astrophysics Data System (ADS)
Gibson, Desmond R.; Brinkley, Ian; Walls, J. M.
2004-11-01
"Closed field" magnetron (CFM) sputtering offers high throughput, flexible deposition process for optical coatings and thin films required in display technologies. CFM sputtering uses two or more different metal targets to deposit multilayers comprising a wide range of dielectrics, metals and conductive oxides. CFM provides a room temperature deposition process with high ion current density, low bias voltage and reactive oxidation in the entire volume around the rotating substrate drum carrier, depositing films over a large surface area at a high rate with excellent and reproducible properties. Machines based on CFM are scaleable to meet a range of batch and in-line size requirements. Thin film thickness control to <+/-1% is accomplished using time, although quartz crystal or optical monitoring are used for more demanding applications. Fine layer thickness control and deposition of graded index layers is also assisted with a special rotating shutter mechanism. This paper presents data on optical properties for CFM deposited coatings relevant to displays, including anti-reflection, IR blocker and color and thermal control filters, graded coatings, barrier coatings as well as conductive transparent oxides such as indium tin oxide. Benefits of the CFM process for a range of display technologies; OLED, EL and projection are described.
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.
Deforming the Maxwell-Sim algebra
Gibbons, G. W.; Gomis, Joaquim; Pope, C. N.
2010-09-15
The Maxwell algebra is a noncentral extension of the Poincare algebra, in which the momentum generators no longer commute, but satisfy [P{sub {mu}},P{sub {nu}}]=Z{sub {mu}{nu}}. The charges Z{sub {mu}{nu}} commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincare, this being the symmetry algebra of very special relativity. It admits an analogous noncentral extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim{sub b}, where b is a nontrivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force. In an appendix is it shown that the DISim{sub b} algebra is isomorphic to the extended Schroedinger algebra with its standard deformation parameter z, when b=(1/1-z).
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.
NASA Astrophysics Data System (ADS)
Jackson, B. V.; Hick, P. P.; Buffington, A.; Yu, H.-S.; Bisi, M. M.; Tokumaru, M.; Zhao, X.
2015-04-01
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.
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].
Extending Fourier transformations to Hamilton's quaternions and Clifford's geometric algebras
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
We show how Fourier transformations can be extended to Hamilton's algebra of quaternions. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Hamilton's algebra of quaternions is only one example of the larger class of Clifford's geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.
Topics in Covariant Closed String Field Theory and Two-Dimensional Quantum Gravity
NASA Astrophysics Data System (ADS)
Saadi, Maha
1991-01-01
The closed string field theory based on the Witten vertex is found to be nonpolynomial in order to reproduce all tree amplitudes correctly. The interactions have a geometrical pattern of overlaps, which can be thought as the edges of a spherical polyhedron with face-perimeters equal to 2pi. At each vertex of the polyhedron there are three faces, thus all elementary interactions are cubic in the sense that at most three strings can coincide at a point. The quantum action is constructed by substracting counterterms which cancel the overcounting of moduli space, and by adding loop vertices in such a way no possible surfaces are missed. A counterterm that gives the correct one-string one-loop amplitude is formulated. The lowest order loop vertices are analyzed in the cases of genus one and two. Also, a one-loop two -string counterterm that restores BRST invariance to the respective scattering amplitude is constructed. An attempt to understand the formulation of two -dimensional pure gravity from the discrete representation of a two-dimensional surface is made. This is considered as a toy model of string theory. A well-defined mathematical model is used. Its continuum limit cannot be naively interpreted as pure gravity because each term of the sum over surfaces is not positive definite. The model, however, could be considered as an analytic continuation of the standard matrix model formulation of gravity. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
Semigroups And Computer Algebra In Discrete Structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2010-10-01
Some concepts in semigroup theory are interpreted in discrete structures such as finite lattices, binary relations, and finite semilattices. An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. By analogy with the linear spaces in the linear algebra semilattice homomorphisms, isomorphisms, projections on Boolean vector spaces are defined and some properties of them are investigated in detail. Maps, corresponding to them in the linear algebra, are connected with matrices and their pseudouinverse. Important properties of these maps, which are essential for solving linear systems, remain the same in the Boolean vector spaces. Stochastic experiments using the maps defined and computer algebra methods have been made for solving linear equations Ax = b. The Hamming distance between b and the projection p(b) = Ax of b is equal or close to the least possible one, if the system has no solutions.
Phase Boundaries in Algebraic Conformal QFT
NASA Astrophysics Data System (ADS)
Bischoff, Marcel; Kawahigashi, Yasuyuki; Longo, Roberto; Rehren, Karl-Henning
2016-02-01
We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These can be formulated in a common framework originating in Algebraic QFT, with the principle of Einstein Causality playing a prominent role. We classify the phase boundary conditions by the centre of a certain universal construction, which produces a reducible representation in which all possible boundary conditions are realized. For a large class of models, the classification reproduces results obtained in a different approach by Fuchs et al. before.
Degenerations of generalized Krichever-Novikov algebras on tori
NASA Astrophysics Data System (ADS)
Schlichenmaier, Martin
1993-08-01
Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e., complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain subalgebras of Lie algebras of meromorphic vector fields on P1, the Riemann sphere, are obtained. In case of some natural choices of the markings these subalgebras are explicitly determined. It is shown that the number of markings can change.
Closed-form SEM solution to the transient far-field response of a thin-wire antenna
NASA Astrophysics Data System (ADS)
Hoorfar, Ahmad
1994-05-01
A closed-form SEM representation for the transient far-field response of a thin-wire cylindrical antenna is derived, and explicit expressions for all of the corresponding SEM parameters are presented. In particular, a so-called time-dependent natural far-field mode is introduced, and its corresponding integral is analytically evaluated. Excellent agreements with the numerical results are obtained.
Algebras with convergent star products and their representations in Hilbert spaces
Soloviev, M. A.
2013-07-15
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.
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
NASA Astrophysics Data System (ADS)
Krupp, N.; Radioti, A.; Roussos, E.; Grodent, D.; Gurnett, D. A.; Mitchell, D. G.; Dougherty, M. K.
2011-10-01
In this presentation we use bi-directional energetic electron distributions from the MIMI-LEMMS instrument onboard Cassini, auroral observations from the Hubble Space Telescope (HST) and data from the UVIS instrument onboard Cassini to characterize the open-closed field line boundary in Saturn's magnetosphere. The high-latitude open-closed field line boundary at Saturn is thought to be related to the main auroral ring of emission of the planet varying in location, intensity and latitudinal extent as well as in its homogeneity. This study extends the work on the plasmapause/open-closed field line boundary published by [1] by covering a larger data set at different local times and comparing the electron distributions with auroral observations. Based on energetic electron data we characterize the open-closed field line boundary in terms of temporal, local time variations and other parameters and we correlate the Cassini in-situ measurements to the observations of the main auroral ring at Saturn.
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.
The arithmetic theory of algebraic groups
NASA Astrophysics Data System (ADS)
Platonov, V. P.
1982-06-01
CONTENTS Introduction § 1. Arithmetic groups § 2. Adèle groups § 3. Tamagawa numbers § 4. Approximations in algebraic groups § 5. Class numbers and class groups of algebraic groups § 6. The genus problem in arithmetic groups § 7. Classification of maximal arithmetic subgroups § 8. The congruence problem § 9. Groups of rational points over global fields § 10. Galois cohomology and the Hasse principle § 11. Cohomology of arithmetic groups References
Algorithmic Questions for Linear Algebraic Groups. Ii
NASA Astrophysics Data System (ADS)
Sarkisjan, R. A.
1982-04-01
It is proved that, given a linear algebraic group defined over an algebraic number field and satisfying certain conditions, there exists an algorithm which determines whether or not two double cosets of a special type coincide in its adele group, and which enumerates all such double cosets. This result is applied to the isomorphism problem for finitely generated nilpotent groups, and also to other problems.Bibliography: 18 titles.
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)
G-identities of non-associative algebras
Bakhturin, Yu A; Zaitsev, M V; Sehgal, S K
1999-12-31
The main class of algebras considered in this paper is the class of algebras of Lie type. This class includes, in particular, associative algebras, Lie algebras and superalgebras, Leibniz algebras, quantum Lie algebras, and many others. We prove that if a finite group G acts on such an algebra A by automorphisms and anti-automorphisms and A satisfies an essential G-identity, then A satisfies an ordinary identity of degree bounded by a function that depends on the degree of the original identity and the order of G. We show in the case of ordinary Lie algebras that if L is a Lie algebra, a finite group G acts on L by automorphisms and anti-automorphisms, and the order of G is coprime to the characteristic of the field, then the existence of an identity on skew-symmetric elements implies the existence of an identity on the whole of L, with the same kind of dependence between the degrees of the identities. Finally, we generalize Amitsur's theorem on polynomial identities in associative algebras with involution to the case of alternative algebras with involution.
Comparison of hydrodynamic and semi-kinetic treatments for plasma flow along closed field lines
NASA Technical Reports Server (NTRS)
Singh, Nagendra; Wilson, G. R.; Horwitz, J. L.
1993-01-01
Hydrodynamic and semi-kinetic treatments of plasma flow along closed geomagnetic field lines are compared. The hydrodynamic treatment is based on a simplified 16-moment set of transport equations as the equations for the heat flows are not solved; the heat flows are treated heuristically. The semi-kinetic treatment is based on a particle code. The comparison deals with the distributions of the plasma density, flow velocity, and parallel and perpendicular temperatures as obtained from the two treatments during the various stages of the flow. In the kinetic treatment, the appropriate boundary condition is the prescription of the velocity distribution functions for the particles entering the flux tubes at the ionospheric boundaries; those particles leaving the system are determined by the processes occurring in the flux tube. The prescribed distributions are half-Maxwellian with temperature T(sub 0) and density n(sub 0). In the hydrodynamic model, the prescribed boundary conditions are on density (n(sub 0)), flow velocity (V(sub 0)) and temperature (T(sub 0). It was found that results from the hydrodynamic treatment critically depend on V(sub 0); for early stages of the flow this treatment yields results in good agreement with those from the kinetic treatment, when V(sub 0) = square root of (kT(sub 0)/2 (pi)m), which is the average velocity of particles moving in a given direction for a Maxwellian distribution. During this early stage, the flows developing form the conjugate ionospheres show some distinct transitions. For the first hour or so, the flows are highly supersonic and penetrate deep into the opposite hemispheres, and both hydrodynamics and kinetic treatments yield almost similar features. It is found that during this period heatflow effects are negligibly small. When a flow penetrates deep into the opposite hemisphere, the kinetic treatment predicts reflection and setting up of counterstreaming. In contrast, the hydrodynamic treatment yields a shock in the
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…
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…
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
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…
NASA Astrophysics Data System (ADS)
Christou, M. A.; Polycarpou, A. C.
