Algebraic properties of compatible Poisson brackets
Zhang, Pumei
2014-05-01
We discuss algebraic properties of a pencil generated by two compatible Poisson tensors A( x) and B( x). From the algebraic viewpoint this amounts to studying the properties of a pair of skew-symmetric bilinear forms A and B defined on a finite-dimensional vector space. We describe the Lie group G P of linear automorphisms of the pencil P = { A + λB}. In particular, we obtain an explicit formula for the dimension of G P and discuss some other algebraic properties such as solvability and Levi-Malcev decomposition.
Degenerate odd Poisson bracket on Grassmann variables
International Nuclear Information System (INIS)
Soroka, V.A.
2000-01-01
A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is proposed. It is revealed that this bracket has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, second and third orders with respect to the Grassmann derivatives. It is shown that these Δ-like operators, together with the Grassmann-odd nilpotent Casimir function of this bracket, form a finite-dimensional Lie superalgebra
Dimensional reduction for generalized Poisson brackets
Acatrinei, Ciprian Sorin
2008-02-01
We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets are always constant. Some examples are given alongside the general theory.
Linear odd Poisson bracket on Grassmann variables
International Nuclear Information System (INIS)
Soroka, V.A.
1999-01-01
A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson bracket having the only Grassmann-odd nilpotent differential Δ-operator of the second order. It is shown that these Δ-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Poisson brackets for fluids and plasmas
International Nuclear Information System (INIS)
Morrison, P.J.
1982-01-01
Noncanonical yet Hamiltonian descriptions are presented of many of the non-dissipative field equations that govern fluids and plasmas. The dynamical variables are the usually encountered physical variables. These descriptions have the advantage that gauge conditions are absent, but at the expense of introducing peculiar Poisson brackets. Clebsch-like potential descriptions that reverse this situations are also introduced
Associative and Lie deformations of Poisson algebras
Remm, Elisabeth
2011-01-01
Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.
Maslov indices, Poisson brackets, and singular differential forms
Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.
2014-06-01
Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
Carlet, Guido; Casati, Matteo; Shadrin, Sergey
2017-04-01
We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D > 1. Hence, in contrast with the D = 1 case, the deformation theory in the multivariable case is non-trivial.
The Poisson algebra of the invariant charges of the Nambu-Goto theory: Casimir elements
International Nuclear Information System (INIS)
Pohlmeyer, K.
1988-01-01
The reparametrization invariant ''non-local'' conserved charges of the Nambu-Goto theory form an algebra under Poisson bracket operation. The center of the formal closure of this algebra is determined. The relation of the central elements to the constraints of the Nambu-Goto theory is clarified. (orig.)
Gyrokinetic energy conservation and Poisson-bracket formulation
International Nuclear Information System (INIS)
Brizard, A.
1988-11-01
An integral expression for the gyrokinetic total energy of a magnetized plasma with general magnetic field configuration perturbed by fully electromagnetic fields was recently derived through the use of a gyro-center Lie transformation. We show that the gyrokinetic energy is conserved by the gyrokinetic Hamiltonian flow to all orders in perturbed fields. This paper is concerned with the explicit demonstration that a gyrokinetic Hamiltonian containing quadratic nonlinearities preserves the gyrokinetic energy up to third order. The Poisson-bracket formulation greatly facilitates this demonstration with the help of the Jacobi identity and other properties of the Poisson brackets. 18 refs
2D sigma models and differential Poisson algebras
Energy Technology Data Exchange (ETDEWEB)
Arias, Cesar [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Boulanger, Nicolas [Service de Mécanique et Gravitation, Université de Mons - UMONS,20 Place du Parc, 7000 Mons (Belgium); Laboratoire de Mathématiques et Physique Théorique,Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson,Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-18
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
On covariant Poisson brackets in classical field theory
International Nuclear Information System (INIS)
Forger, Michael; Salles, Mário O.
2015-01-01
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra
The Quantum Poisson Bracket and Transformation Theory in ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 8. The Quantum Poisson Bracket and Transformation Theory in Quantum Mechanics: Dirac's Early Work in Quantum Theory. Kamal Datta. General Article Volume 8 Issue 8 August 2003 pp 75-85 ...
On covariant Poisson brackets in classical field theory
Energy Technology Data Exchange (ETDEWEB)
Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)
2015-10-15
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
Bering's proposal for boundary contribution to the Poisson bracket
International Nuclear Information System (INIS)
Soloviev, V.O.
1998-11-01
It is shown that the Poisson bracket with boundary terms recently proposed by Bering can be deduced from the Poisson bracket proposed by the present author if one omits terms free of Euler-Lagrange derivatives (''annihilation principle''). This corresponds to another definition of the formal product of distributions (or, saying it in other words, to another definition of the pairing between 1-forms and 1-vectors in the formal variational calculus). We extend the formula initially suggested by Bering only for the ultralocal case with constant coefficients onto the general non-ultralocal brackets with coefficients depending on fields and their spatial derivatives. The lack of invariance under changes of dependent variables (field redefinitions) seems a drawback of this proposal. (author)
Boundary Lax pairs from non-ultra-local Poisson algebras
International Nuclear Information System (INIS)
Avan, Jean; Doikou, Anastasia
2009-01-01
We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.
Beatification: Flattening Poisson brackets for plasma theory and computation
Morrison, P. J.; Viscondi, T. F.; Caldas, I.
2017-10-01
A perturbative method called beatification is presented for producing nonlinear Hamiltonian fluid and plasma theories. Plasma Hamiltonian theories, fluid and kinetic, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding a transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables. Examples will be given. U.S. D.O.E No. #DE-FG02-04ER-54742.
New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology
Pinczon, Georges; Ushirobira, Rosane
2005-01-01
We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.
Equal-Time and Equal-Space Poisson Brackets of the N -Component Coupled NLS Equation
International Nuclear Information System (INIS)
Zhou Ru-Guang; Li Pei-Yao; Gao Yuan
2017-01-01
Two Poisson brackets for the N-component coupled nonlinear Schrödinger (NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation. (paper)
Normal forms of dispersive scalar Poisson brackets with two independent variables
Carlet, Guido; Casati, Matteo; Shadrin, Sergey
2018-03-01
We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants.
Directory of Open Access Journals (Sweden)
Bolsinov Alexey V.
2016-01-01
Full Text Available The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra g there exists a complete set of commuting polynomials on its dual space g*. In terms of the theory of integrable Hamiltonian systems this means that the dual space g* endowed with the standard Lie-Poisson bracket admits polynomial integrable Hamiltonian systems. This conjecture was proved by S. T. Sadetov in 2003. Following his idea, we give an explicit geometric construction for commuting polynomials on g* and consider some examples. (This text is a revised version of my paper published in Russian: A. V. Bolsinov, Complete commutative families of polynomials in Poisson–Lie algebras: A proof of the Mischenko–Fomenko conjecture in book: Tensor and Vector Analysis, Vol. 26, Moscow State University, 2005, 87–109.
International Nuclear Information System (INIS)
Volkov, D.V.; Pashnev, A.I.; Soroka, V.A.; Tkach, V.I.
1986-01-01
Taking as example the Witten supersymmetric mechanics it is shown that the hamiltonian system with equal number of even and odd canonical variables admits simultaneously the introduction of even and odd Poisson brackets. When using bracket operations of different graduation the canonical variable equations are not varied whereas the motion integrals with opposite Grassman graduation become dual transforming into each other at the transition to Poisson bracket with opposite graduation
On the compatible weakly nonlocal Poisson brackets of hydrodynamic type
Directory of Open Access Journals (Sweden)
Andrei Ya. Maltsev
2002-01-01
of hydrodynamic type (Ferapontov brackets and the corresponding integrable hierarchies. We show that, under the requirement of the nondegeneracy of the corresponding first pseudo-Riemannian metric g(0 νμ and also some nondegeneracy requirement for the nonlocal part, it is possible to introduce a canonical set of integrable hierarchies based on the Casimirs, momentum functional and some canonical Hamiltonian functions. We prove also that all the higher positive Hamiltonian operators and the negative symplectic forms have the weakly nonlocal form in this case. The same result is also true for negative Hamiltonian operators and positive symplectic structures in the case when both pseudo-Riemannian metrics g(0 νμ and g(1 νμ are nondegenerate.
Poisson hierarchy of discrete strings
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Poisson hierarchy of discrete strings
International Nuclear Information System (INIS)
Ioannidou, Theodora; Niemi, Antti J.
2016-01-01
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
International Nuclear Information System (INIS)
Daskaloyannis, C.
2000-01-01
The integrals of motion of the classical two-dimensional superintegrable systems close in a restrained polynomial Poisson algebra, whose general form is discussed. Each classical superintegrable problem has a quantum counterpart, a quantum superintegrable system. The polynomial Poisson algebra is deformed to a polynomial associative algebra, the finite-dimensional representations of this algebra are calculated by using a deformed parafermion oscillator technique. It is conjectured that the finite-dimensional representations of the polynomial algebra are determined by the energy eigenvalues of the superintegrable system. The calculation of energy eigenvalues is reduced to the solution of algebraic equations, which are universal for a large number of two-dimensional superintegrable systems. (author)
Fiber-wise linear Poisson structures related to W∗-algebras
Odzijewicz, Anatol; Jakimowicz, Grzegorz; Sliżewska, Aneta
2018-01-01
In the framework of Banach differential geometry we investigate the fiber-wise linear Poisson structures as well as the Lie groupoid and Lie algebroid structures which are defined in the canonical way by the structure of a W∗-algebra (von Neumann algebra) M. The main role in this theory is played by the complex Banach-Lie groupoid G(M) ⇉ L(M) of partially invertible elements of M over the lattice L(M) of orthogonal projections of M. The Atiyah sequence and the predual Atiyah sequence corresponding to this groupoid are investigated from the point of view of Banach Poisson geometry. In particular we show that the predual Atiyah sequence fits in a short exact sequence of complex Banach sub-Poisson V B-groupoids with G(M) ⇉ L(M) as the side groupoid.
The Lie-Poisson structure of integrable classical non-linear sigma models
International Nuclear Information System (INIS)
Bordemann, M.; Forger, M.; Schaeper, U.; Laartz, J.
1993-01-01
The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into the r-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matrices r and s are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrix c. It is proposed that all these Poisson brackets taken together are representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed. (orig.)
Visser, A.
1992-01-01
In this paper we study two (kinds of) systems of brackets in an algebraic way. Lazy brackets have the same effect as introducing or eliminating 'a sufficient amount' of ordinary brackets at the same time. Quarrelsome brackets are brackets corresponding to different types of 'levels': think
On the Fedosov deformation quantization beyond the regular Poisson manifolds
International Nuclear Information System (INIS)
Dolgushev, V.A.; Isaev, A.P.; Lyakhovich, S.L.; Sharapov, A.A.
2002-01-01
A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane
Continuum analogues of contragredient Lie algebras
International Nuclear Information System (INIS)
Saveliev, M.V.; Vershik, A.M.
1989-03-01
We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry
2014-01-01
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...
Division algebras and extended super KdVs
Energy Technology Data Exchange (ETDEWEB)
Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas]. E-mail: toppan@cbpf.br
2001-05-01
The division algebras R, C, H, O are used to construct and analyze the N = 1, 2, 4, 8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N = 8 super-KdV system is introduced and shown to admit a Poisson bracket structure given by the 'Non-Associate N = 8 Superconformal Algebra'. (author)
Division algebras and extended super KdVs
International Nuclear Information System (INIS)
Toppan, F.
2001-05-01
The division algebras R, C, H, O are used to construct and analyze the N = 1, 2, 4, 8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N = 8 super-KdV system is introduced and shown to admit a Poisson bracket structure given by the 'Non-Associate N = 8 Superconformal Algebra'. (author)
Current algebra of classical non-linear sigma models
International Nuclear Information System (INIS)
Forger, M.; Laartz, J.; Schaeper, U.
1992-01-01
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)
The vacuum preserving Lie algebra of a classical W-algebra
International Nuclear Information System (INIS)
Feher, L.; Tsutsui, I.
1993-07-01
We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the 'classical vacuum preserving algebra') containing the Moebius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-fields. In the case of the W S G -subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Moebius sl(2) is identified with S. (orig.)
Affine Malcev Algebra and N = 8 Kdv
Toppan, F.
2002-03-01
In this talk I report the results of two recent papers concerning the realization of the N = 8 supersymmetry from the division algebra of the octonions. At first I discuss a Sugawara realization for the "Non-associative N = 8 SCA" in terms of a superaffinization of the algebra of octonions. Next, I discuss the fact that the N = 8 SCA provides a generalized Poisson brackets structure for an N = 8 super-KdV.
On W1+∞ 3-algebra and integrable system
Directory of Open Access Journals (Sweden)
Min-Ru Chen
2015-02-01
Full Text Available We construct the W1+∞ 3-algebra and investigate its connection with the integrable systems. Since the W1+∞ 3-algebra with a fixed generator W00 in the operator Nambu 3-bracket recovers the W1+∞ algebra, it is intrinsically related to the KP hierarchy. For the general case of the W1+∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu–Poisson evolution equation with the different Hamiltonian pairs of the KP hierarchy. Due to the Nambu–Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of the W1+∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized nonlinear Schrödinger equation and give an application in optical soliton.