2015-10-01
Closed-form expressions were derived for the near-zone scattered fields caused by an obliquely incident plane wave of arbitrary polarization on a sub-wavelength circular aperture on an infinite conducting screen with an infinitesimal thickness. The analysis is based on a quasi-static model of the governing fields in the aperture which was published in the mid 40's by Bethe and improved by Bouwkamp a few years later by incorporating additional terms. Starting with first-order analytical expressions for the magnetic surface current density in the aperture, the scattering problem was formulated using the vector potential F →, the equivalence principle, and the image theory resulting in surface integrals over the aperture which involve the free-space Green's function. Using valid approximations for the near-zone field formulation, closed-form analytical expressions were derived for the corresponding scattered fields along the axis of the aperture. Obtained results based on these closed-form expressions were compared with published data obtained using the spectral-domain method indicating a very good agreement.
Supersymmetric extension of Galilean conformal algebras
Bagchi, Arjun; Mandal, Ipsita
2009-10-15
The Galilean conformal algebra has recently been realized in the study of the nonrelativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field theory. In this paper, we extend the analysis to include supersymmetry. We work at the level of the coordinates in superspace to construct the N=1 super-Galilean conformal algebra. One of the interesting outcomes of the analysis is that one is able to naturally extend the finite algebra to an infinite one. This looks structurally similar to the N=1 superconformal algebra in two dimensions, but is different. We also comment on the extension of our construction to cases of higher N.
An accurate magnetic field solution for medical electromagnetic tracking coils at close range
NASA Astrophysics Data System (ADS)
Schroeder, Tobias
2015-06-01
Electromagnetic tracking uses transmitter field models to determine position and orientation of an object. An important application of this technology is surgical navigation, where instruments are frequently tracked at short distances from the transmitter. At short distances, conventional and widely used dipole field models can lead to errors in tracked position and orientation. To increase tracking accuracy in this scenario, this work describes a novel transmitter field model and compares its performance against the dipole model. Demonstrated tracking accuracy improvements could have far-reaching benefits for medical navigation applications.
On the algebra of gauge invariants for one-flavour chromodynamics
NASA Astrophysics Data System (ADS)
Kijowski, J.; Rudolph, G.; Rudolph, M.
1997-08-01
The structure of the algebra of gauge invariant differential forms built from SU(3)-gauge potentials as well as (Grassmann algebra-valued) quark and antiquark fields is discussed. The relevance to one-flavour chromodynamics is outlined.
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.
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
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…
Fast closed-form calculation of THz field enhancement in a metal nanoslit
Novitsky, A. V.; Lavrinenko, A. V.
2010-10-07
Strong electric field enhancement in a metal nanoslit with THz field illumination is hardly calculated using the standard simulation packages. It is explained by the considerable difference of the values of nano sizes of the slit and the wavelength of the incident radiation (up to 10000 times). Therefore, significant computational resources or/and the home-made simulation code is needed. We offer the simple single-parameter model as an alternative to the time consuming calculations. The single parameter can be calculated either from the experimental or simulation data (one reference point is necessary to determine one parameter). Then we can find the field enhancement for different slit geometries and light wavelengths.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
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.
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.
Can a {open_quotes}superconductor{close_quotes} always expel the generalized magnetic field?
Mahajan, S.M.
1998-03-10
The conservation of generalized helicity in a perfectly conducting fluid may act as an electrodynamic barrier for the transition to the London (superconducting) state when the system is immersed in a topologically nontrival magnetic field (with a nonzero generalized helicity). An experiment is proposed to test whether the mechanism responsible (quantum correlations) for superconductivity respects the electrodynamic constraint.
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
NASA Astrophysics Data System (ADS)
Song, Xinfang; Wang, Wenyuan; Fu, Libin
2016-04-01
Oscillating electric field is chosen to investigate the electron-positron pair production process by using a quantum kinetic theory and the effective mass model [Phys. Rev. Lett. 112, 050402 (2014)]. The particle yield exhibits a characteristic oscillatory structure which is related to the multi-photon thresholds. The true peak positions are typically slightly above the naive threshold estimate, which is defined as frequency shift. During the numerical calculations, we find the frequency shift can be affected by the system parameters under adiabatic closing the external field, it is worthwhile to study in detail. In this paper, we investigate the frequency shift and the sub-band effect in electron-positron pair production with oscillating electric field. First, a quantum kinetic theory and the effective mass are presented to obtain the frequency shift, the results are fitted very well. And we find the frequency shift and the sub-band effect can be influenced by pulse duration, photon number, and strength of the external field. The frequency shift becomes evident as increases of photon number and the external field strength. The sub-band width is relatively lower at longer pulse duration, higher photon number region, and weaker external field. The results shown in the paper are helpful for understanding multi-photon pair production process in the strong field.
NASA Astrophysics Data System (ADS)
Song, Xinfang; Wang, Wenyuan; Fu, Libin
2016-09-01
Oscillating electric field is chosen to investigate the electron-positron pair production process by using a quantum kinetic theory and the effective mass model [Phys. Rev. Lett. 112, 050402 (2014)]. The particle yield exhibits a characteristic oscillatory structure which is related to the multi-photon thresholds. The true peak positions are typically slightly above the naive threshold estimate, which is defined as frequency shift. During the numerical calculations, we find the frequency shift can be affected by the system parameters under adiabatic closing the external field, it is worthwhile to study in detail. In this paper, we investigate the frequency shift and the sub-band effect in electron-positron pair production with oscillating electric field. First, a quantum kinetic theory and the effective mass are presented to obtain the frequency shift, the results are fitted very well. And we find the frequency shift and the sub-band effect can be influenced by pulse duration, photon number, and strength of the external field. The frequency shift becomes evident as increases of photon number and the external field strength. The sub-band width is relatively lower at longer pulse duration, higher photon number region, and weaker external field. The results shown in the paper are helpful for understanding multi-photon pair production process in the strong field.
Open-loop and closed-loop control of dissociative ionization of ethanol in intense laser fields
Yazawa, Hiroki; Tanabe, Takasumi; Okamoto, Tatsuyoshi; Yamanaka, Mio; Kannari, Fumihiko; Itakura, Ryuji; Yamanouchi, Kaoru
2006-05-28
The relative yield of the C-O bond breaking with respect to the C-C bond breaking in ethanol cation C{sub 2}H{sub 5}OH{sup +} is maximized in intense laser fields (10{sup 13}-10{sup 15} W/cm{sup 2}) by open-loop and closed-loop optimization procedures. In the open-loop optimization, a train of intense laser pulses are synthesized so that the temporal separation between the first and last pulses becomes 800 fs, and the number and width of the pulses within a train are systematically varied. When the duration of 800 fs is filled with laser fields by increasing the number of pulses or by stretching all pulses in a triple pulse train, the relative yield of the C-O bond breaking becomes significantly large. In the closed-loop optimization using a self-learning algorithm, the four dispersion coefficients or the phases of 128 frequency components of an intense laser pulse are adopted as optimized parameters. From these optimization experiments it is revealed that the yield ratio of the C-O bond breaking is maximized as far as the total duration of the intense laser field reaches as long as {approx}1 ps and that the intermittent disappearance of the laser field within a pulse does not affect the relative yields of the bond breaking pathways.
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
NASA Astrophysics Data System (ADS)
Huang, Yu; Zhang, Xian; Ringe, Emilie; Hou, Mengjing; Ma, Lingwei; Zhang, Zhengjun
2016-03-01
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.
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
Polynomial Extensions of the Weyl C*-Algebra
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Dhahri, Ameur
2015-09-01
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) nontrivial central extension of the Heisenberg algebra, which can be concretely realized as sub-Lie algebras of the polynomial algebra generated by the creation and annihilation operators in the Schrödinger representation. The simplest nontrivial of these extensions (the quadratic one) is isomorphic to the Galilei algebra, widely studied in quantum physics. By exponentiation of this representation we construct the corresponding polynomial analogue of the Weyl C*-algebra and compute the polynomial Weyl relations. From this we deduce the explicit form of the composition law of the associated nonlinear extensions of the 1-dimensional Heisenberg group. The above results are used to calculate a simple explicit form of the vacuum characteristic functions of the nonlinear field operators of the Galilei algebra, as well as of their moments. The corresponding measures turn out to be an interpolation family between Gaussian and Meixner, in particular Gamma.
Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
Anguelova, Iana I.
2013-12-15
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.
Transverse field effect close to the critical point in the TGS ferroelectric
NASA Astrophysics Data System (ADS)
Fugiel, Bogusław; Kikuta, Toshio; Wojtków, Katarzyna
2011-10-01
A hysteresis loop was measured in a round-plate sample of triglycine sulfate (TGS) ferroelectric using two measurement and one side electrode. Due to a non-zero electric potential, V s, applied to the side electrode the hysteresis loop gradually decayed with time. It was shown that the higher the V s value, the shorter time t d is required for the hysteresis loop to disappear. The value of ? turned out to be proportional to the electric potential V s, generating a transverse field at a constant temperature. Within the limits of experimental error, the inverse of the slope of the dependence ? versus V s is proportional to the difference T C - T. A relationship between the temperature T, the spontaneous polarisation P ± (positive or negative) and the freezing parameter f has been proposed. The parameter f describes the influence of the transverse electric field. Arguments in favour of considering the transverse field effect as occurring due to free electric charges flowing into the crystal are given. A method is proposed by which the parameters of the hysteresis loop can be easily adjusted by an electric potential of an additional side electrode.
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)
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
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.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
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.
Hydrous pyrolysis in the field: closed-system diagenesis at high fluid flow
Hutcheon, I.; Abercrombie, H.; Shevalier, M.; Nahnybida, C.
1989-03-01
Diagenetic processes are studied by observing natural systems or by experimental hydrous pyrolysis of water-organic-rock mixtures. Steam-enhanced recovery is similar to hydrous pyrolysis but is done in a previously undisturbed geological setting with mass, time, and temperature closer to natural diagenetic systems. Chemical and isotopic compositions of produced water and gas were determined for wellhead samples obtained from quartz-rich and lithic reservoirs. Estimates of reservoir temperature were made using the silica and Na-K geothermometers and agree with temperatures estimated from /sup 13/C//sup 13/C partitioning between bicarbonate and CO/sub 2/. Temperature and fluid composition data are portrayed on activity diagrams and show that minerals (illite, chalcedony, chlorite, analcime, and smectite) rapidly reach equilibrium with waters. Mineral reactions inferred from produced waters are different in quartz-rich and lithic reservoirs and agree with mineral reactions observed in post-steam cores. Carbon isotopic data indicate that carbonate minerals are the source of produced CO/sub 2/. Comparison of the buffering potential of aqueous carbonate species, carbonate minerals, organic acids, and silicate hydrolysis shows that silicates have the greatest potential to buffer pH. The authors data are consistent with pH control by silicate hydrolysis and indicate that silicate-carbonate reactions may be a major source of CO/sub 2/ during diagenesis. More generally, their results show that a diagenetic system of high fluid flow can be approximated by closed-system behavior.
[Use of ternary algebra in the analysis of medical data].
Bernard, M J
1976-01-01
Logical methods are most valuable in the field of Medicine. They are usually based on Boolean algebra and can thus only deal with binary data) (Present)/(Absent)). Use of ternary algebra opens the way to treatment of the triple-state variables ((Present)/(absent)/(Don't know)) frequently encountered in medical context. PMID:816530
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
Contact-free measurement of the flow field of a liquid metal inside a closed container
NASA Astrophysics Data System (ADS)
Heinicke, Christiane
2014-03-01
The measurement of flow velocities inside metal melts is particularly challenging. Due to the high temperatures of the melts it is impossible to employ measurement techniques that require either mechanical contact with the melt or are only adaptable to translucent fluids. In the past years a number of electromagnetic techniques have been developed that allows a contact-free measurement of volume flows. One of these techniques is the so-called Lorentz Force Velocimetry (LFV) in which the metal flow is exposed to an external, permanent magnetic field. The interaction between the metal and the magnet not only leads to a force on the fluid, but also on the magnet. The force can be measured and is proportional to the velocity of the melt. Moreover, by using a small permanent magnet it is possible to resolve spatial structures inside the flow.We will demonstrate this using a model experiment that has been investigated with different reference techniques previously. The experimental setup is a cylindrical vessel filled with a eutectic alloy which is liquid at room temperature. The liquid metal can be set into motion by means of a propeller at the top of the liquid. Depending on the direction of rotation of the propeller, the flow inside the vessel takes on different states. Beside the vessel, we place a Lorentz Force Flowmeter (LFF) equipped with a small permanent magnet. By measuring the force on the magnet at different positions and different rotation speeds, we demonstrate that we can qualitatively and quantitatively reconstruct the flow field inside the vessel.
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
Canonical quantisation via conditional symmetries of the closed FLRW model coupled to a scalar field
NASA Astrophysics Data System (ADS)
Zampeli, Adamantia
2015-09-01
We study the classical, quantum and semiclassical solutions of a Robertson-Walker spacetime coupled to a massless scalar field. The Lagrangian of these minisuperspace models is singular and the application of the theory of Noether symmetries is modified to include the conditional symmetries of the corresponding (weakly vanishing) Hamiltonian. These are found to be the simultaneous symmetries of the supermetric and the superpotential. The quantisation is performed adopting the Dirac proposal for constrained systems. The innovation in the approach we use is that the integrals of motion related to the conditional symmetries are promoted to operators together with the Hamiltonian and momentum constraints. These additional conditions imposed on the wave function render the system integrable and it is possible to obtain solutions of the Wheeler-DeWitt equation. Finally, we use the wave function to perform a semiclassical analysis following Bohm and make contact with the classical solution. The analysis starts with a modified Hamilton-Jacobi equation from which the semiclassical momenta are defined. The solutions of the semiclassical equations are then studied and compared to the classical ones in order to understand the nature and behaviour of the classical singularities.
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.
NASA Astrophysics Data System (ADS)
Parisot, Amelie; Costille, Anne; Petit, Cyril; Fusco, Thierry
2010-07-01
Adaptive Optics (AO) has a limited corrected field of view because of the anisoplanatism effect. Wide Field AO (WFAO) concepts, such as Multi-Conjugate AO (MCAO), have been developed to overcome this limitation. These complex WFAO systems raise critical challenges such as tomographic control and calibrations. We present new results obtained in closed-loop configuration with the laboratory bench HOMER which is devoted to implementation and validation of these WFAO concepts in the perspective of future VLT/ELT AO systems. Turbulence is generated with rotating phase screens and multi-directional analysis is performed. Tomographic control relies on Linear Quadratic Gaussian control (LQG). The correction can be applied thanks to two Deformable Mirrors (DM). We also focus on calibration issues and models identification. We investigate in particular identification of relative geometry of the wave front sensors, DM altitude and asterism and its impact on performance.
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2014-01-01
Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…
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
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.
The Gel'fand-Kirillov dimension of relatively free associative algebras
Belov, A Ya
2004-12-31
In this paper the Gel'fand-Kirillov dimension GKdim(A) is calculated for a relatively free associative algebra A over an arbitrary ground field. This dimension is determined by the complexity type of the algebra A or by the set of semidirect products of matrix algebras over a polynomial ring contained in the variety Var(A). The proof is comparatively elementary and does not use the local representability of relatively free algebras.
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
Nagelmüller, Sebastian; Kirchgessner, Norbert; Yates, Steven; Hiltpold, Maya; Walter, Achim
2016-04-01
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
Magnetic charge and non-associative algebras
Guenaydin, M.; Zumino, B.
1985-02-01
We consider the possibility that the quantum mechanics of a nonrelativistic electron in the magnetic field of a magnetic charge distribution can be described in terms of a non-associative algebra of observables. It appears that the case of a point monopole is excluded, while that of a constant charge distribution is acceptable. 21 references.
Algebra 1Q, Mathematics: 5215.12.
ERIC Educational Resources Information Center
Hirigoyen, Hector
This is the second of the six guidebooks on minimum course content for first-year algebra; it includes the ordered field properties of the real number system, solution of linear equations and inequalities, verbal problems, exponents and operations with polynomials. Overall goals for the course are stated; performance objectives for each unit, a…
Piecewise lexsegment ideals in exterior algebras
NASA Astrophysics Data System (ADS)
Shakin, D. A.
2005-02-01
The problem of describing the Hilbert functions of homogeneous ideals of an exterior algebra over a field containing a fixed monomial ideal I is considered. For this purpose the notion of a piecewise lexsegment ideal in an exterior algebra is introduced generalizing the notion of a lexsegment ideal. It is proved that if I is a piecewise lexsegment ideal, then it is possible to describe the Hilbert functions of the homogeneous ideals containing I in a way similar to that suggested by Kruskal and Katona for the situation I=0. Moreover, a generalization of the extremal properties of lexsegment ideals is obtained (the inequality for the Betti numbers).
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).
The early history of current Algebra
NASA Astrophysics Data System (ADS)
Pietschmann, Herbert
2011-07-01
The history of Current Algebra is reviewed up to the appearance of the Adler-Weisberger sum rule. Particular emphasis is given to the role of current algebra in the historical struggle in strong interaction physics of elementary particles between field theory and the S-matrix approach based on dispersion relations. The question as to whether some particles are truly fundamental or all hadrons are bound or resonant states of one another played an important role in this struggle and is thus also regarded.
The Dirac equation and Hestenes' geometric algebra
NASA Astrophysics Data System (ADS)
Hamilton, J. Dwayne
1984-06-01
Hestenes' geometric algebra and Dirac spinors are reviewed and united into a common mathematical formalism, a unification that establishes the Dirac equation as being manifestly covariant under the Lorentz group, and one that needs no matrix representation of the Dirac algebra. New and simple methods of amplitude or ``trace'' calculations are then described. A number of problems are then considered within the context of the new approach, such as relativistic spin projections, new and covariant C and T-transformations and spinors for massless and Majorana fields.
NASA Astrophysics Data System (ADS)
Roitman, Michael
2008-08-01
In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
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.
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…
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.
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
NASA Astrophysics Data System (ADS)
Alecian, E.; Neiner, C.; Wade, G. A.; Mathis, S.; Bohlender, D.; Cébron, D.; Folsom, C.; Grunhut, J.; Le Bouquin, J.-B.; Petit, V.; Sana, H.; Tkachenko, A.; ud-Doula, A.
2015-01-01
It is now well established that a fraction of the massive (M > 8 M ⊙) star population hosts strong, organised magnetic fields, most likely of fossil origin. The details of the generation and evolution of these fields are still poorly understood. The BinaMIcS project takes an important step towards the understanding of the interplay between binarity and magnetism during the stellar formation and evolution, and in particular the genesis of fossil fields, by studying the magnetic properties of close binary systems. The components of such systems are most likely formed together, at the same time and in the same environment, and can therefore help us to disentangle the role of initial conditions on the magnetic properties of the massive stars from other competing effects such as age or rotation. We present here the main scientific objectives of the BinaMIcS project, as well as preliminary results from the first year of observations from the associated ESPaDOnS and Narval spectropolarimetric surveys.
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.
Wenzel, Jan; Wormit, Michael; Dreuw, Andreas
2014-10-01
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. PMID:25130619
The three-dimensional origin of the classifying algebra
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph; Stigner, Carl
2010-01-01
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra. We show how this algebra arises naturally from the three-dimensional geometry of factorization of correlators of bulk fields on the disk. This allows us to derive explicit expressions for the structure constants of the classifying algebra as invariants of ribbon graphs in the three-manifold S×S. Our result unravels a precise relation between intertwiners of the action of the mapping class group on spaces of conformal blocks and boundary conditions in rational conformal field theories.
Teaching Arithmetic and Algebraic Expressions
ERIC Educational Resources Information Center
Subramaniam, K.; Banerjee, Rakhi
2004-01-01
A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Spinors in the hyperbolic algebra
NASA Astrophysics Data System (ADS)
Ulrych, S.
2006-01-01
The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
Laterally closed lattice homomorphisms
NASA Astrophysics Data System (ADS)
Toumi, Mohamed Ali; Toumi, Nedra
2006-12-01
Let A and B be two Archimedean vector lattices and let be a lattice homomorphism. We call that T is laterally closed if T(D) is a maximal orthogonal system in the band generated by T(A) in B, for each maximal orthogonal system D of A. In this paper we prove that any laterally closed lattice homomorphism T of an Archimedean vector lattice A with universal completion Au into a universally complete vector lattice B can be extended to a lattice homomorphism of Au into B, which is an improvement of a result of M. Duhoux and M. Meyer [M. Duhoux and M. Meyer, Extended orthomorphisms and lateral completion of Archimedean Riesz spaces, Ann. Soc. Sci. Bruxelles 98 (1984) 3-18], who established it for the order continuous lattice homomorphism case. Moreover, if in addition Au and B are with point separating order duals (Au)' and B' respectively, then the laterally closedness property becomes a necessary and sufficient condition for any lattice homomorphism to have a similar extension to the whole Au. As an application, we give a new representation theorem for laterally closed d-algebras from which we infer the existence of d-algebra multiplications on the universal completions of d-algebras.
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
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.…
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…
ERIC Educational Resources Information Center
Boiteau, Denise; Stansfield, David
This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
ERIC Educational Resources Information Center
Kennedy, John
This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…
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…
Heisenberg Groups and their Automorphisms over Algebras with Central Involution
NASA Astrophysics Data System (ADS)
Johnson, Robert W.
2015-08-01
Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real and complex quadratic spaces with dimension 4 or less. A model for the representations of these Heisenberg groups and automorphism groups is constructed. A pseudo-differential operator enables a parallel treatment of spaces defined over finite and real fields.
Semigroups And Computer Algebra In Finite Discrete Structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2011-12-01
Some semilattice homomorphisms, isomorphisms, projections on Boolean algebras consisting of Boolean matrices are defined and some properties of them are investigated in detail. Let B and A be any rectangular Boolean matrices. A semilattice homomorphism fA,B and its pseudoinverse fA,B+ are defined. The two possible compositions of them pA,B and pA,B+ are projections with images isomorphic to each other. Moreover pA,B maps every congruence class corresponding to fA,B on the least element of the class as well as fA,B+ does it respectively. Necessary and sufficient conditions for the Boolean matrix equation AXB = C to be solvable are proved. This result is very close to those published by Roger Penrose in 1955 for matrices over complex or real fields. We established that it is not so essential to find out which Boolean matrices have a pseudoinverse but to discover homomorphisms between Boolean semilattices having pseudoinverse in all cases. Many of the important properties of fA,B and fA,B+ remain the same for those corresponding to them in the linear algebra.