Centrally extended symmetry algebra of asymptotically Goedel spacetimes
International Nuclear Information System (INIS)
Compere, Geoffrey; Detournay, Stephane
2007-01-01
We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative
Lie 3-algebra and multiple M2-branes
International Nuclear Information System (INIS)
Ho, Pei-Ming; Hou, Ru-Chuen; Matsuo, Yutaka
2008-01-01
Motivated by the recent proposal of an N = 8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also discuss the application of Lie 3-algebra to the membrane physics, including the Basu-Harvey equation and the Bagger-Lambert model.
n-ary algebras: a review with applications
International Nuclear Information System (INIS)
De Azcarraga, J A; Izquierdo, J M
2010-01-01
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A 4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. (topical
Affine Malcev algebra and N=8 KdV
Energy Technology Data Exchange (ETDEWEB)
Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas]. E-mail: toppan@cbpf.br
2001-09-01
In this talk I report the results of two recent papers concerning the realization of the N = 8 supersymmetry from the division algebra of the octonions. At first I discuss a Sugawara realization for the 'Non-associative N = 8 SCA' in terms of a superaffinization of the algebra of octonions. Next, I discuss the fact that the N = 8 SCA provides a generalized Poisson brackets structure for an N = 8 super-KdV. (author)
Lie 3-Algebra and Multiple M2-branes
Ho, Pei-Ming; Hou, Ru-Chuen; Matsuo, Yutaka
2008-01-01
Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also ...
International Nuclear Information System (INIS)
Curtright, Thomas L.; Fairlie, David B.; Zachos, Cosmas K.
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
Constructions and classifications of projective Poisson varieties
Pym, Brent
2018-03-01
This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.
Non-local matrix generalizations of W-algebras
International Nuclear Information System (INIS)
Bilal, A.
1995-01-01
There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinary m th -order linear differential operators L=-d m +U 1 d m-1 +U 2 d m-2 +..+U m . In this paper, I consider in detail the case where the U k are nxn-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifold U 1 =0. This reduction gives rise to matrix generalizations of (the classical version of) the non-linear W m -algebras, called V n,m -algebras. The non-commutativity of the matrices leads to non-local terms in these V n,m -algebras. I show that these algebras contain a conformal Virasoro subalgebra and that combinations W k of the U k can be formed that are nxn-matrices of conformally primary fields of spin k, in analogy with the scalar case n=1. In general however, the V m,n -algebras have a much richer structure than the W m -algebras as can be seen on the examples of the non-linear and non-local Poisson brackets {(U 2 ) ab (σ),(U 2 ) cd (σ')}, {(U 2 ) ab (σ),(W 3 ) cd (σ')} and {(W 3 ) ab (σ),(W 3 ) cd (σ')} which I work out explicitly for all m and n. A matrix Miura transformation is derived, mapping these complicated (second Gelfand-Dikii) brackets of the U k to a set of much simpler Poisson brackets, providing the analogue of the free-field representation of the W m -algebras. (orig.)
Tabak, John
2004-01-01
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.
On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action
Chekhov, L. O.; Mazzocco, M.
2017-12-01
Let \\mathscr A be the space of bilinear forms on C^N with defining matrices A endowed with a quadratic Poisson structure of reflection equation type. The paper begins with a short description of previous studies of the structure, and then this structure is extended to systems of bilinear forms whose dynamics is governed by the natural action A\\mapsto B ABT} of the {GL}_N Poisson-Lie group on \\mathscr A. A classification is given of all possible quadratic brackets on (B, A)\\in {GL}_N× \\mathscr A preserving the Poisson property of the action, thus endowing \\mathscr A with the structure of a Poisson homogeneous space. Besides the product Poisson structure on {GL}_N× \\mathscr A, there are two other (mutually dual) structures, which (unlike the product Poisson structure) admit reductions by the Dirac procedure to a space of bilinear forms with block upper triangular defining matrices. Further generalisations of this construction are considered, to triples (B,C, A)\\in {GL}_N× {GL}_N× \\mathscr A with the Poisson action A\\mapsto B ACT}, and it is shown that \\mathscr A then acquires the structure of a Poisson symmetric space. Generalisations to chains of transformations and to the quantum and quantum affine algebras are investigated, as well as the relations between constructions of Poisson symmetric spaces and the Poisson groupoid. Bibliography: 30 titles.
Invariants and labels for Lie-Poisson Systems
International Nuclear Information System (INIS)
Thiffeault, J.L.; Morrison, P.J.
1998-04-01
Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system
Flanders, Harley
1975-01-01
Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
International Nuclear Information System (INIS)
Aoyama, Shogo
2014-01-01
The Poisson brackets for non-linear σ-models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is shown to satisfy the classical exchange algebra
Wronski Brackets and the Ferris Wheel
Martin, Keye
2005-11-01
We connect the Bayesian order on classical states to a certain Lie algebra on C^infty[0,1]. This special Lie algebra structure, made precise by an idea we introduce called a Wronski bracket, suggests new phenomena the Bayesian order naturally models. We then study Wronski brackets on associative algebras, and in the commutative case, discover the beautiful result that they are equivalent to derivations.
Sepanski, Mark R
2010-01-01
Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems
Algebric generalization of symmetry Dirac bracket. Application to field theory
International Nuclear Information System (INIS)
Rocha Filho, T.M. da.
1987-01-01
The A set of observable of a physical system with finite e infinite number of degrees of freedom and submitted to certain constraint conditions, is considered. Using jordan algebra structure on A in relation to bymmetric Poisson bracket obtained by Droz-Vincent, a jordan product is obtained on the A/I quocient set with regard to I ideal generated by constraints of second class. It is shown that this product on A/I corresponds to symmetric Dirac bracket. The developed formulation is applied to a system corresponding to harmonic oscillators, non relativistic field, Rarita-Schwinger field and the possibility of its utilization in fermionic string theories is discussed. (M.C.K.)
Homogeneous Poisson structures
International Nuclear Information System (INIS)
Shafei Deh Abad, A.; Malek, F.
1993-09-01
We provide an algebraic definition for Schouten product and give a decomposition for any homogenenous Poisson structure in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in R k is also characterized. (author). 4 refs
Mølsted, K
1992-01-01
Because of the many drawbacks of the hard and brittle material, ceramic brackets should not be used uncritically for orthodontic treatments. If ceramic brackets are used, the following guidelines should be observed: 1. If large and complicated tooth movements are involved, conventional bracket systems should be considered. 2. Occlusion on ceramic brackets is to be avoided. 3. Sharp instruments should be used with extreme care to avoid scratching the ceramic surface. Metal ligatures must not be used. 4. The length of the treatment is extended, probably because of the increased friction. 5. The problems connected with removing the brackets have not yet been solved. Be particularly careful of weakened teeth. 6. Esthetically, ceramic brackets function satisfactorily, but transparent elastic ligatures do not. They rapidly become discoloured and need frequent replacement. Nor are there as yet any "invisible arch wires", apart from some few, extremely flexible "white" arch wires. The ceramic bracket has no doubt come to stay, but there have been many difficulties in the "running-in" period, and the problems are far from solved yet. New ceramic brackets are coming onto the market all the time, and only future clinical studies can show whether they will become a genuine alternative to the conventional bracket.
Bihamiltonian Cohomology of KdV Brackets
Carlet, G.; Posthuma, H.; Shadrin, S.
2016-01-01
Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular, this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups.
Identities and derivations for Jacobian algebras
International Nuclear Information System (INIS)
Dzhumadil'daev, A.S.
2001-09-01
Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-Jacobian algebra are found. (author)
Study on generalized Toda mechanics system with loop algebra L(Dr)
International Nuclear Information System (INIS)
Zhu Qiao; Yang Zhanying; Shi Kangjie
2005-01-01
The authors generalize the Toda mechanics system with long range interaction to the case of Loop algebra L(D r ). By using a pair of ordered positive integer (X, Y) to describe Toda chains, authors extract the equation of motion and the Hamiltonian structure of this system for (3, 2) Toda chain. It turns out that both extra coordinates and standard Toda variables are Poisson non-commutative in the case of nontrivial generalization, and for some case, extra variables appear linearly on the right hand side of the Poisson bracket. (authors)
On the completeness of the set of classical W-algebras obtained from DS reductions
International Nuclear Information System (INIS)
Feher, L.; Ruelle, P.; Tsutsui, I.
1993-04-01
We clarify the notions of the DS-generalized Drinfeld-Sokolov-reduction approach to classical W-algebras and collect evidence supporting the conjecture that the canonical W-algebras (called W S G -algebras), defined by the highest weights of the sl(2) embeddings S contains or equal to G into the simple Lie algebras, essentially exhaust the set of W-algebras that may be obtained by reducing the affine Kac-Moody (KM) Poisson bracket algebras in this approach. We first prove that an sl(2) embedding S contains or equal to G can be associated to every DS reduction and then derive restrictions on the possible cases belonging to the same sl(2) embedding. We find examples of noncanonical DS reductions, but in all those examples the resultant noncanonical W-algebra decouples into the direct product of the corresponding W S G -algebra and a system of 'free fields' with conformal weights Δ element of {0, 1/2, 1}. We also show that if the conformal weights of the generators of a W-algebra obtained from DS reduction are nonnegative Δ ≥ 0 (which is the case for all DS reductions known to date), then the Δ ≥ 3/2 subsectors of the weights are necessarily the same as in the corresponding W S G -algebra. The paper is concluded by a list of open problems concerning DS reductions and more general Hamiltonian KM reductions. (orig.)
Nonassociativity, Malcev algebras and string theory
Energy Technology Data Exchange (ETDEWEB)
Guenaydin, M. [Institute for Gravitation and the Cosmos and Physics Department, Penn State University, University Park, PA (United States); Minic, D. [Department of Physics, Virginia Tech, Blacksburg, VA (United States)
2013-10-15
Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Nonassociativity, Malcev algebras and string theory
International Nuclear Information System (INIS)
Guenaydin, M.; Minic, D.
2013-01-01
Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Division algebras and extended N = 2, 4, 8 super KdVs
International Nuclear Information System (INIS)
Carrion, H.L.; Rojas, M.; Toppan, F.
2001-09-01
The first example of an N = 8 supersymmetric extension of the KdV equation is here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It corresponds to the unique N = 8 solution based a generalized hamiltonian dynamics with (generalized) Poisson brackets given by the Non-associate N = 8 Superconformal Algebra. The complete list of inequivalent classes of parametric-dependent N = 3 and N = 4 superKdVs obtained from the 'Non-associative N= 8 SCA' is also furnished. Furthermore, a fundamental domain characterizing the class of inequivalent N = 4 superKdVs based on the 'minimal N = 4 SCA' is given. (author)
Poisson structure of the equations of ideal multispecies fluid electrodynamics
International Nuclear Information System (INIS)
Spencer, R.G.
1984-01-01
The equations of the two- (or multi-) fluid model of plasma physics are recast in Hamiltonian form, following general methods of symplectic geometry. The dynamical variables are the fields of physical interest, but are noncanonical, so that the Poisson bracket in the theory is not the standard one. However, it is a skew-symmetric bilinear form which, from the method of derivation, automatically satisfies the Jacobi identity; therefore, this noncanonical structure has all the essential properties of a canonical Poisson bracket
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
DEFF Research Database (Denmark)
Nafziger, Julia; Koch, Alexander
It is a puzzle why people often evaluate consequences of choices separately (narrow bracketing) rather than jointly (broad bracketing). We study the hypothesis that a present-biased individual, who faces two tasks, may bracket his goals narrowly for motivational reasons. Goals motivate because th...... of the tasks. Narrow goals have a stronger motivational force and thus can be optimal. In particular, if one task outcome becomes known before working on the second task, narrow bracketing is always optimal.......It is a puzzle why people often evaluate consequences of choices separately (narrow bracketing) rather than jointly (broad bracketing). We study the hypothesis that a present-biased individual, who faces two tasks, may bracket his goals narrowly for motivational reasons. Goals motivate because...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...... series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some...
On BRST quantization of second class constraint algebras
International Nuclear Information System (INIS)
Niemi, A.J.
1988-01-01
A BRST quantization of second-class constraint algebras that avoids Dirac brackets is constructed, and the BRST operator is shown to be related to the BRST operator of a first class algebra by a nonunitary canonical transformation. The transformation converts the second class algebra into an effective first class algebra with the help of an auxiliary second class algebra constructed from the dynamical Lagrange multipliers of the Dirac approach. The BRST invariant path integral for second class algebras is related to the path integral of the pertinent Dirac brackets, using the Parisi-Sourlas mechanism. As an application the possibility of string theories in subcritical dimensions is considered. (orig.)
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-06-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
2009-01-01
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies to the condi......In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... ergodicity proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen to be arbitrarily...