D-algebra structure of topological insulators
NASA Astrophysics Data System (ADS)
Estienne, B.; Regnault, N.; Bernevig, B. A.
2012-12-01
In the quantum Hall effect, the density operators at different wave vectors generally do not commute and give rise to the Girvin-MacDonald-Plazmann (GMP) algebra, with important consequences such as ground-state center-of-mass degeneracy at fractional filling fraction, and W1+∞ symmetry of the filled Landau levels. We show that the natural generalization of the GMP algebra to higher-dimensional topological insulators involves the concept of a D commutator. For insulators in even-dimensional space, the D commutator is isotropic and closes, and its structure factors are proportional to the D/2 Chern number. In odd dimensions, the algebra is not isotropic, contains the weak topological insulator index (layers of the topological insulator in one fewer dimension), and does not contain the Chern-Simons θ form. This algebraic structure paves the way towards the identification of fractional topological insulators through the counting of their excitations. The possible relation to D-dimensional volume-preserving diffeomorphisms and parallel transport of extended objects is also discussed.
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yao, JingTao
2004-04-01
The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.
(I,q)-graded Lie algebraic extensions of the Poincaré algebra, constraints on I and q
NASA Astrophysics Data System (ADS)
Wills Toro, Luis Alberto
1995-04-01
The constraints on the index set I and on the function q of the (I,q)-graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single-grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∈N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2-gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space-time parameter can either commute or anticommute with the further parameters of the (I,q)-graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity.
Deformed Maxwell Algebras and their Realizations
Gomis, Joaquim; Kamimura, Kiyoshi; Lukierski, Jerzy
2009-12-15
We study all possible deformations of the Maxwell algebra. In D = d+1not =3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1, 1)+so(d, 1) or to so(d, 2)+so(d, 1) depending on the signs of the deformation parameter. We construct in the dS(AdS) space a model of massive particle interacting with Abelian vector field via nonlocal Lorentz force. In D = 2+1 the deformations depend on two parameters b and k. We construct a phase diagram, with two parts of the (b, k) plane with so(3, 1)+so(2, 1) and so( 2, 2)+so(2, 1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2, 1)+so(2, 1). We introduce in D = 2+1 the Volkov-Akulov type model for a Abelian Goldstone-Nambu vector field described by a non-linear action containing as its bilinear term the free Chern-Simons Lagrangean.
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.
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.
NASA Astrophysics Data System (ADS)
Chisham, Gareth
2015-04-01
Spatiotemporal variations of ionospheric vorticity are a measure of the dynamical coupling of the magnetosphere to the ionosphere via magnetic field-aligned currents (FACs). Indeed, ionospheric vorticity measurements have often been used as proxy measurements for FACs. Previously, we have determined statistical models of ionospheric vorticity using 6 years of ionospheric convection velocity measurements made by the SuperDARN HF radar network in the northern hemisphere ionosphere and shown that the spatial variation of these probability distributions is well organised according to the well-established large-scale FAC structure in the polar ionosphere. However, to date, these statistical models have been parameterised solely by the state of the interplanetary magnetic field (IMF), and as such do not account for the range of polar cap sizes that occur for a single IMF state. This leads to a distortion of the shape of the resulting statistical maps that makes features in the statistical variations appear smoother than those in instantaneous/short-time averaged measurements. This is because the averaging process does not consider the variable size of the polar cap, by which spatial features in the ionospheric vorticity variation are ordered. Using open-closed magnetic field line boundary measurements determined from FUV imager data from the IMAGE spacecraft, we investigate the parameterisation of the statistical ionospheric vorticity models with polar cap size in addition to the state of the IMF. The results of this analysis have implications for other statistical models determined in this way, such as those for FACs and ionospheric convection.
The algebra of diffeomorphisms from the world sheet
NASA Astrophysics Data System (ADS)
Schulgin, Waldemar; Troost, Jan
2014-09-01
The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Yang, J. S.; Chen, K. W.
1989-10-01
It was known from a complete model analysis1,2 that the wake potential in the pill-box cavity is predominantly determined by a few longitudinal modes counting from the fundamental longitudinal mode. An approach to find the longitudinal modes of an elliptical cavity is developed by means of the coordinate transformation method. It is found that the field configuration and eigenfrequencies of the elliptical cavity can be expressed in a closed form in terms of Mathieu functions. Inserting the closed form solution of modes into the previous analytical formula for the wake field, the wake field is expressed too in a closed form solution, which is convenient for numerical calculation. Thus, a numerical method to calculate expediently the wake field is developed, and a model calculation is presented.
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.
NASA Astrophysics Data System (ADS)
Zhou, Helin; Diendorfer, Gerhard; Thottappillil, Rajeev; Pichler, Hannes; Mair, Martin
2012-04-01
We examine in detail the simultaneous lightning current waveforms, close electric field changes, and lightning location system data for upward lightning discharges initiated from the Gaisberg Tower (GBT) from 2005 to 2009. Out of 205 upward flashes, most of them (87% or 179/205) were initiated from the tower top without any nearby preceding lightning activity (called "self-initiated"), whereas 26 upward flashes (13%) were initiated from the tower top with immediately preceding nearby lightning activity (called "nearby-lightning-triggered"), including 15 positive ground flashes, one negative ground flashes, and 10 cloud discharges. The possible reasons for self-initiated upward flashes dominating at the GBT could be the field enhancement due to the Gaisberg Mountain above the surrounding terrain and low altitude of charge region during non-convective season (September to March), since we note that self-initiated lightning at the GBT occurred predominantly (79% or 142/179) during non-convective season. On the other hand the majority (85% or 22/26) of nearby-lightning-triggered upward flashes at the GBT occurring during convective season (April to August) and 80 nearby-lightning-triggered upward flashes out of 81 upward flashes observed at the ten tall towers in Rapid City in South Dakota of USA occurring during summer seasons, could be due to the result of high altitude of charge region. The triggering flashes were detected to be within 1 and 18 km distance and the time intervals between them and upward lightning initiation are in the range of 0.3 to 90.7 ms.
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.
Ideals and primitive elements of some relatively free Lie algebras.
Ekici, Naime; Esmerligil, Zerrin; Ersalan, Dilek
2016-01-01
Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a primitive element [Formula: see text] but, [Formula: see text] and [Formula: see text] are not conjugate by means of an inner automorphism. PMID:27386282
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
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.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
NASA Astrophysics Data System (ADS)
Hasheminiasari, Masood
"Smart" high temperature piezoelectric aluminum nitride (AlN) thin films were synthesized by reactive magnetron sputtering using DC; pulsed-DC, and deep oscillation modulated pulsed power (DOMPP) systems on variety of substrate materials. Process optimization was performed to obtain highly c-axis texture films with improved piezoelectric response via studying the interplay between process parameters, microstructure and properties. AlN thin films were sputtered with DC and pulsed-DC systems to investigate the effect of various deposition parameters such as reactive gas ratio, working pressure, target power, pulsing frequency, substrate bias, substrate heating and seed layers on the properties and performance of the film device. The c-axis texture, orientation, microstructure, and chemical composition of AlN films were characterized by means of X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), and x-ray photoelectron spectroscopy (XPS). A Michelson laser interferometer was designed and built to obtain the converse piezoelectric response of the deposited AlN thin films. Thin films with narrow AlN-(002) rocking curve of 2.5° were obtained with preliminary studies of DOMPP reactive sputtering. In-situ high temperature XRD showed excellent thermal stability and oxidation resistance of AlN films up to 1000 °C. AlN films with optimized processing parameters yielded an inverse piezoelectric coefficient, d33 of 4.9 pm/V close to 90 percent of its theoretical value.
Lie Triple Derivations of CSL Algebras
NASA Astrophysics Data System (ADS)
Yu, Weiyan; Zhang, Jianhua
2013-06-01
Let [InlineEquation not available: see fulltext.] be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space [InlineEquation not available: see fulltext.] with [InlineEquation not available: see fulltext.], and [InlineEquation not available: see fulltext.] the associated CSL algebra. It is proved that every Lie triple derivation from [InlineEquation not available: see fulltext.] into any σ-weakly closed algebra [InlineEquation not available: see fulltext.] containing [InlineEquation not available: see fulltext.] is of the form X→ XT- TX+ h( X) I, where [InlineEquation not available: see fulltext.] and h is a linear mapping from [InlineEquation not available: see fulltext.] into ℂ such that h([[ A, B], C])=0 for all [InlineEquation not available: see fulltext.].
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
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. PMID:27171890
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.
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
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…
NASA Astrophysics Data System (ADS)
Tanaka, H.; Uchida, M.; Maekawa, T.; Bae, Y.-S.; Joung, M.; Jeong, J. H.; KSTAR Team
2016-04-01
An experiment on non-inductive plasma current start-up by electron cyclotron (EC) heating and current drive (ECH/ECCD) has been carried out on KSTAR by injecting the fundamental O-mode wave from the low-field side obliquely to the toroidal magnetic field. A plasma current up to 14.5 kA is generated by 180 kW of 84 GHz microwave power and the magnetic measurement shows the formation of a large last-closed flux surface with a diameter of 0.4 m. The soft x-ray emission profile and fast CCD images also support the existence of closed flux surfaces. The current of the cross-field-passing electrons (CFPEs) is calculated according to the paper Nucl. Fusion 52 083008 in these experimental conditions, and it is shown that a CFPE current can produce the initial closed flux surfaces. The observed large increase of EC emission supports the generation of energetic electrons, like CFPEs. After the formation of the closed flux surfaces, the pressure-driven current and CFPE current do not flow in the closed flux surfaces. EC-driven current should flow in these surfaces and ramp up the plasma current. It is estimated that an EC-driven current of about one third of the total plasma current flows in the closed flux surface at the last stage.
Quantum Phase Space from Schwinger's Measurement Algebra
NASA Astrophysics Data System (ADS)
Watson, P.; Bracken, A. J.
2014-07-01
Schwinger's algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking distinct values, where is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is thereby related to definite experimental configurations.
Invariants of triangular Lie algebras with one nil-independent diagonal element
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-08-01
The invariants of solvable triangular Lie algebras with one nil-independent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan's method of moving frames and the special technique developed for triangular and closed algebras in Boyko et al (J. Phys. A: Math. Theor. 2007 40 7557). The conjecture of Tremblay and Winternitz (J. Phys. A: Math. Gen. 2001 34 9085) on the number and form of elements in the bases is completed and proved.
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.