Quantum affine algebras and deformations of the virasoro and W-algebras
International Nuclear Information System (INIS)
Frenkel, E.; Reshetikhin, N.
1996-01-01
Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which are q-deformations of the classical W-algebras. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method. (orig.)
Poisson-Jacobi reduction of homogeneous tensors
International Nuclear Information System (INIS)
Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P
2004-01-01
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N
Dimension of the c-nilpotent multiplier of Lie algebras
Indian Academy of Sciences (India)
By a Lie algebra we mean a vector space over a field F with the Lie bracket [ , ]. The finite dimensional Lie algebra analogous to the Schur multiplier was developed in. [4, 5] and has been studied by various authors [7, 8, 14]. Let L be a finite dimensional. Lie algebra, its Schur multiplier, M(L), can be defined as a second ...
Algebraic partial Boolean algebras
Smith, D
2003-01-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial...
Algebraic partial Boolean algebras
Smith, Derek
2003-04-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space Script H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E8.
Algebraic partial Boolean algebras
Energy Technology Data Exchange (ETDEWEB)
Smith, Derek [Math Department, Lafayette College, Easton, PA 18042 (United States)
2003-04-04
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A{sub 5} sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E{sub 8}.
Canonical form of Nambu–Poisson bracket: A pedestrian approach
Indian Academy of Sciences (India)
Therefore, Hamilton's equations for the coordinates, and by the derivation property for a general dynamical variable F, are equivalent to the. Nambu form. We have also the liberty of going back to the original canonical coordinates. {x} because the transformation {x}↔{x } has unit Jacobian and we see that the Hamilton's.
Correlates of Narrow Bracketing
DEFF Research Database (Denmark)
Koch, Alexander; Nafziger, Julia
We examine whether different phenomena of narrow bracketing can be traced back to some common characteristic and whether and how different phenomena are related. We find that making dominated lottery choices or ignoring the endowment when making risky choices are related phenomena and are both as...
A Simplified Lingual Bracket Positioner
Directory of Open Access Journals (Sweden)
Sharath Kumar Shetty
2014-01-01
Full Text Available The indirect bonding system for lingual brackets may be broadly classified as; techniques using setup models and those using diagnostic models. The techniques using setup models are more accurate and many of them require the use of lingual bracket positioners for determining the correct position of brackets. We have devised a simpler yet reliable and effective bracket positioner ′Lingual Bracket Positioner′ in our department. Although many variants are available commercially, this design is easy to fabricate, cheap and ready to use.
International Nuclear Information System (INIS)
Garcia, R.L.
1983-11-01
The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Bracketing effects on risk tolerance
Directory of Open Access Journals (Sweden)
Ester Moher
2010-08-01
Full Text Available Research has shown that risk tolerance increases when multiple decisions and associated outcomes are presented together in a broader ``bracket'' rather than one at a time. The present studies disentangle the influence of problem bracketing (presenting multiple investment options together from that of outcome bracketing (presenting the aggregated outcomes of multiple decisions, factors which have been deliberately confounded in previous research. In the standard version of the bracketing task, in which participants decide how much of an initial endowment to invest into each in a series of repeated, identical gambles, we find a problem bracketing effect but not an outcome bracketing effect. However, this pattern of results does not generalize to the cases of non-identical gambles nor discrete choice, where we fail to find the standard bracketing effect.
Beilinson, Alexander
2004-01-01
Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras. The exposition of this book covers the following topics: the "classical" counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries; the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the ch
Division algebras and extended N = 2, 4, 8 super KdVs
Energy Technology Data Exchange (ETDEWEB)
Carrion, H.L.; Rojas, M.; Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas]. E-mail: lenyj@cbpf.br; mrojas@cbpf.br; toppan@cbpf.br
2001-09-01
The first example of an N = 8 supersymmetric extension of the KdV equation is here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It corresponds to the unique N = 8 solution based a generalized hamiltonian dynamics with (generalized) Poisson brackets given by the Non-associate N = 8 Superconformal Algebra. The complete list of inequivalent classes of parametric-dependent N = 3 and N = 4 superKdVs obtained from the 'Non-associative N= 8 SCA' is also furnished. Furthermore, a fundamental domain characterizing the class of inequivalent N = 4 superKdVs based on the 'minimal N = 4 SCA' is given. (author)
Poisson integrators for Lie-Poisson structures on R3
International Nuclear Information System (INIS)
Song Lina
2011-01-01
This paper is concerned with the study of Poisson integrators. We are interested in Lie-Poisson systems on R 3 . First, we focus on Poisson integrators for constant Poisson systems and the transformations used for transforming Lie-Poisson structures to constant Poisson structures. Then, we construct local Poisson integrators for Lie-Poisson systems on R 3 . Finally, we present the results of numerical experiments for two Lie-Poisson systems and compare our Poisson integrators with other known methods.
Hamiltonian field description of the one-dimensional Poisson-Vlasov equations
International Nuclear Information System (INIS)
Morrison, P.J.
1981-07-01
The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained
Generalized Galilean algebras and Newtonian gravity
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.
Observable algebras for the rational and trigonometric Euler-Calogero-Moser Models
International Nuclear Information System (INIS)
Avan, J.; Billey, E.
1995-01-01
We construct polynomial Poisson algebras of observables for the classical Euler-Calogero-Moser (ECM) models. Their structure connects them to flavour-indexed non-linear W ∞ algebras, albeit with qualitative differences. The conserved Hamiltonians and symmetry algebras derived in a previous work are subsets of these algebra. We define their linear, N →∞ limits, realizing W ∞ type algebras coupled to current algebras. ((orig.))
Warner, Seth
1990-01-01
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Goodstein, R L
2007-01-01
This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
Operator theory, operator algebras and applications
Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya
2014-01-01
This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...
Leibniz Algebras and Lie Algebras
Directory of Open Access Journals (Sweden)
Geoffrey Mason
2013-10-01
Full Text Available This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
Formality theory from Poisson structures to deformation quantization
Esposito, Chiara
2015-01-01
This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.
Adhesives for orthodontic bracket bonding
Directory of Open Access Journals (Sweden)
Déborah Daniella Diniz Fonseca
2010-04-01
Full Text Available The advent of acid etching, introduced by Buonocore in 1955, brought the possibility of bonding between the bracket base and enamel, contributing to more esthetic and conservative orthodontics. This direct bracket bonding technique has brought benefits such as reduced cost and time in performing the treatment, as well as making it easier to perform oral hygiene. The aim of this study was to conduct a survey of published studies on orthodontic bracket bonding to dental enamel. It was verified that resin composites and glass ionomer are the most studied and researched materials for this purpose. Resin-modified glass ionomer, with its biocompatibility, capacity of releasing fluoride and no need for acid etching on the tooth structure, has become increasingly popular among dentists. However, due to the esthetic and mechanical properties of light polymerizable resin composite, it continues to be one of the adhesives of choice in the bracket bonding technique and its use is widely disseminated.
Invisible orthodontics part 3: aesthetic orthodontic brackets.
Waring, David; McMullin, Ailbhe; Malik, Ovais H
2013-09-01
In this, the third part of the series, aesthetic orthodontic treatment will be considered. The previous two articles have looked at invisible orthodontics with Invisalign and lingual brackets. This article will discuss the properties and use of aesthetic brackets, along with examples of orthodontic treatment cases using the aesthetic brackets. Increasing demand for aesthetics during orthodontic treatment has resulted in a significant increase in the use of aesthetic brackets. Clinicians need to be aware of the benefits and drawbacks of aesthetic brackets.
Suzuki, Yukihito
2018-03-01
A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn-Hilliard and Allen-Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.
Derivation of the Hall and extended magnetohydrodynamics brackets
Energy Technology Data Exchange (ETDEWEB)
D' Avignon, Eric C., E-mail: cavell@physics.utexas.edu; Morrison, Philip J., E-mail: morrison@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States); Lingam, Manasvi, E-mail: mlingam@princeton.edu [Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 (United States)
2016-06-15
There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this paper, we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously. As an important step in this process, we exhibit each theory's two advected fluxes (in analogy to ideal MHD's advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Lie-dragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the Euler-Lagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones.
Ford, Timothy J
2017-01-01
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
The relaxed three-algebras: their matrix representation and implications for multi M2-brane theory
International Nuclear Information System (INIS)
Ali-Akbari, M.; Sheikh-Jabbari, M.M.; Simon, J.
2008-01-01
We argue that one can relax the requirements of the non-associative three-algebras recently used in constructing D = 3, N = 8 superconformal field theories, and introduce the notion of 'relaxed three-algebras'. We present a specific realization of the relaxed three-algebras in terms of classical Lie algebras with a matrix representation, endowed with a non-associative four-bracket structure which is prescribed to replace the three-brackets of the three-algebras. We show that both the so(4)-based solutions as well as the cases with non-positive definite metric find a uniform description in our setting. We discuss the implications of our four-bracket representation for the D = 3, N = 8 and multi M2-brane theory and show that our setup can shed light on the problem of negative kinetic energy degrees of freedom of the Lorentzian case.
International Nuclear Information System (INIS)
Odesskii, A V
2002-01-01
This survey is devoted to associative Z ≥0 -graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations
National Research Council Canada - National Science Library
Hartshorne, Robin
1977-01-01
.... 141 BECKERIWEISPFENNINGIKREDEL. Grabner Bases. A Computational Approach to Commutative Algebra. 142 LANG. Real and Functional Analysis. 3rd ed. 143 DOOB. Measure Theory. 144 DENNIS/FARB. Noncommutat...
Integrable systems in the realm of algebraic geometry
Vanhaecke, Pol
2001-01-01
This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out. In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry.
International Nuclear Information System (INIS)
Krishnaswami, Govind S.
2006-01-01
Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren't differential equations as they involve left annihilation, which doesn't satisfy the Leibnitz rule with concatenation. But left annihilation is a derivation of the commutative shuffle product. Moreover shuffle and concatenation combine to define a bialgebra. Motivated by deformation quantization, we expand concatenation around shuffle in powers of q, whose physical value is 1. At zeroth order the loop equations become quadratic PDEs in the shuffle algebra. If the variation of the action is linear in iterated commutators of left annihilations, these quadratic PDEs linearize by passage to shuffle reciprocal of correlations. Remarkably, this is true for regularized versions of the Yang-Mills, Chern-Simons and Gaussian actions. But the linear equations are underdetermined just as the loop equations were. For any particular solution, the shuffle reciprocal is explicitly inverted to get the zeroth order gluon correlations. To go beyond zeroth order, we find a Poisson bracket on the shuffle algebra and associative q-products interpolating between shuffle and concatenation. This method, and a complementary one of deforming annihilation rather than product are shown to give over and underestimates for correlations of a gaussian matrix model
African Journals Online (AJOL)
Tadesse
Department of Mathematics, Faculty of Computer and Mathematical Sciences, Addis Ababa. University, Addis Ababa, Ethiopia(*drkvenkateswarlu@gmail.com, **berhanufk@yahoo.co.uk). ABSTRACT. In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra ...
African Journals Online (AJOL)
Tadesse
metric space. Also we prove that every implicative algebra can be made into a regular. Autometrized Algebra of Swamy (1964) (see theorem 2.9). We recall the definition of Xu (1993). Defintion [2]: Let (L,∨,∧,0,1) be a bounded lattice with order reversing involution. “ ' ”and a binary operation → satisfying the following ...
Linear Algebra and Smarandache Linear Algebra
Vasantha, Kandasamy
2003-01-01
The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...
Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
Martínez-Torres, David; Miranda, Eva
2018-01-01
We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.
A new 2 D bracket positioning gauge
Directory of Open Access Journals (Sweden)
Bhuwan Saklecha
2017-01-01
Full Text Available Bracket positioning is the basic premise of pre-adjusted system, which allows the teeth to be placed with a straight wire into an occlusal contact with an excellent mesiodistal inclination (tip and excellent faciolingual inclination (torque. Improper bracket placement may lead to poorly placed teeth and necessitate bracket repositioning and archwire adjustments. This can lead to an increased treatment time or poor occlusion. Therefore, a bracket positioning gauge has been designed using both the planes and evaluated for its accuracy in bonding of brackets. It was found that the gauge not only helped in the placement of brackets accurately, but also reduced chairside time.
International Nuclear Information System (INIS)
Harwood, L.H.
1981-01-01
At MSU we have used the POISSON family of programs extensively for magnetic field calculations. In the presently super-saturated computer situation, reducing the run time for the program is imperative. Thus, a series of modifications have been made to POISSON to speed up convergence. Two of the modifications aim at having the first guess solution as close as possible to the final solution. The other two aim at increasing the convergence rate. In this discussion, a working knowledge of POISSON is assumed. The amount of new code and expected time saving for each modification is discussed
Motivational Goal Bracketing: An Experiment
DEFF Research Database (Denmark)
Koch, Alexander; Nafziger, Julia
a one-week period. Our theoretical model predicts (i) that weekly goals create incentives to compensate for a lower than desired performance today with the promise to work harder tomorrow, whereas daily goals exclude such excuses; (ii) that subjects with daily goals set higher goals in aggregate......We study in an online, real-effort experiment how the bracketing of non-binding goals affects performance in a work-leisure self-control problem. We externally induce the goal bracket - daily goals or a weekly goal - and within that bracket let subjects set goals for how much they want to work over...... and work harder than those with weekly goals. Our data support these predictions. Surprisingly, however, when goals are combined with an externally enforced commitment that requires subjects to spend less than a minute each day on the task to get started working, performance deteriorates because of high...
International Nuclear Information System (INIS)
Cufaro-Petroni, N.; Dewdney, C.; Holland, P.; Kyprianidis, T.; Vigier, J.P.
1985-01-01
The deduction by Guerra and Marra of the usual quantum operator algebra from a canonical variable Hamiltonian treatment of Nelson's hydrodynamical stochastic description of real nonrelativistic Schroedinger waves is extended to the causal stochastic interpretation given by Guerra and Ruggiero and by Vigier of relativistic Klein-Gordon waves. A specific representation shows that the Poisson brackets for canonical hydrodynamical observables become ''averages'' of quantum observables in the given state. Stochastic quantization thus justifies the standard procedure of replacing the classical particle (or field) observables with operators according to the scheme p/sub μ/→-ihpartial/sub μ/ and L/sub munu/→-ih(x/sub μ/partial/sub ν/-x/sub ν/partial/sub μ/ )
Scaling the Poisson Distribution
Farnsworth, David L.
2014-01-01
We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Extended Poisson Exponential Distribution
Directory of Open Access Journals (Sweden)
Anum Fatima
2015-09-01
Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
Algebraic quantum field theory, perturbation theory, and the loop expansion
International Nuclear Information System (INIS)
Duetsch, M.; Fredenhagen, K.
2001-01-01
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)
Poisson branching point processes
International Nuclear Information System (INIS)
Matsuo, K.; Teich, M.C.; Saleh, B.E.A.
1984-01-01
We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage. In addition, each initiating event independently contributes a nonstationary Poisson point process (whose rate is a specified function) located at that point. The additional contributions from all points of a given stage constitute a doubly stochastic Poisson point process (DSPP) whose rate is a filtered version of the initiating point process at that stage. The process studied is a generalization of a Poisson branching process in which random time delays are permitted in the generation of events. Particular attention is given to the limit in which the number of branching stages is infinite while the average number of added events per event of the previous stage is infinitesimal. In the special case when the branching is instantaneous this limit of continuous branching corresponds to the well-known Yule--Furry process with an initial Poisson population. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers
Fine, Henry Burchard
2005-01-01
At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten. In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discus
Garrett, Paul B
2007-01-01
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal
Kolman, Bernard
1985-01-01
College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
McKeague, Charles P
1986-01-01
Elementary Algebra, Third Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first ponders on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the elimination method, solving linear systems by graphing, word problems, addition property of equality, solving linear equations, linear inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then takes a look at exponents and polynomials, factoring, and rational expressions. Topics include reducing ra
McKeague, Charles P
1981-01-01
Elementary Algebra 2e, Second Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first tackles the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the substitution method, solving linear systems by graphing, solutions to linear equations in two variables, multiplication property of equality, word problems, addition property of equality, and subtraction, addition, multiplication, and division of real numbers. The manuscript then examines exponents and polynomials, factoring, and rational e
International Nuclear Information System (INIS)
Arkad'ev, V.A.; Pogrebkov, A.K.; Polivanov, M.K.
1988-01-01
The concept of tangent vector is made more precise to meet the specific nature of the Sturm-Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov-Faddeev symplectic form. This bracket is nondegenerate, and in it the variables of the discrete and continuous spectra are separated
The algebra of non-local charges in non-linear sigma models
Abdalla, Elcio; Brunelli, J C; Zadra, Ayrton
1994-01-01
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower.
A-KAM, bracket positioning device
Directory of Open Access Journals (Sweden)
Anand Ambekar
2018-01-01
Full Text Available Bracket positioning is the heart of preadjusted edgewise appliance. Accuracy of bracket positioning directly affects the treatment outcome. A number of hand-held instruments are available for bracket positioning accuracy including Boon's gauge, MBT gauges, and various other modifications. However, the most commonly used MBT gauges come in a set of two or four jigs with gauges on each end of the instrument making it difficult to carry in the instrument tray for the orthodontists. Our new bracket positioning instrument, A-KAM, bracket positioning device surpasses these difficulties and can be used for reproducible bracket placement from 2.5 mm to 5.5 mm from the base of bracket.
Adhesive performance of precoated brackets after expiration.
Cloud, Cayce C; Trojan, Terry M; Suliman, Sam N; Tantbirojn, Daranee; Versluis, Antheunis
2016-03-01
To evaluate adhesive performance in terms of debonding forces of precoated metal and ceramic brackets 4 years after expiration. Buccal and lingual surfaces of embedded extracted maxillary premolars were etched with 34% Tooth Conditioner Gel (Dentsply Caulk, Milford, Del), rinsed, and dried. Transbond MIP (3M Unitek, Monrovia, Calif) was applied prior to placing adhesive precoated brackets (APC II Victory stainless steel and APC Plus Clarity ceramic brackets, 3M Unitek). The preexpiration brackets had 29-35 months before, and the postexpiration brackets were 45-52 months past, their expiration dates. Sample size was 17-21 per group. Debonding forces were determined by subjecting the bonded brackets to a shear force in a universal testing machine. Debonding forces were compared using two-way ANOVA. Debonded surfaces were examined under a stereomicroscope to determine failure modes, which were compared using the chi-square test. No statistically significant difference was found in debonding forces (P = .8581) or failure modes (P = .4538) between expired and unexpired brackets. Metal brackets required statistically significantly higher debonding forces than did ceramic brackets (P = .0001). For both expired and unexpired brackets, failure modes were mostly cohesive in the adhesive layer for ceramic brackets, and mixed between adhesive and cohesive failure in the adhesive layer for metal brackets. Adhesive precoated brackets did not have any reduction in enamel-adhesion properties up to 4 years after their expiration date. Extended shelf life testing for precoated dental brackets may be worth considering.
Cluster algebras in mathematical physics
International Nuclear Information System (INIS)
Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-01-01
This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm
Effect of delayed polymerization time and bracket manipulation on orthodontic bracket bonding
Ponikvar, Michael J.
This study examined the effect of bracket manipulation in combination with delayed polymerization times on orthodontic bracket shear bond strength and degree of resin composite conversion. Orthodontics brackets were bonded to extracted third molars in a simulated oral environment after a set period of delayed polymerization time and bracket manipulation. After curing the bracket adhesive, each bracket underwent shear bond strength testing followed by micro-Raman spectroscopy analysis to measure the degree of conversion of the resin composite. Results demonstrated the shear bond strength and the degree of conversion of ceramic brackets did not vary over time. However, with stainless steel brackets there was a significant effect (p ≤ 0.05) of delay time on shear bond strength between the 0.5 min and 10 min bracket groups. In addition, stainless steel brackets showed significant differences related to degree of conversion over time between the 0.5 min and 5 min groups, in addition to the 0.5 min and 10 min groups. This investigation suggests that delaying bracket adhesive polymerization up to a period of 10 min then adjusting the orthodontic bracket may increase both shear bond strength and degree of conversion of stainless steel brackets while having no effect on ceramic brackets.
Shingle assembly with support bracket
Almy, Charles
2007-01-02
A shingle system, mountable to a support surface, includes overlapping shingle assemblies. Each shingle assembly comprises a support bracket, having upper and lower ends, secured to a shingle body. The upper end has an upper support portion, extending away from the shingle body, and an upper support-surface-engaging part, engageable with a support surface so that the upper edge of the shingle body is positionable at a first distance from the support surface to create a first gap therebetween. The lower end has a lower support portion extending away from the lower surface. The support brackets create: (1) a second gap between shingle bodies of the first and second shingle assemblies, and (2) an open region beneath the first shingle assembly fluidly coupling the first and second gaps.
Adhesives for fixed orthodontic brackets.
Mandall, N A; Millett, D T; Mattick, C R; Hickman, J; Macfarlane, T V; Worthington, H V
2003-01-01
Bonding of orthodontic brackets to teeth is important to enable effective and efficient treatment with fixed appliances. The problem is bracket failure during treatment which increases operator chairside time and lengthens treatment time. A prolonged treatment is likely to increase the oral health risks of orthodontic treatment with fixed appliances one of which is irreversible enamel decalcification. To evaluate the effectiveness of different orthodontic adhesives for bonding. Electronic databases: the Cochrane Oral Health Group's Trials Register, the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE and EMBASE. Date of most recent searches: August 2002 (CENTRAL) (The Cochrane Library Issue 2, 2002). Trials were selected if they met the following criteria: randomised controlled trials (RCTs) and controlled clinical trials (CCTs) comparing two different adhesive groups. Participants were patients with fixed orthodontic appliances. The interventions were adhesives that bonded stainless steel brackets to all teeth except the molars. The primary outcome was debond or bracket failure. Data were recorded on decalcification as a secondary outcome, if present. Information regarding methods, participants, interventions, outcome measures and results were extracted in duplicate by pairs of reviewers (Nicky Mandall (NM) and Rye Mattick (CRM); Declan Millett (DTM) and Joy Hickman (JH2)). Since the data were not presented in a form that was amenable to meta-analysis, the results of the review are presented in narrative form only. Three trials satisfied the inclusion criteria. A chemical cured composite was compared with a light cure composite (one trial), a conventional glass ionomer cement (one trial) and a polyacid-modified resin composite (compomer) (one trial). The quality of the trial reports was generally poor. It is difficult to draw any conclusions from this review, however, suggestions are made for methods of improving future research involving
Frictional Characteristics of Active and Passive Self-Ligation Bracket Systems: An in vitro Study
Directory of Open Access Journals (Sweden)
K M Shahul Hameed Faizee
2011-01-01
Conclusion : Self-ligating brackets offered less frictional resistance than conventional brackets. Passive bracket systems offered less frictional resistance than active self-ligating bracket systems and Damon 3 brackets offered the least frictional resistance among all the brackets studied.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Kinematics of semiclassical spin and spin fiber bundle associated with so(n) Lie-Poisson manifold
International Nuclear Information System (INIS)
Deriglazov, A A
2013-01-01
We describe geometric construction underlying the Lagrangian actions for non-Grassmann spinning particles proposed in our recent works. If we discard the spatial variables (the case of frozen spin), the problem reduces to formulation of a variational problem for Hamiltonian system on a manifold with so(n) Lie-Poisson bracket. To achieve this, we identify dynamical variables of the problem with coordinates of the base of a properly constructed fiber bundle. In turn, the fiber bundle is embedded as a surface into the phase space equipped with canonical Poisson bracket. This allows us to formulate the variational problem using the standard methods of Dirac theory for constrained systems.
Bell, Eric T
1927-01-01
The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the BÃ´cher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, ellipti
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Jacobson, Nathan
2009-01-01
A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L
Material testing of reconditioned orthodontic brackets.
Reimann, S; Rewari, A; Keilig, L; Widu, F; Jäger, A; Bourauel, C
2012-12-01
While all manufacturers of orthodontic brackets label these products for single use, there are commercial providers offering bracket reconditioning (or "recycling"). We conducted this study to investigate the effects of different recycling techniques on material-related parameters in orthodontic brackets, aiming to derive indications for clinical use and conclusions about the biocompatibility, longevity, and application of recycled brackets. New metal brackets (equilibrium(®); Dentaurum, Ispringen, Germany) were compared to brackets recycled by different techniques, including direct flaming with a Bunsen burner, chemical reconditioning in an acid bath, a commercial unit (Big Jane; Esmadent, IL, USA), and outsourcing to a company (Ortho Clean, Dellstedt, Germany). Material-related examinations included the following: (1) corrosion behavior by static immersion testing and use of a mass spectrometer to determine nickel-ion concentrations in the corrosive medium, (2) surface features in scanning electron micrographs before and after corrosion testing, (3) Vickers hardness using a hardness testing machine, (4) shear bond strength as defined in DIN 13990-1, (5) dimensional stability of the bracket slots by light microscopy, and (6) frictional loss as assessed by an orthodontic measurement and simulation system (OMSS). Each examination was performed on ten brackets. Student's t-test was used for statistical analysis. Compared to the new brackets, those recycled in an acid bath or by a commercial provider revealed significant dimensional changes (p<0.05). Corrosion on the recycled brackets varied according to the recycling techniques employed. The group of brackets recycled by one company revealed hardness values that differed from those of all the other groups. No significant differences were observed in nickel-ion release, frictional loss, and shear bond strength. Recycling was found to significantly reduce the corrosion resistance and dimensional stability of
Quadratic Hamiltonians on non-symmetric Poisson structures
International Nuclear Information System (INIS)
Arribas, M.; Blesa, F.; Elipe, A.
2007-01-01
Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
Eliazar, Iddo; Klafter, Joseph
2008-05-01
Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ` Paretian Poisson processes'. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.