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. PMID:20355462
Andrés, Jose A; Larson, Erica L; Bogdanowicz, Steven M; Harrison, Richard G
2013-02-01
One of the central questions in evolutionary genetics is how much of the genome is involved in the early stages of divergence between populations, causing them to be reproductively isolated. In this article, we investigate genomic differentiation in a pair of closely related field crickets (Gryllus firmus and G. pennsylvanicus). These two species are the result of allopatric divergence and now interact along an extensive hybrid zone in eastern North America. Genes encoding seminal fluid proteins (SFPs) are often divergent between species, and it has been hypothesized that these proteins may play a key role in the origin and maintenance of reproductive isolation between diverging lineages. Hence, we chose to scan the accessory gland transcriptome to enable direct comparisons of differentiation for genes known to encode SFPs with differentiation in a much larger set of genes expressed in the same tissue. We have characterized differences in allele frequency between two populations for >6000 SNPs and >26,000 contigs. About 10% of all SNPs showed nearly fixed differences between the two species. Genes encoding SFPs did not have significantly elevated numbers of fixed SNPs per contig, nor did they seem to show larger differences than expected in their average allele frequencies. The distribution of allele frequency differences across the transcriptome is distinctly bimodal, but the relatively high proportion of fixed SNPs does not necessarily imply "ancient" divergence between these two lineages. Further studies of linkage disequilibrium and introgression across the hybrid zone are needed to direct our attention to those genome regions that are important for reproductive isolation. PMID:23172857
Integrated ExoMars PanCam, Raman, and close-up imaging field tests on AMASE 2009
NASA Astrophysics Data System (ADS)
Foss Amundsen, Hans Erik; Westall, Frances; Steele, Andrew; Vago, Jorge; Schmitz, Nicole; Bauer, Arnold; Cousins, Claire; Rull, Fernando; Sansano, Antonio; Midtkandal, Ivar
2010-05-01
Arctic Mars Analog Svalbard Expedition (AMASE) uses Mars analog field sites on the Arctic islands of Svalbard (Norway) for research within astrobiology and for testing of payload instruments onboard Mars missions Mars Science Laboratory, ExoMars and Mars Sample Return. AMASE 2009 marked the seventh consecutive year of field testing. Instrument shakedowns were arranged to mimic rover operations on Mars and included the panoramic camera (PanCam), mineral- and organic chemistry sensors (Raman-LIBS) and ground penetrating radar (Wisdom) onboard ExoMars together with CheMin and SAM instruments onboard MSL and testing of sampling and caching protocols using JPĹs Fido rover. Test sites included volcanic rocks within the Bockfjord Volcanic Complex (BVC) with carbonate deposits identical to those in ALH84001 and Carboniferous sandstones and paleosols at Ismåsestranda. In view of the 2018 ExoMars mission, field models of the PanCam and Raman instruments, as well as an Olympus E410 camera having similar technical specifications to the ExoMars Close-Up Imager (CLUPI) were used in an integrated exercise to characterise the geology and habitability of the different field sites. The BVC locality consisted of volcanclastic sediments deposited on the flanks of the 1 Ma old Sverrefjell volcano. This volcano is constructed of primitive alkaline basalt with abundant mantle xenoliths. The sediments were a mixture of hyaloclastite, ash, volcanic bombs, lava detritus, and xenoliths (peridotites, granulites) deposited in a roughly laminated fashion on the slopes of the volcano. Late stage carbonate deposits were also present. The Ismåsestranda locality consisted of fine-grained sandstone deposited in a littoral environment. The sandstones were characterised by a variety of sedimentary structures reflecting a marginal marine depositional environment. They were highly variegated in colour due to diagenetic remobilisation of trace elements. PanCam made general context observations using
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Handheld Computer Algebra Systems in the Pre-Algebra Classroom
ERIC Educational Resources Information Center
Gantz, Linda Ann Galofaro
2010-01-01
This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…
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…
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…
Philip, Bobby; Chartier, Dr Timothy
2012-01-01
methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.
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
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
The Weyl realizations of Lie algebras, and left-right duality
NASA Astrophysics Data System (ADS)
Meljanac, Stjepan; Krešić-Jurić, Saša; Martinić, Tea
2016-05-01
We investigate dual realizations of non-commutative spaces of Lie algebra type in terms of formal power series in the Weyl algebra. To each realization of a Lie algebra 𝔤 we associate a star-product on the symmetric algebra S(𝔤) and an ordering on the enveloping algebra U(𝔤). Dual realizations of 𝔤 are defined in terms of left-right duality of the star-products on S(𝔤). It is shown that the dual realizations are related to an extension problem for 𝔤 by shift operators whose action on U(𝔤) describes left and right shift of the generators of U(𝔤) in a given monomial. Using properties of the extended algebra, in the Weyl symmetric ordering we derive closed form expressions for the dual realizations of 𝔤 in terms of two generating functions for the Bernoulli numbers. The theory is illustrated by considering the κ-deformed space.
Twisted fermionic oscillator algebra in κ-minkowski space-time
NASA Astrophysics Data System (ADS)
Verma, Ravikant
2015-04-01
In this paper, we investigate the twisted algebra of the fermionic oscillators associated with Dirac field defined in κ-Minkowski space-time. Starting from κ-deformed Dirac theory, which is invariant under the undeformed κ-Poincaré algebra, using the twisted flip operator, we derive the deformed algebra of the creation and annihilation operators corresponding to the Dirac field quanta in κ-Minkowski space-time. In the limit a → 0, the deformed algebra reduces to the commutative result.
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…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
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…
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.)
Condensing Algebra for Technical Mathematics.
ERIC Educational Resources Information Center
Greenfield, Donald R.
Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
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.)
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…
Exploring Algebraic Patterns through Literature.
ERIC Educational Resources Information Center
Austin, Richard A.; Thompson, Denisse R.
1997-01-01
Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…
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…
NASA Astrophysics Data System (ADS)
Yao, Zh. Q.; Yang, P.; Huang, N.; Sun, H.; Wan, G. J.; Leng, Y. X.; Chen, J. Y.
2005-11-01
Silicon nitride (SiNx) thin films are of special interest in both scientific research and industrial applications due to their remarkable properties such as high thermal stability, chemical inertness, high hardness and good dielectric properties. In this work, SiNx films were fabricated by pulsed reactive closed-field unbalanced magnetron sputtering of high purity single crystal silicon targets in an Ar-N2 mixture. The effect of N2 partial pressure on the film composition, chemical bonding configurations, surface morphology, surface free energy, optical and mechanical properties were investigated. We showed that with increased N2 partial pressure, the N to Si ratio (N/Si) in the film increased and N atoms are preferentially incorporated in the NSi3 stoichiometric configuration. It leads the Si-N network a tendency to chemical order. Films deposited at a high N2 fraction were consistently N-rich. The film surface transformed from a loose granular structure with microporosity to a homogeneous, continuous, smooth and dense structure. A progressive densification of the film microstructure occurs as the N2 fraction is increased. The reduced surface roughness and the increased N incorporation in the film give rise to the increased contact angle with double-distilled water from 24° to 49.6°. To some extent, the SiNx films deposited by pulsed magnetron sputtering are hydrophilic in nature. The as-deposited SiNx films exhibit good optical transparency in the visible region and the optical band gap Eopt can be varied from 1.68 eV for a-Si to 3.62 eV for SiNx films, depending on the synthesis parameters. With the increase of the N/Si atomic ratio, wear resistance of the SiNx films was improved, a consequence of increased hardness and elastic modulus. The SiNx films have lower friction coefficient and better wear resistance than 316L stainless steel under dry sliding friction, where the SiNx films experienced only fatigue wear.
A Renormalisation Group Method. I. Gaussian Integration and Normed Algebras
NASA Astrophysics Data System (ADS)
Brydges, David C.; Slade, Gordon
2015-05-01
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving both boson and fermion fields, which arises as a representation of the continuous-time weakly self-avoiding walk. In this paper, we define normed algebras suitable for a renormalisation group analysis, and develop methods for performing analysis on these algebras. We also develop the theory of Gaussian integration on these normed algebras, and prove estimates for Gaussian integrals. The concepts and results developed here provide a foundation for the continuation of the method presented in subsequent papers in the series.
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…
Boolean Operations with Prism Algebraic Patches.
Bajaj, Chandrajit; Paoluzzi, Alberto; Portuesi, Simone; Lei, Na; Zhao, Wenqi
2008-01-01
In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C(1)-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation. PMID:21516262
Algebraic aspects of Tremblay-Turbiner-Winternitz Hamiltonian systems
NASA Astrophysics Data System (ADS)
Calzada, J. A.; Celeghini, E.; del Olmo, M. A.; Velasco, M. A.
2012-02-01
Using the factorization method we find a hierarchy of Tremblay-Turbiner-Winternitz Hamiltonians labeled by discrete indices. The shift operators (those connecting eigenfunctions of different Hamiltonians of the hierarchy) as well the ladder operators (they connect eigenstates of a determined Hamiltonian) obtained in this way close different algebraic structures that are presented here.
Bosonization of Bosons in Vertex Operator Representations of Affine Kac-Moody Algebras
NASA Astrophysics Data System (ADS)
Sakamoto, M.
1990-08-01
It is shown that various compactified closed string theories on orbifolds and tori are connected with one another through the change of bases of affine Kac-Moody algebras in vertex operator representations.
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.
Higher Sugawara Operators for the Quantum Affine Algebras of Type A
NASA Astrophysics Data System (ADS)
Frappat, Luc; Jing, Naihuan; Molev, Alexander; Ragoucy, Eric
2016-07-01
We give explicit formulas for the elements of the center of the completed quantum affine algebra in type A at the critical level that are associated with the fundamental representations. We calculate the images of these elements under a Harish-Chandra-type homomorphism. These images coincide with those in the free field realization of the quantum affine algebra and reproduce generators of the q-deformed classical {{mathcal W}}-algebra of Frenkel and Reshetikhin.
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.
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.
NASA Astrophysics Data System (ADS)
de Souza, Mariano; Brühl, Andreas; Strack, Christian; Schweitzer, Dieter; Lang, Michael
2012-08-01
We present ultra-high-resolution dilatometric studies in magnetic fields on a quasi-two-dimensional organic conductor κ-(D8-BEDT-TTF)2Cu[N(CN)2]Br, which is located close to the Mott metal-insulator (MI) transition. The obtained thermal expansion coefficient, α(T), reveals two remarkable features: (i) the Mott MI transition temperature TMI=(13.6±0.6) K is insensitive to fields up to 10 T, the highest applied field; (ii) for fields along the interlayer b axis, a magnetic field induced (FI) phase transition at TFI=(9.5±0.5) K is observed above a threshold field Hc˜1 T, indicative of a spin reorientation with strong magnetoelastic coupling.
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)
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.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
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.
Minimal dynamics and the classification of C*-algebras.
Toms, Andrew S; Winter, Wilhelm
2009-10-01
Let X be an infinite, compact, metrizable space of finite covering dimension and alpha: X --> X a minimal homeomorphism. We prove that the crossed product C(X) times sign, right closed(alpha) Z absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms. PMID:19805164
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.
Closing the Performance Gap in a 4th Wave and Post-Modern Society: Lessons from the Field
ERIC Educational Resources Information Center
Adams, J. Q.
2005-01-01
The USA is undergoing tremendous cultural changes as we open the first decade of the 21st century. In this paper the author discusses the need to close the performance gap that exists between White, African American, and Latino/a students. To do so, educators must carefully consider several important cultural forces. The author examines the shift…
Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.
ERIC Educational Resources Information Center
Leitze, Annette Ricks; Kitt, Nancy A.
2000-01-01
Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
Loop Virasoro Lie conformal algebra
Wu, Henan Chen, Qiufan; Yue, Xiaoqing
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
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.
Quantized Nambu-Poisson manifolds and n-Lie algebras
DeBellis, Joshua; Saemann, Christian; Szabo, Richard J.
2010-12-15
We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of R{sup n} by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.
Scaling Linear Algebra Kernels using Remote Memory Access
Krishnan, Manoj Kumar; Lewis, Robert R.; Vishnu, Abhinav
2010-09-13
This paper describes the scalability of linear algebra kernels based on remote memory access approach. The current approach differs from the other linear algebra algorithms by the explicit use of shared memory and remote memory access (RMA) communication rather than message passing. It is suitable for clusters and scalable shared memory systems. The experimental results on large scale systems (Linux-Infiniband cluster, Cray XT) demonstrate consistent performance advantages over ScaLAPACK suite, the leading implementation of parallel linear algebra algorithms used today. For example, on a Cray XT4 for a matrix size of 102400, our RMA-based matrix multiplication achieved over 55 teraflops while ScaLAPACK’s pdgemm measured close to 42 teraflops on 10000 processes.
Quantized Nambu-Poisson manifolds and n-Lie algebras
NASA Astrophysics Data System (ADS)
DeBellis, Joshua; Sämann, Christian; Szabo, Richard J.
2010-12-01
We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of {{R}}^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.
Sequential products on effect algebras
NASA Astrophysics Data System (ADS)
Gudder, Stan; Greechie, Richard
2002-02-01
A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.
Curvature calculations with spacetime algebra
Hestenes, D.
1986-06-01
A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
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)
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.
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.
Semiclassical states on Lie algebras
Tsobanjan, Artur
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
NASA Astrophysics Data System (ADS)
Lannes, A.; Teunissen, P. J. G.
2011-05-01
The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called `phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be `closure-phase ambiguities:' the so-called `closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is
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
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).
2005-04-11
The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.
Majorana-Oppenheimer Approach to Proca Field Equations
NASA Astrophysics Data System (ADS)
Tomazelli, J. L.; Fernandes, G. A. M. A.
2014-09-01
A Dirac-like equation for a massive field obeying the classical Proca equations of motion (PMO) is proposed in close analogy with Majorana's construct for Maxwell electrodynamics. Its underlying algebraic structure is examined and a plausible physical interpretation is discussed. The behavior of the PMO equations in the presence of an external electromagnetic field is also investigated in the low energy limit, via unitary transformations similar to the Foldy-Wouthuysen canonical transformation for a Dirac fermion.
NASA Astrophysics Data System (ADS)
Posner, Arik; Zurbuchen, Thomas H.; Schwadron, Nathan A.; Fisk, Lennard A.; Gloeckler, George; Linker, Jon A.; Mikić, Zoran; Riley, Pete
2001-08-01
Recently, Fisk et al. [1999] have presented a theory that describes a number of features of the large-scale coronal and heliospheric magnetic field. This theory predicts large-scale transport of magnetic flux across the boundaries of the polar coronal holes, which leads to reconnection processes of open field lines with preliminary closed magnetic structures. Reconnection processes reveal themselves in solar wind composition data: Plasma released out of previously closed magnetic field structures exhibits hotter charge state distributions and has a tendency to be enriched by elements with low first ionization potentials. The idea of reconnection at the boundaries of coronal holes is not new. For example, Wang and Sheeley [1993] and Luhmann et al. [1999] found evidence for that mechanism by comparison of observations of the rotation and evolution of coronal holes with potential field models of the solar corona. We use Ulysses Solar Wind Ion Composition Spectrometer composition measurements and sophisticated numerical models [Linker et al., 1999; Riley et al., 1999] to accurately map these observations back to the solar surface. We then constrain the thickness of the stream interface at the Sun and compare the location of the source region with SOHO observations of the low corona. The results are discussed in the context of the global structure of the heliospheric magnetic field.
Explicit Closed Forms for Parametric Integrals. Classroom Notes
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2004-01-01
Closed forms are computed for parametric integrals, generally using induction formulas. It is shown that these integrals can be core activities, mixing hand-work, computations with a computer algebra system and experimental mathematics with an interactive website.
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.
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel
Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.
NASA Astrophysics Data System (ADS)
Saur, Joachim; Neubauer, Fritz M.; Strobel, Darrell F.; Summers, Michael E.
2002-12-01
We interpret plasma and magnetic field observations taken during the Galileo spacecraft Io flybys I0 in December 1995, I24 in October 1999, and I27 in February 2000, and we give predictions for a generic pass over Io's northern pole with a three-dimensional, two-fluid plasma model. We show that all previous field and plasma observations by the Galileo spacecraft can be explained without the assumption of an internal magnetic field of Io in contrast to claims by [1996a, 1996b] and [1997]. We are also able to reproduce both the magnitude and the structure of the double-peak magnetic field signature of the I0 flyby. The origin of this structure can be attributed to diamagnetic and inertia currents. Observations by a polar flyby should answer Io's internal magnetic field question decisively. We also study the effect of different neutral atmosphere models on Io's electrodynamic interaction. Our analysis suggests that Io's atmosphere is longitudinally asymmetric with the scale height on the upstream side smaller than on the downstream side due to the drag force of the flowing plasma on Io's atmosphere. We also show how the Hall effect in Io's ionosphere generates rotated Alfvén wings. In addition, the high-energy electrons observed by [1996, 1999] and [1999] might play an important role for the formation of Io's downstream wake.
Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.
ERIC Educational Resources Information Center
Stoutemyer, David R.
1983-01-01
Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)
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.
Class Numbers and Groups of Algebraic Groups
NASA Astrophysics Data System (ADS)
Platonov, V. P.; Bondarenko, A. A.; Rapinčuk, A. S.
1980-06-01
The class number of an algebraic group G defined over a global field is the number of double cosets of the adele group GA with respect to the subgroups of integral and principal adeles. In most cases the set of double cosets has the natural structure of an abelian group, called the class group of G. In this article the class number of a semisimple group G is computed, and it is proved that any finite abelian group can be realized as a class group.Bibliography: 24 titles.
Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces
Koibuchi, H. )
1991-10-10
In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.
Invertible linear transformations and the Lie algebras
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Guo, Fukui
2008-07-01
With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
Beyond Dirac - a Unified Algebra
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2001-10-01
A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.
Taiwanese Arithmetic and Algebra
ERIC Educational Resources Information Center
Lo, Jane-Jane; Tsai, Feng-Chiu
2011-01-01
Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…
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. PMID:25535181
Yang-Mills connections valued on the octonionic algebra
NASA Astrophysics Data System (ADS)
Restuccia, A.; Veiro, J. P.
2016-05-01
We consider a formulation of Yang-Mills theory where the gauge field is valued on an octonionic algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge formulations are the usual su(2) or u(1) Yang-Mills theories.
The Effects of the Content Enhancement Model in College Algebra
ERIC Educational Resources Information Center
VanCleave, Janet Milleret
2010-01-01
The purpose of this study was to investigate The Content Enhancement Model in the field of college algebra in a mid-western community college. The Content Enhancement Model is a teaching technique that teachers use to help students acquire the content information by helping them identify, organize, comprehend, and memorize material. This study…
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…
NASA Technical Reports Server (NTRS)
Rubinstein, Marcos; Uman, Martin A.; Thomson, Ewen M.; Medelius, Pedro J.
1991-01-01
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.
Steinmaus, Craig M; George, Christine M; Kalman, David A; Smith, Allan H
2006-05-15
Millions of people worldwide are exposed to arsenic-contaminated drinking water. Arsenic field test kits may offer a cost-effective approach for measuring these exposures in the field, although the accuracy of some kits used in the past has been poor. In this study, arsenic concentrations were measured in 136 water sources in western Nevada using two relatively new arsenic test kits and compared to laboratory measurements using atomic fluorescence spectroscopy (AFS). Spearman's rank correlation coefficients comparing the Quick Arsenic and Hach EZ kits to laboratory measurements were 0.96 (p < 0.001) and 0.95 (p < 0.001), respectively. When analyzed in seven exposure categories (0-9, 10-19, 20-49, 50-99, 100-199, 200-499, and > or = 500 microg/L), test kit and AFS measurements were in the same category in 71% (Quick Arsenic) and 62% (Hach EZ) of samples, and within one category of each other in 99% (Quick Arsenic) and 97% (Hach EZ) of samples. Both kits identified all water samples with high arsenic concentrations (> 15 microg/L) as being above the United States Environmental Protection Agency's drinking water standard and the World Health Organization's guideline value for arsenic of 10 microg/L. These results suggestthatthese easily portable kits can be used to identify water sources with high arsenic concentrations and may provide an important tool for arsenic surveillance and remediation programs. PMID:16749706
On squares of representations of compact Lie algebras
Zeier, Robert; Zimborás, Zoltán
2015-08-15
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.
Categorical Formulation of Finite-Dimensional Quantum Algebras
NASA Astrophysics Data System (ADS)
Vicary, Jamie
2011-06-01
We describe how †-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional `quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between finite-dimensional C*-algebras and certain types of †-Frobenius monoids in the category of Hilbert spaces. Using this technology, we recast the spectral theorems for commutative C*-algebras and for normal operators into an explicitly categorical language, and we examine the case that the results of measurements do not form finite sets, but rather objects in a finite Boolean topos. We describe the relevance of these results for topological quantum field theory.
NASA Astrophysics Data System (ADS)
Braitenberg, C. F.; Pivetta, T.; Mariani, P.
2011-12-01
The gravity satellite missions GRACE and GOCE have boosted the resolution of the global Earth gravity models (EGM), opening new possibilities of investigation. The EGMs must be distinguished in models based on pure satellite or mixed satellite-terrestrial observations. Satellite-only models are truly global, whereas satellite-terrestrial models have inhomogeneous quality, depending on availability and accuracy of the terrestrial data set. The advantage of the mixed models (e.g. EGM2008 by Pavlis et al. 2008) is their greater spatial resolution, reaching nominally 9 km, against the 80 km of the pure satellite models of satellite GOCE. The disadvantage is the geographically varying reliability due to problems in the terrestrial data, compiled from different measuring campaigns, using various acquisition methods, and different national geodetic reference systems. We present a method for quality assessment of the higher-resolution fields through the lower-resolution GOCE-field and apply it to northern Africa. We find that the errors locally are as great as 40 mGal, but can be flagged as "bad areas" by our method, leaving the "good areas" for reliable geophysical modeling and investigation. We analyze gravity and gravity gradients and their invariants over North-Central Africa derived from the EGM2008 and GOCE (e.g. Migliaccio et al., 2010) and quantify the resolution in terms of density variations associated to crustal thickness variations, rifts and magmatic underplating. We focus on the Benue rift and the Chad lineament, a 1300 km arcuate feature which links the Benue to the Tibesti Volcanic province. The existing seismological investigations are integrated to constrain the lithosphere structure in terms of seismic velocities, crustal thickness and top asthenosphere boundary, together with physical constraints based on thermal and isostatic considerations (McKenzie stretching model). Our modeling shows that the gravity signal can only be explained if the Benue rift
Groove dimensioning using remote field eddy current inspection
NASA Astrophysics Data System (ADS)
Davoust, M.-E.; Fleury, G.