Delayed bracket placement in orthodontic treatment
Directory of Open Access Journals (Sweden)
Chandra Wigati
2008-12-01
Full Text Available Background: Beside bracket position, the timing of bracket placement is one of the most essential in orthodontic treatment with fixed appliances. Even it seems simple the timing of bracket placement can be crucial and significantly influence the result of orthodontic treatment. However it is often found brackets are placed without complete understanding of its purpose and effects, which could be useless and even detrimental for the case. Purpose: The aim of this case report is to show that the timing of bracket placement could be different depending on the cases. Case: Five different cases are presented here with different timing of bracket placement. Case management: On these cases, brackets were placed on the upper arch first, on the lower arch first, or even only on some teeth first. Good and efficient orthodontic treatment results were achieved. Conclusion: For every orthodontic case, from the very beginning of treatment, bracket should be placed with the end result in mind. If brackets are correctly placed at a correct time, better treatment result could be achieved without unnecessary round tripping tooth movement.
Observable currents and a covariant Poisson algebra of physical observables
Díaz-Marín, Homero G.; Zapata, José A.
2017-01-01
Observable currents are conserved gauge invariant currents; physical observables may be calculated integrating them on appropriate hypersurfaces. Due to the conservation law the hypersurfaces become irrelevant up to homology, and the main objects of interest become the observable currents them selves. Gauge inequivalent solutions can be distinguished by means of observable currents. With the aim of modelling spacetime local physics, we work on spacetime domains $U\\subset M$ which may have bou...
Algebraic characterizations of measure algebras
Czech Academy of Sciences Publication Activity Database
Jech, Thomas
2008-01-01
Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008
International Nuclear Information System (INIS)
Mohammad, N.; Siddiqui, A.H.
1987-11-01
The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.
Fractional Poisson Fields and Martingales
Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely
2018-01-01
We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.
Fractional Poisson Fields and Martingales
Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely
2018-02-01
We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.
A scanning electron microscopic investigation of ceramic orthodontic brackets
International Nuclear Information System (INIS)
McDonald, F.; Toms, A.P.
1990-01-01
Ceramic brackets were introduced to overcome the esthetic disadvantages of stainless steel brackets. The clinical impression of these brackets is very favorable. However, the sliding mechanics used in the Straightwire (A Company, San Diego, CA, USA) system appear to produce slower tooth movements with ceramic compared to stainless steel brackets. To determine whether this was due to any obvious mechanical problem in the bracket slot, Transcend (Unitek Corporation/3M, Monrovia, CA, USA) ceramic brackets were examined by a scanning electron microscope and compared to stainless steel brackets.Consistently, large surface defects were found in the ceramic bracket slots that were not present in the metal bracket slots. These irregularities could obviously hinder the sliding mechanics of the bracket slot-archwire system and create a greater demand on anchorage. Conversely, the fitting surface of the Transcend ceramic bracket showed extremely smooth surface characteristics, and it would seem advisable for the manufacturers to incorporate this surface within the bracket slot. (author)
Iachello, F
1995-01-01
1. The Wave Mechanics of Diatomic Molecules. 2. Summary of Elements of Algebraic Theory. 3. Mechanics of Molecules. 4. Three-Body Algebraic Theory. 5. Four-Body Algebraic Theory. 6. Classical Limit and Coordinate Representation. 8. Prologue to the Future. Appendices. Properties of Lie Algebras; Coupling of Algebras; Hamiltonian Parameters
Canonical formulation of the self-dual Yang-Mills system: Algebras and hierarchies
International Nuclear Information System (INIS)
Chau, L.; Yamanaka, I.
1992-01-01
We construct a canonical formulation of the self-dual Yang-Mills system formulated in the gauge-invariant group-valued J fields and derive their Hamiltonian and the quadratic algebras of the fundamental Dirac brackets. We also show that the quadratic algebras satisfy Jacobi identities and their structure matrices satisfy modified Yang-Baxter equations. From these quadratic algebras, we construct Kac-Moody-like and Virasoro-like algebras. We also discuss their related symmetries, involutive conserved quantities, and hierarchies of nonlinear and linear equations
The Poisson aggregation process
International Nuclear Information System (INIS)
Eliazar, Iddo
2016-01-01
In this paper we introduce and analyze the Poisson Aggregation Process (PAP): a stochastic model in which a random collection of random balls is stacked over a general metric space. The scattering of the balls’ centers follows a general Poisson process over the metric space, and the balls’ radii are independent and identically distributed random variables governed by a general distribution. For each point of the metric space, the PAP counts the number of balls that are stacked over it. The PAP model is a highly versatile spatial counterpart of the temporal M/G/∞ model in queueing theory. The surface of the moon, scarred by circular meteor-impact craters, exemplifies the PAP model in two dimensions: the PAP counts the number of meteor-impacts that any given moon-surface point sustained. A comprehensive analysis of the PAP is presented, and the closed-form results established include: general statistics, stationary statistics, short-range and long-range dependencies, a Central Limit Theorem, an Extreme Limit Theorem, and fractality.
Directory of Open Access Journals (Sweden)
Maria Regina Guerra MONTEIRO
2014-06-01
Full Text Available Objective: To compare the influence of archwire material (NiTi, beta-Ti and stainless steel and brackets design (self-ligating and conventional on the frictional force resistance. Material and Methods: Two types of brackets (self-ligating brackets - Smartclip, 3M/Unitek - and conventional brackets - Gemini, 3M/Unitek with three (0, 5, and 10 degrees slot angulation attached with elastomeric ligatures (TP Orthodontics were tested. All brackets were tested with archwire 0.019"x0.025" nickel-titanium, beta-titanium, and stainless steel (Unitek/3M. The mechanical testing was performed with a universal testing machine eMIC DL 10000 (eMIC Co, Brazil. The wires were pulled from the bracket slots at a cross-head speed of 3 mm/min until 2 mm displacement. Results: Self-ligating brackets produced significantly lower friction values compared with those of conventional brackets. Frictional force resistance values were directly proportional to the increase in the bracket/ wire angulation. With regard to conventional brackets, stainless steel wires had the lowest friction force values, followed by nickel-titanium and beta-titanium ones. With regard to self-ligating brackets, the nickel-titanium wires had the lowest friction values, significantly lower than those of other materials. Conclusion: even at different angulations, the self-ligating brackets showed significantly lower friction force values than the conventional brackets. Combined with nickel-titanium wires, the self-ligating brackets exhibit much lower friction, possibly due to the contact between nickel-titanium clips and wires of the same material.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
International Nuclear Information System (INIS)
Yau, Donald
2011-01-01
We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.
Bliss, Gilbert Ames
1933-01-01
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t
Are torque values of preadjusted brackets precise?
Directory of Open Access Journals (Sweden)
Alessandra Motta Streva
Full Text Available OBJECTIVE: The aim of the present study was to verify the torque precision of metallic brackets with MBT prescription using the canine brackets as the representative sample of six commercial brands. MATERIAL AND METHODS: Twenty maxillary and 20 mandibular canine brackets of one of the following commercial brands were selected: 3M Unitek, Abzil, American Orthodontics, TP Orthodontics, Morelli and Ortho Organizers. The torque angle, established by reference points and lines, was measured by an operator using an optical microscope coupled to a computer. The values were compared to those established by the MBT prescription. RESULTS: The results showed that for the maxillary canine brackets, only the Morelli torque (-3.33º presented statistically significant difference from the proposed values (-7º. For the mandibular canines, American Orthodontics (-6.34º and Ortho Organizers (-6.25º presented statistically significant differences from the standards (-6º. Comparing the brands, Morelli presented statistically significant differences in comparison with all the other brands for maxillary canine brackets. For the mandibular canine brackets, there was no statistically significant difference between the brands. CONCLUSIONS: There are significant variations in torque values of some of the brackets assessed, which would clinically compromise the buccolingual positioning of the tooth at the end of orthodontic treatment.
Grätzer, George
1979-01-01
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...
Miyanishi, Masayoshi
2000-01-01
Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...
Generalized Hermitian Algebras
Foulis, David J.; Pulmannová, Sylvia
2009-05-01
We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. In this paper we define and launch a study of a class of generalized Hermitian (GH) algebras. Among the examples of GH-algebras are ordered special Jordan algebras, JW-algebras, and AJW-algebras, but unlike these more restricted cases, a GH-algebra is not necessarily a Banach space and its lattice of projections is not necessarily complete. In this paper we develop the basic theory of GH-algebras, identify their unit intervals as effect algebras, and observe that their projection lattices are sigma-complete orthomodular lattices. We show that GH-algebras are spectral order-unit spaces and that they admit a substantial spectral theory.
Universal enveloping algebras for Malcev color algebras
de-la-Concepción, Daniel
2015-01-01
In this paper we give a construction of the universal enveloping algebra of a Malcev algebra in categories of group algebra comodules with a symmetry given by a bicharacter of the group. A particular example of such categories is the category of super vector spaces.
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Poisson traces, D-modules, and symplectic resolutions
Etingof, Pavel; Schedler, Travis
2018-03-01
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.
Indian Academy of Sciences (India)
Introduction and preliminaries. The class of Malcev algebras contains one of the Lie algebras and so a question arises whether some known results on Lie algebras can be extended to the framework of Malcev algebras (see [4, 7, 9, 10]). In the present paper, we are interested in studying the structure of arbitrary Malcev ...
Embeddings of Heyting Algebras
Jongh, D.H.J. de; Visser, A.
In this paper we study embeddings of Heyting Algebras. It is pointed out that such embeddings are naturally connected with Derived Rules. We compare the Heyting Algebras embeddable in the Heyting Algebra of the Intuitionistic Propositional Calculus (IPC), i.e. the free Heyting Algebra on countably
Dzhumadil'daev, A. S.
2002-01-01
Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.
Further validation of bracket pillar design methodology
CSIR Research Space (South Africa)
Vieira, F
1998-07-01
Full Text Available of seismic risk along the bracketed feature. Once an informed decision is made regarding the level of seismic risk to be accepted for a given layout, the rock engineer obtains from "design charts" a recommendable pillar width, assumed to keep the risk... for each area were produced. Seismic data from the selected site was processed and interpreted. Back analyses were carried out which attempted to compare modelling data and field seismic data for the actual bracket pillar layouts. Seismic moments...
Introduction to relation algebras relation algebras
Givant, Steven
2017-01-01
The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...
International Nuclear Information System (INIS)
Ludu, A.; Greiner, M.
1995-09-01
A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs
Analysis of mesiodistal angulations of preadjusted brackets
Directory of Open Access Journals (Sweden)
Marcos Rogério de MENDONÇA
2014-08-01
Full Text Available Manufacturers offer various prescriptions of preadjusted brackets for use in the “straight-wire” orthodontic technique. However, the need to incorporate bends in the rectangular wires during orthodontic finishing has led to concerns regarding the type of prescription chosen and the credibility of information provided by the manufacturer. The aim of this study was to compare the slot angulations of Roth prescription preadjusted metallic brackets for the maxillary left central incisor and maxillary left canine. For each tooth type, 10 brackets of three commercial brands (GAC, Forestadent and Morelli were selected. Two individual metal matrices for brackets and tooth positioning were made for each group of teeth. Captured images were obtained by standardized ortho-radial photography with a digital camera. Images were exported and analyzed with the Image J software package. One-way ANOVA and Tukey statistical analyses were performed at the 5% significance level. For brackets of the maxillary left central incisor, differences in mean angulation were observed between the Morelli and GAC groups (p < 0.01 and between the Forestadent and GAC groups (p < 0.01. For brackets of the maxillary left canine, differences in mean angulation were found between the Morelli and GAC groups (p < 0.01 and between the Morelli and Forestadent groups (p < 0.05. In conclusion, despite their same prescription name, the different brands exhibited significantly different angulation measurements.
A note on the time decay of solutions for the linearized Wigner-Poisson system
Gamba, Irene
2009-01-01
We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.
A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity
Cattaneo, Alberto S.; Perez, Alejandro
2017-05-01
We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.
The influence of bracket design on frictional losses in the bracket/arch wire system.
Schumacher, H A; Bourauel, C; Drescher, D
1999-01-01
In arch guided tooth movement, the essential role played by bracket configuration with respect to sliding friction has been recognized by the manufacturers, a fact which has had an increasing impact on the design and marketing of new bracket models in recent years. The aim of the present in-vitro study was to investigate the influence of different bracket designs on sliding mechanics. Five differently shaped stainless steel brackets (Discovery: Dentaurum, Damon SL: A-Company, Synergy: Rocky Mountain Orthodontics, Viazis bracket and Omni Arch appliance: GAC) were compared in the 0.022"-slot system. The Orthodontic Measurement and Simulation System (OMSS) was used to quantify the difference between applied force (NiTi coil spring, 1.0 N) and orthodontically effective force and to determine leveling losses occurring during the sliding process in arch guided tooth movement. Simulated canine retraction was performed using continuous arch wires with the dimensions 0.019" x 0.025" (Standard Steel, Unitek) and 0.020" x 0.020" (Ideal Gold, GAC). Comparison of the brackets revealed friction-induced losses ranging from 20 to 70%, with clear-cut advantages resulting from the newly developed bracket types. However, an increased tendency towards leveling losses in terms of distal rotation (maximum 15 degrees) or buccal root torque (maximum 20 degrees) was recorded, especially with those brackets giving the arch wire increased mobility due to their shaping or lack of ligature wire.
Goldmann, H
1990-01-01
The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorphic functions on Stein spaces) within the class of Fréchet algebras.
Abrams, Gene; Siles Molina, Mercedes
2017-01-01
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...
Analysis on Poisson and Gamma spaces
Kondratiev, Yuri; Silva, Jose Luis; Streit, Ludwig; Us, Georgi
1999-01-01
We study the spaces of Poisson, compound Poisson and Gamma noises as special cases of a general approach to non-Gaussian white noise calculus, see \\cite{KSS96}. We use a known unitary isomorphism between Poisson and compound Poisson spaces in order to transport analytic structures from Poisson space to compound Poisson space. Finally we study a Fock type structure of chaos decomposition on Gamma space.
Directory of Open Access Journals (Sweden)
Jefferson Vinicius Bozelli
2013-12-01
Full Text Available OBJECTIVE: The aim of this study was to assess the time spent for direct (DBB - direct bracket bonding and indirect (IBB - indirect bracket bonding bracket bonding techniques. The time length of laboratorial (IBB and clinical steps (DBB and IBB as well as the prevalence of loose bracket after a 24-week follow-up were evaluated. METHODS: Seventeen patients (7 men and 10 women with a mean age of 21 years, requiring orthodontic treatment were selected for this study. A total of 304 brackets were used (151 DBB and 153 IBB. The same bracket type and bonding material were used in both groups. Data were submitted to statistical analysis by Wilcoxon non-parametric test at 5% level of significance. RESULTS: Considering the total time length, the IBB technique was more time-consuming than the DBB (p < 0.001. However, considering only the clinical phase, the IBB took less time than the DBB (p < 0.001. There was no significant difference (p = 0.910 for the time spent during laboratorial positioning of the brackets and clinical session for IBB in comparison to the clinical procedure for DBB. Additionally, no difference was found as for the prevalence of loose bracket between both groups. CONCLUSION: the IBB can be suggested as a valid clinical procedure since the clinical session was faster and the total time spent for laboratorial positioning of the brackets and clinical procedure was similar to that of DBB. In addition, both approaches resulted in similar frequency of loose bracket.
Samuel, Pierre
2008-01-01
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal
Osborn, J
1989-01-01
During the academic year 1987-1988 the University of Wisconsin in Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the workshop was the long-standing problem of classifying the simple finite-dimensional Lie algebras over algebraically closed field of prime characteristic. However, other lectures at the workshop dealt with the related areas of algebraic groups, representation theory, and Kac-Moody Lie algebras. Fourteen papers were presented and nine of these (eight research articles and one expository article) make up this volume.
Coordination of Conditional Poisson Samples
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Grafström Anton
2015-12-01
Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.
A note on the Akivis algebra of a smooth hyporeductive loop
International Nuclear Information System (INIS)
Issa, A.N.
2002-05-01
Using the fundamental tensors of a smooth loop and the differential geometric characterization of smooth hyporeductive loops, the Akivis operations of a local smooth hyporeductive loop are expressed through the two binary and the one ternary operations of the hyporeductive triple algebra (h.t.a.) associated with the given hyporeductive loop. Those Akivis operations are also given in terms of Lie brackets of a Lie algebra of vector fields with the hyporeductive decomposition which generalizes the reductive decomposition of Lie algebras. A nontrivial real two-dimensional h.t.a. is presented. (author)
Relation between dual S-algebras and BE-algebras
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Arsham Borumand Saeid
2015-05-01
Full Text Available In this paper, we investigate the relationship between dual (Weak Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.
Frictional Resistance of Three Types of Ceramic Brackets
Directory of Open Access Journals (Sweden)
Claire L Williams
2014-01-01
Full Text Available Objectives: To investigate the static frictional resistance at the bracket/archwire interface in two recently introduced bracket systems and compare them to conventional ceramic and conventional metal bracket systems. Three variables were considered including the bracket system, archwire type and archwire angulation. Material and Methods: Four bracket systems were tested in vitro: Self ligating ceramic, ceramic with metal slot and module, conventional ceramic with module and conventional metal with module. A specially constructed jig and an Instron testing machine were used to measure the static frictional resistance for 0.014 inches round and 0.018 x 0.025 inches rectangular stainless steel wires at 0° and 7° angulations. Main outcome measures: static frictional force at the bracket/archwire interface; recorded and measured in units of force (Newtons. Results: Self ligating ceramic and metal slot ceramic bracket systems generated significantly less static frictional resistance than conventional ceramic bracket systems with the wire at both angulations (P < 0.05. Changing the wire from 0.014 round to 0.018 x 0.025 rectangular wire significantly increased frictional forces for metal slot ceramic and conventional metal bracket systems (P < 0.01. Increasing wire angulation significantly increased frictional resistance at the bracket/archwire interface for all four types of bracket systems tested (P < 0.001. Conclusions: Compared to conventional ceramic, self ligating ceramic and metal slot ceramic bracket systems should give improved clinical performance, matching that of conventional metal brackets.
Algebraic isotopy in genetics.
Campos, T M; Holgate, P
1987-01-01
It is shown that many of the algebras arising in nonselective genetics are isotopes of the algebras for particularly simple systems of inheritance. Moreover, interesting aspects of the structure are preserved under the relevant isotopies.
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Cylindric-like algebras and algebraic logic
Ferenczi, Miklós; Németi, István
2013-01-01
Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.
Algebraic statistics computational commutative algebra in statistics
Pistone, Giovanni; Wynn, Henry P
2000-01-01
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
Indian Academy of Sciences (India)
We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras is of the form M = U + ∑ j I j with U a subspace of the abelian Malcev subalgebra and any I j a well described ideal of satisfying [ I j , I k ] = 0 if ≠ .
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
L{sub ∞} algebras and field theory
Energy Technology Data Exchange (ETDEWEB)
Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY (United States); Zwiebach, Barton [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)
2017-03-15
We review and develop the general properties of L{sub ∞} algebras focusing on the gauge structure of the associated field theories. Motivated by the L{sub ∞} homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L{sub ∞} structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L{sub ∞} algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L{sub ∞} algebra for the interacting theory. The analysis suggests that L{sub ∞} algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The algebra of non-local charges in non-linear sigma models
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.
1993-07-01
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower. (author). 22 refs, 5 figs
21 CFR 872.5470 - Orthodontic plastic bracket.
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Orthodontic plastic bracket. 872.5470 Section 872...) MEDICAL DEVICES DENTAL DEVICES Therapeutic Devices § 872.5470 Orthodontic plastic bracket. (a) Identification. An orthodontic plastic bracket is a plastic device intended to be bonded to a tooth to apply...
International Nuclear Information System (INIS)
Krivonos, S.O.; Sorin, A.S.
1994-06-01
We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
[Precision of three-dimensional printed brackets].
Zhang, D; Wang, L C; Zhou, Y H; Liu, X M; Li, J
2017-08-18
This study was based on digital orthodontic diagnosis work flow for indirect bonding transfer tray model design and three-dimensional (3D) printing, and the aim of this paper was to inspect the dimensional accuracyof 3D printed brackets, which is the foundation of the follow up work and hoped that will illuminate the clinical application of the digital orthodontics work flow. The samples which consisted of 14 cases of patients with malocclusion from Department of Orthodontics Peking University were selected, including 8 cases with tooth extraction and 6 cases without tooth extraction. All the 14 patients were taken intra-oral scan (Trios 3Shape, Denmark) and cone-beam computed tomography (CBCT, NewTom 3G volumetric scanner, Aperio Service,Italy)shooting after periodontal treatment. STL data and DICOM data were obtained from intraoral scans and CBCT images.Data segmentation, registration, fusion, automatic tooth arrangement, virtual positioning of orthodontic appliance and conversion the coordinates of malocclusion model were all done with self-programming software. The data of 3D printing model with brackets on it were output finally and printed out with EDEN260V (Objet Geometries, Israel) to make indirect bonding transfer tray. Digital vernier caliper was used to measure the length and width of upper and lower left brackets and buccal tubes on those 3D models after removal of surrounding supporting material by ultrasonic vibration and water-spray. Intra-examiner reliability was assessed by using intra-class correlation coefficients (ICC), and one-sample T test was used to compare the measurements with the standard dimensional data of the brackets. There were significant differences which range in 0.04-0.17 mm between the 13 items out of the 19 measurement items. Except for the length of the lower left premolars'brackets, mean values of the other items were greater than the test value. Although the measurement results in the width of brackets and the width and
International Nuclear Information System (INIS)
Feigin, B.L.; Semikhatov, A.M.
2004-01-01
We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W n (2) generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W 3 (2) algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W n (2) algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras
Algebraic conformal field theory
International Nuclear Information System (INIS)
Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1991-11-01
Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs
Discrete Minimal Surface Algebras
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Joakim Arnlind
2010-05-01
Full Text Available We consider discrete minimal surface algebras (DMSA as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself. A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
Bicovariant quantum algebras and quantum Lie algebras
International Nuclear Information System (INIS)
Schupp, P.; Watts, P.; Zumino, B.
1993-01-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)
The Boolean algebra and central Galois algebras
Directory of Open Access Journals (Sweden)
George Szeto
2001-01-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb for all x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.
Towards classical spectrum generating algebras for f-deformations
Energy Technology Data Exchange (ETDEWEB)
Kullock, Ricardo, E-mail: ricardokullock@gmail.com [Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro, Instituto de Aplicação Fernando Rodrigues da Silveira, Departamento de Ciências da Natureza, Rua Santa Alexandrina 288, 20261-232, Rio de Janeiro, RJ (Brazil); Latini, Danilo [Department of Mathematics and Physics and INFN, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy)
2016-01-28
In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion. - Highlights: • We study the classical analog of f-deformed oscillators. • We use the classical spectrum generating algebra. • The deformed trajectories have energy dependent frequencies. • The method leads to exact results for any acceptable f-deformation.
Quantum algebras as quantizations of dual Poisson–Lie groups
International Nuclear Information System (INIS)
Ballesteros, Ángel; Musso, Fabio
2013-01-01
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U z (g), Δ z ) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δ z is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λ g ) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by the dual map δ*. From this perspective, the coproduct for U z (g) is just the pull-back of the group law for G*, and the Poisson analogues of the quantum commutation rules for U z (g) are given by the unique Poisson–Lie structure Λ g on G* whose linearization is the Poisson analogue of the initial Lie algebra g. This approach is shown to be a very useful technical tool in order to solve the Lie bialgebra quantization problem explicitly since, once a Lie bialgebra (g, δ) is given, the full dual Poisson–Lie group (G*, Λ) can be obtained either by applying standard Poisson–Lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs. As a consequence, the quantization of (G*, Λ) will give rise to the full U z (g) quantum algebra, provided that ordering problems are appropriately fixed through the choice of certain local coordinates on G* whose coproduct fulfils a precise ‘quantum symmetry’ property. The applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant Lie algebras such as sl(2,R), the (2+1) anti-de Sitter algebra so(2, 2) and the Poincaré algebra in (3+1) dimensions. (paper)
Hurwitz Algebras and the Octonion Algebra
Burdik, Čestmir; Catto, Sultan
2018-02-01
We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.
A foundation for props, algebras, and modules
Yau, Donald
2015-01-01
PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of p
Linear algebra meets Lie algebra: the Kostant-Wallach theory
Shomron, Noam; Parlett, Beresford N.
2008-01-01
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
AT -algebras and extensions of AT-algebras
Indian Academy of Sciences (India)
algebra by an AT-algebra and E has real rank zero, then E is an AT-algebra if and only if the index maps are both zero. Accordingly, in this paper, we attempt to describe a characterization of an extension E of an AT-algebra by an AF-algebra if E ...
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
a left (2, hQ − 2)-Koszul algebra (see Definition 2.1 below), and the Yoneda algebra of. A is isomorphic to a twisted ... is quadratic if R is a subspace of V ⊗ V . The quadratic dual A! of A is defined to be. T (V ∗)/(R⊥) .... (Q, ρ) is a stable bound quiver of Loewy length p + 1, and the Nakayama translation on. Q0 is induced by a ...
Evolution algebras and their applications
Tian, Jianjun Paul
2008-01-01
Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.