2000-09-01
The remote field eddy current technique is used for dimensioning the grooves that may occur in the ferromagnetic pipes. We propose a method to estimate the depth and the length of corrosion grooves from measurement of a pick-up coil signal phase at different positions close to the defect. Groove dimensioning requires the knowledge of the physical relation between measurements and defect dimensions; therefore finite-element calculations are performed to design parametric algebraic functions for modeling the physical phenomena. Different models are possible; the choice of this algebraic function is discussed from identification criteria. By means of new measurement formalism and two previously defined measurement relations, estimates of groove sizes may be given. In the first approach, algebraic function parameters and groove dimensions are linked through a polynomial function; this approach is proved to be better than a second one which tries to take advantage of more physical considerations.
Generalized Galilean algebras and Newtonian gravity
NASA Astrophysics Data System (ADS)
González, N.; Rubio, G.; Salgado, P.; Salgado, S.
2016-04-01
The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Computer Algebra Systems in Undergraduate Instruction.
ERIC Educational Resources Information Center
Small, Don; And Others
1986-01-01
Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)
Motivating Activities that Lead to Algebra
ERIC Educational Resources Information Center
Menon, Ramakrishnan
2004-01-01
Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.
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.
Computational triadic algebras of signs
Zadrozny, W.
1996-12-31
We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.
Characters of the N = 4 superconformal algebra with two central extensions
NASA Astrophysics Data System (ADS)
Petersen, J. L.; Taormina, A.
1990-02-01
We derive formulas for the characters of the N = 4 algebra Aγ which contains two overlineSU(2) Kac-Moody subalgebras. We present results for unitary, highest weight, massive representations in the Ramond and Neveu-Schwarz sectors. Massive characters are given for the Ãγ algebra, which is closely related to Aγ, with no dimension- {1}/{2} operators but rather composite operators in the OPE's. Comparison with previously known results in relevant limits are performed.
ERIC Educational Resources Information Center
Star, Jon R.; Rittle-Johnson, Bethany
2009-01-01
Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…
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.
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.
Deformed twistors and higher spin conformal (super-)algebras in four dimensions
NASA Astrophysics Data System (ADS)
Govil, Karan; Günaydin, Murat
2015-03-01
Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5. The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS 5 for which certain 4 d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2| N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4 d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3 d conformal group admits only two massless representations (minreps), namely the scalar and spinor singletons.
The weak Hopf algebras related to generalized Kac-Moody algebra
Wu Zhixiang
2006-06-15
We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying J{sup m}=J{sup m-1} for some integer m. We denote this algebra by wU{sub q}{sup {tau}}(G). This algebra is a weak Hopf algebra if and only if m=2. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra U{sub q}(G) of a generalized Kac-Moody algebra G.
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…
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…
Graphing Calculator Use in Algebra Teaching
ERIC Educational Resources Information Center
Dewey, Brenda L.; Singletary, Ted J.; Kinzel, Margaret T.
2009-01-01
This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed.…
Build an Early Foundation for Algebra Success
ERIC Educational Resources Information Center
Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela
2016-01-01
Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…
A Balancing Act: Making Sense of Algebra
ERIC Educational Resources Information Center
Gavin, M. Katherine; Sheffield, Linda Jensen
2015-01-01
For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…
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…
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"…
Lessons for Algebraic Thinking. Grades K-2.
ERIC Educational Resources Information Center
von Rotz, Leyani; Burns, Marilyn
Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help K-2 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…
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…
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.
Non-Abelian gerbes and enhanced Leibniz algebras
NASA Astrophysics Data System (ADS)
Strobl, Thomas
2016-07-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e., dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge-invariant functional enforces that the most general semistrict Lie 2-algebra describing the bundle of a non-Abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p , solved here for p =2 .
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…
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…
ERIC Educational Resources Information Center
Bosse, Michael J.; Ries, Heather; Chandler, Kayla
2012-01-01
Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…
Implementing Change in College Algebra
ERIC Educational Resources Information Center
Haver, William E.
2007-01-01
In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…
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…
Fuzzy-algebra uncertainty assessment
Cooper, J.A.; Cooper, D.K.
1994-12-01
A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.
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 national…
ERIC Educational Resources Information Center
Oishi, Lindsay
2011-01-01
"Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS…
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…
An Introduction to Algebraic Multigrid
Falgout, R D
2006-04-25
Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments
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…
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…
Kinds of Knowledge in Algebra.
ERIC Educational Resources Information Center
Lewis, Clayton
Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…
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…
Algebra from Chips and Chopsticks
ERIC Educational Resources Information Center
Yun, Jeong Oak; Flores, Alfinio
2012-01-01
Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…
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.
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.
Principals + Algebra (- Fear) = Instructional Leadership
ERIC Educational Resources Information Center
Carver, Cynthia L.
2010-01-01
Recent state legislation in Michigan mandates that all graduating seniors successfully pass algebra I and II. Numerous initiatives have been enacted to help mathematics teachers meet this challenge, yet school principals have had little preparation for the necessary curricular and instructional changes. To address this unmet need, university-based…
Experts Question California's Algebra Edict
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…
Very extended Kac Moody algebras and their interpretation at low levels
NASA Astrophysics Data System (ADS)
Kleinschmidt, Axel; Schnakenburg, Igor; West, Peter
2004-05-01
We analyse the very extended Kac Moody algebras as representations in terms of certain Ad-1 subalgebras and find the generators at low levels. Our results for low levels agree precisely with the bosonic field content of the theories containing gravity, forms and scalars which upon reduction to three dimensions can be described by a nonlinear realization. We explain how the Dynkin diagrams of the very extended algebras encode information about the field content and generalized T-duality transformations.
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.
The Exocenter of a Generalized Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2011-12-01
Elements of the exocenter of a generalized effect algebra (GEA) correspond to decompositions of the GEA as a direct sum and thus the exocenter is a generalization to GEAs of the center of an effect algebra. The exocenter of a GEA is shown to be a boolean algebra, and the notion of a hull mapping for an effect algebra is generalized to a hull system for a GEA. We study Dedekind orthocompleteness of GEAs and extend to GEAs the notion of a centrally orthocomplete effect algebra.
Large chiral diffeomorphisms on Riemann surfaces and W-algebras
Bandelloni, G.; Lazzarini, S.
2006-10-15
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims.
Spacetime algebra as a powerful tool for electromagnetism
NASA Astrophysics Data System (ADS)
Dressel, Justin; Bliokh, Konstantin Y.; Nori, Franco
2015-08-01
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-15
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.
Atomic effect algebras with compression bases
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-15
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
Atomic effect algebras with compression bases
NASA Astrophysics Data System (ADS)
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-01
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
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.
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.
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
Deformed twistors and higher spin conformal (super-)algebras in six dimensions
NASA Astrophysics Data System (ADS)
Govil, Karan; Günaydin, Murat
2014-07-01
Massless conformal scalar field in six dimensions corresponds to the minimal unitary representation (minrep) of the conformal group SO(6, 2). This minrep admits a family of "deformations" labelled by the spin t of an SU(2) T group, which is the 6 d analog of helicity in four dimensions. These deformations of the minrep of SO(6 , 2) describe massless conformal fields that are symmetric tensors in the spinorial representation of the 6 d Lorentz group. The minrep and its deformations were obtained by quantization of the nonlinear realization of SO(6 , 2) as a quasiconformal group in arXiv:1005.3580. We give a novel reformulation of the generators of SO(6 , 2) for these representations as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group SO(5 , 1) and apply them to define higher spin algebras and superalgebras in AdS 7. The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 7 is simply the enveloping algebra of SO(6 , 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 7. Furthermore, the enveloping algebras of the deformations of the minrep define a discrete infinite family of HS algebras in AdS 7 for which certain 6 d Lorentz covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras OSp(8*|2 N ) and we find a discrete infinite family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a discrete family of (supersymmetric) HS theories in AdS 7 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 6 d.
Partially-massless higher-spin algebras and their finite-dimensional truncations
NASA Astrophysics Data System (ADS)
Joung, Euihun; Mkrtchyan, Karapet
2016-01-01
The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS d+1 are studied. The algebras involving PM generators up to depth 2 ( ℓ - 1) are defined as the maximal symmetries of free conformal scalar field with 2 ℓ order wave equation in d dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of ( A) dS d+1 isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of ℓ - d/2 , which coincides with the annihilator of the one-row ℓ-box Young diagram representation of s{o}_{d+2} . Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
NASA Astrophysics Data System (ADS)
Khongsap, Ta; Wang, Weiqiang
2009-01-01
We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras.
2003-06-03
The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less
Single axioms for Boolean algebra.
McCune, W.
2000-06-30
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.
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.
Galois algebras of squeezed quantum phase states
NASA Astrophysics Data System (ADS)
Planat, Michel; Saniga, Metod
2005-12-01
Coding, transmission and recovery of quantum states with high security and efficiency, and with as low fluctuations as possible, is the main goal of quantum information protocols and their proper technical implementations. The paper deals with this topic, focusing on the quantum states related to Galois algebras. We first review the constructions of complete sets of mutually unbiased bases in a Hilbert space of dimension q = pm, with p being a prime and m a positive integer, employing the properties of Galois fields Fq (for p>2) and/or Galois rings of characteristic four R4m (for p = 2). We then discuss the Gauss sums and their role in describing quantum phase fluctuations. Finally, we examine an intricate connection between the concepts of mutual unbiasedness and maximal entanglement.
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.
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.
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.}
Matrix De Rham Complex and Quantum A-infinity algebras
NASA Astrophysics Data System (ADS)
Barannikov, S.
2014-04-01
I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A ∞-algebras, introduced in Barannikov (Modular operads and non-commutative Batalin-Vilkovisky geometry. IMRN, vol. 2007, rnm075. Max Planck Institute for Mathematics 2006-48, 2007), is represented via de Rham differential acting on the supermatrix spaces related with Bernstein-Leites simple associative algebras with odd trace q( N), and gl( N| N). I also show that the matrix Lagrangians from Barannikov (Noncommutative Batalin-Vilkovisky geometry and matrix integrals. Isaac Newton Institute for Mathematical Sciences, Cambridge University, 2006) are represented by equivariantly closed differential forms.
NASA Astrophysics Data System (ADS)
Gardella, Emilio Eusebio
This dissertation is concerned with representations of locally compact groups on different classes of Banach spaces. The first part of this work considers representations of compact groups by automorphisms of C*-algebras, also known as group actions on C*-algebras. The actions we study enjoy a freeness-type of property, namely finite Rokhlin dimension. We investigate the structure of their crossed products, mainly in relation to their classifiability, and compare the notion of finite Rokhlin dimension with other existing notions of noncommutative freeness. In the case of Rokhlin dimension zero, also known as the Rokhlin property, we prove a number of classification theorems for these actions. Also, in this case, much more can be said about the structure of the crossed products. In the last chapter of this part, we explore the extent to which actions with Rokhlin dimension one can be classified. Our results show that even for Z2-actions on O2, their classification is not Borel, and hence it is intractable. The second part of the present dissertation focuses on isometric representations of groups on Lp-spaces. For p=2, these are the unitary representations on Hilbert spaces. We study the Lp-analogs of the full and reduced group C*-algebras, particularly in connection to their rigidity. One of the main results of this work asserts that for p different from 2, the isometric isomorphism type of the reduced group L p-operator algebra recovers the group. Our study of group algebras acting on Lp-spaces has also led us to answer a 20-year-old question of Le Merdy and Junge: for p different from 2, the class of Banach algebras that can be represented on an Lp-space is not closed under quotients. We moreover study representations of groupoids, which are a generalization of groups where multiplication is not always defined. The algebras associated to these objects provide new examples of Lp-operator algebras and recover some previously existing ones. Groupoid L p
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2014-05-01
A complex key feature of turbulence is that the velocity is a vector field, whereas intermittency, another key feature, has been mostly understood, analysed and simulated in scalar frameworks. This gap has prevented many developments. Some years ago, the general framework of 'Lie cascades' was introduced (Schertzer and Lovejoy, 1993) to deal with both features by considering cascades generated by stochastic Lie algebra. However, the theoretical efforts were mostly concentrated on the decomposition of this algebra into its radical and a semi-simple algebra and faced too many degrees of freedom. In this communication, we show that the class of Clifford algebra is already wide enough, very convenient and physically meaningful to understand, analyse and simulate intermittent vector fields.
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).
Walendziak, Andrzej
2015-01-01
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050
Lax operator algebras and integrable systems
NASA Astrophysics Data System (ADS)
Sheinman, O. K.
2016-02-01
A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite-dimensional integrable systems with a spectral parameter on a Riemann surface such as the Calogero-Moser and Hitchin systems. In particular, the approach includes (non-twisted) Kac-Moody algebras and integrable systems with a rational spectral parameter. The presentation is based on quite simple ideas about the use of gradings of semisimple Lie algebras and their interaction with the Riemann-Roch theorem. The basic properties of Lax operator algebras and the basic facts about the theory of the integrable systems in question are treated (and proved) from this general point of view. In particular, the existence of commutative hierarchies and their Hamiltonian properties are considered. The paper concludes with an application of Lax operator algebras to prequantization of finite-dimensional integrable systems. Bibliography: 51 titles.
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.…
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Stability of algebraically unstable dispersive flows
NASA Astrophysics Data System (ADS)
King, Kristina; Zaretzky, Paula; Weinstein, Steven; Cromer, Michael; Barlow, Nathaniel
2015-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to a class of partial differential equations describing wave propagation in dispersive media. There are several morphological differences between algebraically growing disturbances and the exponentially growing wave packets inherent to classical linear stability analysis, and these are elucidated in this study.
Explicit travelling waves and invariant algebraic curves
NASA Astrophysics Data System (ADS)
Gasull, Armengol; Giacomini, Hector
2015-06-01
We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.
Lowest weight representations of super Schroedinger algebras in one dimensional space
Aizawa, N.
2011-01-15
Lowest weight modules, in particular, Verma modules over the N=1,2 super Schroedinger algebras in (1 + 1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors. The classification of the irreducible lowest weight modules is given for both massive and massless representations. A vector field realization of the N=1,2 super Schroedinger algebras is also presented.
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.
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.
Representations of Super Yang-Mills Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
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.
Literal algebra for satellite dynamics. [perturbation analysis
NASA Technical Reports Server (NTRS)
Gaposchkin, E. M.
1975-01-01
A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.
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.
Type-Decomposition of an Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2010-10-01
Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras. We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice.
NASA Astrophysics Data System (ADS)
Chajda, Ivan
2014-10-01
Commutative BCI-algebras can be considered as semilattices whose sections are equipped with certain involutions. A similar view can be applied to commutative BCK-algebras. However, for general BCK-algebras a certain construction was settled by the author and J. Kühr (Miskolc Math. Notes 8:11-21, 2007) showing that they can be considered as structures essentially weaker than semilattices but still with certain involutions in sections. The aim of this paper is to involve a similar approach for BCI-algebras.
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…
Results of Using Algebra Tiles as Meaningful Representations of Algebra Concepts.
ERIC Educational Resources Information Center
Sharp, Janet M.
Mathematical meanings can be developed when individuals construct translations between algebra symbol systems and physical systems that represent one another. Previous research studies indicated (1) few high school students connect whole number manipulations to algebraic manipulations and (2) students who encounter algebraic ideas through…
Some C∗-algebras which are coronas of non-C∗-Banach algebras
NASA Astrophysics Data System (ADS)
Voiculescu, Dan-Virgil
2016-07-01
We present results and motivating problems in the study of commutants of hermitian n-tuples of Hilbert space operators modulo normed ideals. In particular, the C∗-algebras which arise in this context as coronas of non-C∗-Banach algebras, the connections with normed ideal perturbations of operators, the hyponormal operators and the bidual Banach algebras one encounters are discussed.
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
NASA Astrophysics Data System (ADS)
Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.
2016-03-01
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.
Parafermionic representation of the affine /sl(21C) algebra at fractional level
NASA Astrophysics Data System (ADS)
Bowcock, P.; Hayes, M.; Taormina, A.
1999-12-01
The four fermionic currents of the affine superalgebra /sl(21C) at fractional level
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.
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.
Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-01-01
In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac-Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.
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.
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.
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. PMID:26652421
Leroch, Michaela; Plesken, Cecilia; Weber, Roland W. S.; Kauff, Frank; Scalliet, Gabriel
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. PMID:23087030
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.
Automorphisms and Derivations of the Insertion-Elimination Algebra and Related Graded Lie Algebras
NASA Astrophysics Data System (ADS)
Ondrus, Matthew; Wiesner, Emilie
2016-07-01
This paper addresses several structural aspects of the insertion-elimination algebra {mathfrak{g}}, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of {mathfrak{g}}, the automorphism group of {mathfrak{g}}, the derivation Lie algebra of {mathfrak{g}}, and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras.
Intermediate grouping on remotely sensed data using Gestalt algebra
NASA Astrophysics Data System (ADS)
Michaelsen, Eckart
2014-10-01
Human observers often achieve striking recognition performance on remotely sensed data unmatched by machine vision algorithms. This holds even for thermal images (IR) or synthetic aperture radar (SAR). Psychologists refer to these capabilities as Gestalt perceptive skills. Gestalt Algebra is a mathematical structure recently proposed for such laws of perceptual grouping. It gives operations for mirror symmetry, continuation in rows and rotational symmetric patterns. Each of these operations forms an aggregate-Gestalt of a tuple of part-Gestalten. Each Gestalt is attributed with a position, an orientation, a rotational frequency, a scale, and an assessment respectively. Any Gestalt can be combined with any other Gestalt using any of the three operations. Most often the assessment of the new aggregate-Gestalt will be close to zero. Only if the part-Gestalten perfectly fit into the desired pattern the new aggregate-Gestalt will be assessed with value one. The algebra is suitable in both directions: It may render an organized symmetric mandala using random numbers. Or it may recognize deep hidden visual relationships between meaningful parts of a picture. For the latter primitives must be obtained from the image by some key-point detector and a threshold. Intelligent search strategies are required for this search in the combinatorial space of possible Gestalt Algebra terms. Exemplarily, maximal assessed Gestalten found in selected aerial images as well as in IR and SAR images are presented.
Analysis on singular spaces: Lie manifolds and operator algebras
NASA Astrophysics Data System (ADS)
Nistor, Victor
2016-07-01
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called "Lie manifolds" -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.
NASA Astrophysics Data System (ADS)
Pasko, V. P.
2013-12-01
Winn et al. [JGR, 116, D23115, 2011] have reported time resolved observations of electric field components parallel and perpendicular to the intra-cloud (IC) stepped leader that passed within 200 m of a balloon-borne electric field change instrument at 9.1 km altitude and covered total length of ~11.6 km, with an average velocity of ~10^5 m/s. The stepping distances ranged between 50 m and 600 m and during each step the electric field component perpendicular to the channel exhibited a fast (during several 10s of microseconds) decrease on the order of 2 kV/m, followed by a slow recovery. We report quantitative modeling results allowing interpretation of these observations using the electrostatic moment method solutions for charges induced on a long (overall charge neutral) conducting leader channel placed in an external electric field, closely following approaches recently developed for calculations of electric fields and potential differences developing near tips of long lightning leaders that lead to terrestrial gamma ray flashes (TGFs) [e.g., Celestin et al., JGR, 117, A05315, 2012, and references cited therein]. It is demonstrated that the observed reduction of the electric field component perpendicular to the channel during step of the negative leader is a result of spatial shift of the negative charge in the direction of travel of the negative leader head, followed by the slow recovery to approximately pre-step levels during continuous advancement of the positive leader on the opposite end of the bi-directional leader system. In context of TGFs, results of Winn et al. [2011] are of special interest as they provide better understanding of step phenomenology and temporal evolution of large-scale charge distributions on long IC lightning leaders. In the considered electrostatic modeling the leader electric dipole moment is a quadratic function of the leader length, and the dipole moment changes due to the leader steps increase proportionally to the overall leader
Realizations of conformal current-type Lie algebras
Pei Yufeng; Bai Chengming
2010-05-15
In this paper we obtain the realizations of some infinite-dimensional Lie algebras, named 'conformal current-type Lie algebras', in terms of a two-dimensional Novikov algebra and its deformations. Furthermore, Ovsienko and Roger's loop cotangent Virasoro algebra, which can be regarded as a nice generalization of the Virasoro algebra with two space variables, is naturally realized as an affinization of the tensor product of a deformation of the two-dimensional Novikov algebra and the Laurent polynomial algebra. These realizations shed new light on various aspects of the structure and representation theory of the corresponding infinite-dimensional Lie algebras.
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…
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 solve"…
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)
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…
Algebra in the Early Years? Yes!
ERIC Educational Resources Information Center
Taylor-Cox, Jennifer
2003-01-01
Suggests ways early years educators can begin teaching young children to think algebraically and prepare them for success in algebra. Focuses on ways to promote mathematical patterns, mathematical situations and structures, models of quantitative relationship, and change. Describes how first-graders used real object representations to better…
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…
New directions in algebraic dynamical systems
NASA Astrophysics Data System (ADS)
Schmidt, Klaus; Verbitskiy, Evgeny
2011-02-01
The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.
Solving Absolute Value Equations Algebraically and Geometrically
ERIC Educational Resources Information Center
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Low Performers Found Unready to Take Algebra
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared. "The Misplaced Math Student: Lost in Eighth Grade Algebra," scheduled for release by the Brookings Institution…
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.
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…
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…