Effect of Bracket Base Sandblasting on Bonding of Orthodontic Brackets on Enamel Surface
Directory of Open Access Journals (Sweden)
Mohammad Farahani
2016-01-01
Full Text Available Introduction: In evaluating bond failure, considerable attention has been paid to the various factors that affect bond strength. The bracket–resin interface is the site of usual bond failure. Therefore, many efforts have been accomplished on this interface. The aim of this study was to compare the effects of sandblasting on shear bond strength of three different metal brackets. Materials and Methods: For this experimental study, 180 human maxillary first and second premolars teeth were cleaned and stored in 0.1% thymol solution. The teeth were randomly assigned to either the control (n = 90 or experimental group (n = 90. Each group was subdivided into three equal groups (n = 30. In the control group, three different non-sandblasted metal brackets (American Orthodontics, Dentarum, and 3M Unitek were bonded with 3M (Unitek no-mix resin. In the next stage of the experiment, similar brackets were sandblasted and bonded. All samples were pumiced and etched with 37% phosphoric acid for 15 s. The teeth were embedded in blocks of autopolymerization polymethyl methacrylate, utilizing a special device to make their slots parallel to the horizontal. Samples were stored in distilled water for 24 h before testing. Shear bond testing was carried out with UTM Instron machine. Results: Mean shear bond strength of untreated groups was 15.51, 16.60, and 18.58 MPa for American Orthodontics, Dentarum, and 3M Unitek brackets, respectively. Mean shear bond strength of sandblasted brackets was 15.8, 19.36, and 18.66 for American Orthodontics, Dentarum, and 3M Unitek brackets, respectively. Conclusion: This study showed that there was a significant difference in the mean shear bond strength between untreated and sandblasted specimens only in the Dentarum bracket groups.
Finely homogeneous computations in free Lie algebras
Directory of Open Access Journals (Sweden)
Philippe Andary
1997-12-01
Full Text Available We first give a fast algorithm to compute the maximal Lyndon word (with respect to lexicographic order of Ly α (A for every given multidegree alpha in N k. We then give an algorithm to compute all the words living in Ly α (A for any given α in N k. The best known method for generating Lyndon words is that of Duval [1], which gives a way to go from every Lyndon word of length n to its successor (with respect to lexicographic order by length, in space and worst case time complexity O(n. Finally, we give a simple algorithm which uses Duval's method (the one above to compute the next standard bracketing of a Lyndon word for lexicographic order by length. We can find an interesting application of this algorithm in control theory, where one wants to compute within the command Lie algebra of a dynamical system (letters are actually vector fields.
Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India); Hebrew University of Jerusalem, Racah Institute of Physics, Jerusalem (Israel); Chakraborty, Sumanta [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India)
2014-05-15
Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein-Hawking form, is not modified. (orig.)
Borzooei, R. A.; Dudek, W. A.; Koohestani, N.
2006-01-01
We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.
Directory of Open Access Journals (Sweden)
R. A. Borzooei
2006-01-01
Full Text Available We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.
Givant, Steven
2017-01-01
This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatme...
Twisted classical Poincare algebras
International Nuclear Information System (INIS)
Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.
1993-11-01
We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)
Iachello, Francesco
2015-01-01
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...
Introduction to abstract algebra
Smith, Jonathan D H
2008-01-01
Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduc
Conceptual design for PSP mounting bracket
Energy Technology Data Exchange (ETDEWEB)
Ransom, G.; Stein, R. [Martin Marietta Energy Systems, Inc., Piketon, OH (United States)
1991-12-31
Protective structural packages (PSP`s or overpacks) used to ship 2 1/2-ton UF{sub 6} product cylinders are bolted to truck trailers. All bolts penetrate two longitudinal rows of wooden planks. Removal and replacement is required at various intervals for maintenance and routine testing. A conceptual design is presented for mounting brackets which would securely attach PSP`s to trailer frames, reduce removal and replacement time, and minimize risk of personnel injury.
Nambu brackets in fluid mechanics and magnetohydrodynamics
International Nuclear Information System (INIS)
Salazar, Roberto; Kurgansky, Michael V
2010-01-01
Concrete examples of the construction of Nambu brackets for equations of motion (both 3D and 2D) of Boussinesq stratified fluids and also for magnetohydrodynamical equations are given. It serves a generalization of Hamiltonian formulation for the considered equations of motion. Two alternative Nambu formulations are proposed, first by using fluid dynamical (kinetic) helicity and/or enstrophy as constitutive elements and second, by using the existing conservation laws of the governing equation.
Kurosh, A G; Stark, M; Ulam, S
1965-01-01
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the
Solomon, Alan D
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean
Directory of Open Access Journals (Sweden)
Frank Roumen
2017-01-01
Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.
Albert, A A
1939-01-01
The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI con
Toothpaste prevents debonded brackets on erosive enamel.
Barros, Érico Luiz Damasceno; Pinto, Shelon Cristina Souza; Borges, Alvaro Henrique; Tonetto, Mateus Rodrigues; Ellwood, Roger Phillip; Pretty, Ian; Bandéca, Matheus Coelho
2015-01-01
This study evaluated the effect of high fluoride dentifrice on the bond strength of brackets after erosive challenge. Eighty-four enamel specimens were divided into seven groups (n = 12): WN (distilled water/no acid challenge), W3C (distilled water/3 cycles of acid challenge), and W6C (distilled water/6 cycles of acid challenge) were not submitted to dentifrice treatment. Groups RF3C (regular fluoride dentifrice/3 cycles of acid challenge) and RF6C (regular fluoride dentifrice/6 cycles of acid challenge) were treated with dentifrices containing 1450 μg F(-)/g and HF3C (high fluoride dentifrice/3 cycles of acid challenge) and HF6C (high fluoride dentifrice/6 cycles of acid challenge) were with 5000 μg F(-)/g. Acid challenges were performed for seven days. After bond strength test, there was no significant difference among groups submitted to 3 cycles of acid challenge (P > 0.05). Statistically significant difference was found between the regular and high fluoride dentifrices after 6 cycles of acid challenge (<0.05). Similar areas of adhesive remaining were found among control groups and among groups W6C, RF3C, RF6C, HF3C, and HF6C. The high fluoride dentifrice was able to prevent the reduction of bond strength values of brackets submitted to acid challenge. the high fluoride toothpaste prevents debonded brackets on erosive enamel.
Toothpaste Prevents Debonded Brackets on Erosive Enamel
Directory of Open Access Journals (Sweden)
Érico Luiz Damasceno Barros
2015-01-01
Full Text Available This study evaluated the effect of high fluoride dentifrice on the bond strength of brackets after erosive challenge. Eighty-four enamel specimens were divided into seven groups (n=12: WN (distilled water/no acid challenge, W3C (distilled water/3 cycles of acid challenge, and W6C (distilled water/6 cycles of acid challenge were not submitted to dentifrice treatment. Groups RF3C (regular fluoride dentifrice/3 cycles of acid challenge and RF6C (regular fluoride dentifrice/6 cycles of acid challenge were treated with dentifrices containing 1450 μg F−/g and HF3C (high fluoride dentifrice/3 cycles of acid challenge and HF6C (high fluoride dentifrice/6 cycles of acid challenge were with 5000 μg F−/g. Acid challenges were performed for seven days. After bond strength test, there was no significant difference among groups submitted to 3 cycles of acid challenge (P>0.05. Statistically significant difference was found between the regular and high fluoride dentifrices after 6 cycles of acid challenge (<0.05. Similar areas of adhesive remaining were found among control groups and among groups W6C, RF3C, RF6C, HF3C, and HF6C. The high fluoride dentifrice was able to prevent the reduction of bond strength values of brackets submitted to acid challenge. Clinical relevance: the high fluoride toothpaste prevents debonded brackets on erosive enamel.
From Rota-Baxter algebras to pre-Lie algebras
International Nuclear Information System (INIS)
An Huihui; Ba, Chengming
2008-01-01
Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension ≤3 and their corresponding pre-Lie algebras
Independent production and Poisson distribution
International Nuclear Information System (INIS)
Golokhvastov, A.I.
1994-01-01
The well-known statement of factorization of inclusive cross-sections in case of independent production of particles (or clusters, jets etc.) and the conclusion of Poisson distribution over their multiplicity arising from it do not follow from the probability theory in any way. Using accurately the theorem of the product of independent probabilities, quite different equations are obtained and no consequences relative to multiplicity distributions are obtained. 11 refs
Algebraic monoids, group embeddings, and algebraic combinatorics
Li, Zhenheng; Steinberg, Benjamin; Wang, Qiang
2014-01-01
This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure and representation theory of reductive algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids from algebraic combinatorics v endomorphism monoids induced from vector bundles v Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semigroups are strongly π-regular. Graduate students as well a...
Assessment of bracket surface morphology and dimensional change
Directory of Open Access Journals (Sweden)
Pillai Devu Radhakrishnan
2017-01-01
Full Text Available Objective: The objective of this study was to compare the surface morphology and dimensional stability of the bracket slot at the onset of treatment and after 12 months of intraoral exposure. The study also compared the amount of calcium at the bracket base which indicates enamel loss among the three orthodontic brackets following debonding after 12 months of intraoral exposure. Materials and Methods: The sample consisted of 60 (0.022” MBT canine brackets. They were divided into three groups: self-ligating, ceramic bracket with metal slot, and stainless steel (SS brackets. The slot dimensions, micromorphologic characteristics of as-received and retrieved brackets were measured with a stereomicroscope and scanning electron microscope (SEM, respectively. The amount of calcium at the bracket base which indicates enamel damage was quantified using energy-dispersive X-ray spectrometry (EDX. Results: The results showed statistically significant alterations (P < 0.05 in the right vertical dimension, internal tie wing width (cervical, right and left depth of the slot (Kruskal–Wallis test. Multiple comparison using Mann–Whitney test showed that ceramic brackets underwent (P < 0.05 minimal alterations in the right vertical dimension, internal tie wing width (cervical, right and left depth of the slot (0.01 mm, −0.003 mm, 0.006 mm, −0.002 mm, respectively when compared with the changes seen in SS and self-ligating brackets. SEM analysis revealed an increase in the surface roughness of ceramic with metal slot brackets and self-ligating bracket showed the least irregularity. The presence of calcium was noted on all evaluated brackets under EDX, but ceramic with metal slot brackets showed a significantly greater amount of enamel loss (P = 0.001. Conclusion: Ceramic brackets were found to be dimensionally stable when compared to SS and self-ligating. Self-ligating bracket showed minimal surface irregularity. Ceramic with metal slot brackets showed a
Bär, Christian; Becker, Christian
In this chapter we will collect those basic concepts and facts related to C*-algebras that will be needed later on. We give complete proofs. In Sects. 1, 2, 3, and 6 we follow closely the presentation in [1]. For more information on C*-algebras, see, e.g. [2-6].
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.
Seo, Young Joo; Kim, Young Hee
2016-01-01
In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d -algebra.
Hayden, Dunstan; Cuevas, Gilberto
The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…
International Nuclear Information System (INIS)
Calmet, J.
1982-01-01
A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)
Indian Academy of Sciences (India)
Discourses on Algebra. Rajaram Nityananda. Discourses on Algebra. Igor R Shafarevich. Narosa Publishing. Pages: 273, Price in India: | 1750. To the Indian reader, the word discourse, evokes a respected figure interpreting divine wisdom to common folk in an accessible fash- ion. I dug a bit deeper with Google trans-.
Algebraic Description of Motion
Davidon, William C.
1974-01-01
An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)
International Nuclear Information System (INIS)
Talon, M.
1987-01-01
The algebraic set up for anomalies, a la Stora, is reviewed. Then a brief account is provided of the work of M. Dubois Violette, M. Talon, C. Viallet, in which the general algebraic solution to the consistency conditions is described. 34 references
Algebraic Reconstruction of Current Dipoles and Quadrupoles in Three-Dimensional Space
Directory of Open Access Journals (Sweden)
Takaaki Nara
2013-01-01
Full Text Available This paper presents an algebraic method for an inverse source problem for the Poisson equation where the source consists of dipoles and quadrupoles. This source model is significant in the magnetoencephalography inverse problem. The proposed method identifies the source parameters directly and algebraically using data without requiring an initial parameter estimate or iterative computation of the forward solution. The obtained parameters could be used for the initial solution in an optimization-based algorithm for further refinement.
Impact of Orthodontic Brackets on the Intraoral Scan Data Accuracy
Park, Ji-Man; Choi, Shin-Ae; Myung, Ji-Yun; Chun, Youn-Sic
2016-01-01
This study aims to compare the impact of buccal and lingual brackets on the accuracy of dental arch data acquired by 4 different digital intraoral scanners. Two pairs of dental casts, one with buccal brackets and the other with lingual brackets, were used. Digital measurements of the 3D images were compared to the actual measurements of the dental models, which were considered standard values. The horizontal measurements included intercanine widths and intermolar widths. The Mann–Whitney U test was performed for comparisons. iTero® and Trios® both showed high accuracy with relatively small maximum deviation of measurements. iTero showed a significantly higher accuracy in most of the arch width measurements on the buccal bracket model than on the lingual model (P scanners should be used more cautiously in arches with lingual brackets than in those with buccal brackets. PMID:27999798
Elements of mathematics algebra
Bourbaki, Nicolas
2003-01-01
This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and...
A comparative assessment of torque generated by lingual and conventional brackets
Sifakakis, I.; Pandis, N.; Makou, M.; Eliades, T.; Katsaros, C.; Bourauel, C.
2013-01-01
The aim of this study was to assess the effect of bracket type on the labiopalatal moments generated by lingual and conventional brackets. Incognito lingual brackets (3M Unitek), STb lingual brackets (Light Lingual System; ORMCO), In-Ovation L lingual brackets (DENTSPLY GAC), and conventional 0.018
Experimental study of some mounting brackets to support fuel elements
International Nuclear Information System (INIS)
Aubert, M.; Poglia, S.; Roche, R.
1958-09-01
In an atomic pile with vertical channels, fuel elements are stacked on one another. According to a possible assembly, fuel element can be contained by a graphite sleeve and be supported by a mounting bracket in this sleeve. Sleeves are then stacked on one another. The authors report the investigation of different designs for these mounting brackets. They describe their mechanical role and their mechanical, aerodynamic, neutronic and test conditions. They report tests performed on brackets made in graphite and on brackets made in stainless steel and graphite, and discuss the obtained results
Cluster algebras bases on vertex operator algebras
Czech Academy of Sciences Publication Activity Database
Zuevsky, Alexander
2016-01-01
Roč. 30, 28-29 (2016), č. článku 1640030. ISSN 0217-9792 Institutional support: RVO:67985840 Keywords : cluster alegbras * vertex operator algebras * Riemann surfaces Subject RIV: BA - General Mathematics Impact factor: 0.736, year: 2016 http://www.worldscientific.com/doi/abs/10.1142/S0217979216400300
Classical mechanics on noncommutative space with Lie-algebraic structure
International Nuclear Information System (INIS)
Miao Yangang; Wang Xudong; Yu Shaojie
2011-01-01
Highlights: → Suggest a useful method to look for new Lie-algebraic noncommutative spaces. → Find out two new Lie-algebraic noncommutative spaces. → Derive Newton and Hamilton equations that present unimaginable extra forces. → Analyse the source of unimaginable extra forces from space noncummutativity. → Provide various intriguing classical trajectories. - Abstract: We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two new sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle interacting with a constant external force by means of the Hamiltonian formalism on a Poisson manifold. Our results not only include that of a recent work as our special cases, but also provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable tx-dot-,(xx-dot)-, and (xx-double dot)-dependence besides with the usual t-, x-, and x-dot-dependence, originating from a variety of noncommutativity between different spatial coordinates and between spatial coordinates and momenta as well, deform greatly the particle's ordinary trajectories we are quite familiar with on the Euclidean (commutative) space.
Directory of Open Access Journals (Sweden)
Balajee Jayachandran
2016-01-01
Full Text Available Aims and Objectives: This clinical study was conducted to compare the interactive self-ligating twin brackets and the standard double width brackets for their efficiency in Rate of Retraction. Materials and Methods: A total of 20 patients with Angle's class I or class II or class III dento-alveolar malocclusions between the age group of 18-25 years were selected. 10 patients in each group both males and females were randomly selected for the study. Ten patients were bonded using conventional brackets (Group I the other ten patients were bonded using Interactive self-ligating brackets (Group II. The Rate of retraction was quantified using the scanned models. Pretreatment and post treatment models were taken and scanned to measure the amount of Incisor movement and Anchor loss. Results: (1 Interactive Self-ligating brackets showed significant Rate of retraction when compared with conventional brackets on right and left quadrant. (Group I 0.545 ± .205: Group II 0.827 ± .208 P= .013* (Group I 0.598 ± .160: Group II 0.804 ± .268 P= .071 (2 Interactive self-ligating brackets when compared with conventional brackets had significant amount of incisor movement on right and left quadrant. (Group I 3.51 ± .548: Group II 4.38 ± .1.06 P= .047* and (Group I 3.66 ± .899: Group II 4.67 ± 1.02 P= .047* (3 Conventional brackets showed significant Amount of Anchor loss when compared with that of Interactive self-ligating brackets on right and left quadrant. (Group I .948 ± .392: Group II 0.501 ± .229 P= .013*. In the left side (Group I 0.861 ± .464: Group II 0.498 ± .227 P= .060. Conclusion: The interactive self-ligating brackets show more efficiency in Rate of Retraction, Amount of Incisor movement and Amount of Anchor loss when compared with the conventional brackets.
Cacciafesta, Vittorio; Sfondrini, Maria Francesca; Ricciardi, Andrea; Scribante, Andrea; Klersy, Catherine; Auricchio, Ferdinando
2003-10-01
This study measured and compared the level of frictional resistance generated between stainless steel self-ligating brackets (Damon SL II, SDS Ormco, Glendora, Calif), polycarbonate self-ligating brackets (Oyster, Gestenco International, Göthenburg, Sweden), and conventional stainless steel brackets (Victory Series, 3M Unitek, Monrovia, Calif), and 3 different orthodontic wire alloys: stainless steel (Stainless Steel, SDS Ormco), nickel-titanium (Ni-Ti, SDS Ormco), and beta-titanium (TMA, SDS Ormco). All brackets had a.022-in slot, whereas the orthodontic wire alloys were tested in 3 different sections:.016,.017 x.025, and.019 x 0.025 in. Each of the 27 bracket and archwire combinations was tested 10 times, and each test was performed with a new bracket-wire sample. Both static and kinetic friction were measured on a custom-designed apparatus. All data were statistically analyzed (Kruskal-Wallis and Mann Whitney U tests). Stainless steel self-ligating brackets generated significantly lower static and kinetic frictional forces than both conventional stainless steel and polycarbonate self-ligating brackets, which showed no significant differences between them. Beta-titanium archwires had higher frictional resistances than stainless steel and nickel-titanium archwires. No significant differences were found between stainless steel and nickel-titanium archwires. All brackets showed higher static and kinetic frictional forces as the wire size increased.
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D......_E of C*(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show...
Schneider, Hans
1989-01-01
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t
Chatterjee, D
2007-01-01
About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the
Orthogonal symmetries and Clifford algebras
Indian Academy of Sciences (India)
algebra over a field K, can be regarded as the Clifford algebra of a suitable nondegenerate quadratic form q over the base field K. In [13], such a form q is also explicitly constructed. The Grassmann algebra (or the exterior algebra) may also be regarded as the Clifford alge- bra of the null (totally isotropic) quadratic form.
Coreflections in Algebraic Quantum Logic
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.
Evaluation of frictional forces of polycarbonate self-ligating brackets.
Fernandes, Daniel J; Miguel, José Augusto M; Quintão, Catia C A; Elias, Carlos N
2010-01-01
To evaluate the frictional forces generated by ceramic- (Opal, Ultradent) and glass-fiber-reinforced polycarbonate self-ligating brackets (Oyster, Gestenco) and compare the effectiveness of these ligatureless systems with glass-fiber-reinforced polycarbonate conventional brackets (Blonde, Gestenco). The hypothesis is that there is no difference between frictional forces generated by ceramic- and glass-fiber-reinforced polycarbonate self-ligating and glass-fiber-reinforced polycarbonate conventional brackets. Twelve preadjusted 0.022 3 0.028-inch maxillary canine brackets were tested, divided into three groups: Opal, Oyster, and Blonde. Frictional tests were conducted with the Emic DL 10000 testing machine with a 20 N loadcell for 40 seconds at a 0.5 cm/min speed. Each bracket-wire combination was tested five times. The data generated were analyzed by parametric analysis of variance (one-way ANOVA) and Bonferroni tests. Analysis of variance indicated significant differences for the three groups (Pfrictional forces of the Oyster glass-fiber-reinforced polycarbonate self-ligating brackets were significantly lower (37.0 ± 8.9 cN) than those of the Opal ceramic-reinforced polycarbonate self-ligating brackets (49.5 ± 10.1 cN), while the Blonde glass-fiber-reinforced conventional bracket frictional forces were 105.8 ± 6.4 cN. Oyster glass-fiber-reinforced polycarbonate brackets produced less friction than Opal ceramic-reinforced polycarbonate brackets. The polycarbonate ligatureless system showed significantly lower frictional forces compared to Blonde conventional polycarbonate brackets tied with elastomeric ligatures. The study rejected the initial hypothesis because there are significant differences of frictional forces among the tested systems. © 2010 BY QUINTESSENCE PUBLISHING CO, INC.
Bonding brackets to porcelain: in vitro study
Directory of Open Access Journals (Sweden)
Sant'Anna Eduardo Franzotti
2002-01-01
Full Text Available The aim of this research was to verify, in vitro, the effect of various porcelain surface treatments on the shear strength of orthodontic brackets bonded to porcelain and the mode of fracture after debonding. Eighty-eight samples of metallic supported feldspathic porcelain were randomly divided into four groups according to their surface preparation as follows: the porcelain was maintained intact (GI, roughened with a diamond bur (GII, etched with 10% hydrofluoric acid (GIII, or sandblasted with aluminum oxide (GIV. The specimens were treated with silane (Scothprime and brackets were bonded with Concise. Each sample was subjected to a shear load at a crosshead speed of 1 mm/min and a recording was made at the point of failure. Bond strengths, adequate to withstand the application of orthodontic forces, were achieved in all groups. The Kruskal-Wallis statistical test showed no significant differences in bond strength between the groups (p>0.05. However, many more porcelain fractures occurred on deglazed porcelain. This study indicates that with the appropriate material selection, the silane/composite procedure alone may be adequate for bonding.
Axler, Sheldon
2015-01-01
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...
Özen, Kahraman Esen; Tosun, Murat
2018-01-01
In this study, we define the elliptic biquaternions and construct the algebra of elliptic biquaternions over the elliptic number field. Also we give basic properties of elliptic biquaternions. An elliptic biquaternion is in the form A0 + A1i + A2j + A3k which is a linear combination of {1, i, j, k} where the four components A0, A1, A2 and A3 are elliptic numbers. Here, 1, i, j, k are the quaternion basis of the elliptic biquaternion algebra and satisfy the same multiplication rules which are satisfied in both real quaternion algebra and complex quaternion algebra. In addition, we discuss the terms; conjugate, inner product, semi-norm, modulus and inverse for elliptic biquaternions.
Algebraic Semantics for Narrative
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)
Comparative Analysis of Bracket Slot Dimensions Evaluating Different Manufacturing Techniques
2015-04-24
images to ensure that brackets were not tilted. The images were calibrated and processed using Zen Pro 2011 commercial software (Carl Zeiss...Orthodontics. 5th ed. St. Louis: El Sevier Mosby; 2013: 369-370. 22. Reimann S et al. Material Testing of Reconditioned Orthodontic Brackets
Laser Guided Automated Calibrating System for Accurate Bracket ...
African Journals Online (AJOL)
appliance. When bands were used originally, Angle[1] thought the best position to place the bracket was at the center of the tooth. Later Ricketts[2] used ... In orthodontic literature, the advantages and disadvantages of ... Keywords: Hough transforms, Indirect bonding technique, Laser, Orthodontic bracket placement.
Laser guided automated calibrating system for accurate bracket ...
African Journals Online (AJOL)
It is widely recognized that accurate bracket placement is of critical importance in the efficient application of biomechanics and in realizing the full potential of a preadjusted edgewise appliance. Aim: The purpose of ... placement. Keywords: Hough transforms, Indirect bonding technique, Laser, Orthodontic bracket placement ...
3D-printed orthodontic brackets - proof of concept.
Krey, Karl-Friedrich; Darkazanly, Nawras; Kühnert, Rolf; Ruge, Sebastian
Today, orthodontic treatment with fixed appliances is usually carried out using preprogrammed straight-wire brackets made of metal or ceramics. The goal of this study was to determine the possibility of clinically implementing a fully digital workflow with individually designed and three-dimensionally printed (3D-printed) brackets. Edgewise brackets were designed using computer-aided design (CAD) software for demonstration purposes. After segmentation of the malocclusion model generated based on intraoral scan data, the brackets were digitally positioned on the teeth and a target occlusion model created. The thus-defined tooth position was used to generate a template for an individualized arch form in the horizontal plane. The base contours of the brackets were modified to match the shape of the tooth surfaces, and a positioning guide (fabricated beforehand) was used to ensure that the brackets were bonded at the correct angle and position. The brackets, positioning guide, and retainer splint, digitally designed on the target occlusion model, were 3D printed using a Digital Light Processing (DLP) 3D printer. The archwires were individually pre-bent using the template. In the treatment sequence, it was shown for the first time that, in principle, it is possible to perform treatment with an individualized 3D-printed brackets system by using the proposed fully digital workflow. Technical aspects of the system, problems encountered in treatment, and possible future developments are discussed in this article.
Parasites et parasitoses des poissons
De Kinkelin, Pierre; Morand, Marc; Hedrick, Ronald; Michel, Christian
2014-01-01
Cet ouvrage, richement illustré, offre un panorama représentatif des agents parasitaires rencontrés chez les poissons. S'appuyant sur les nouvelles conceptions de la classification phylogénétique, il met l'accent sur les propriétés biologiques, l'épidémiologie et les conséquences cliniques des groupes d'organismes en cause, à la lumière des avancées cognitives permises par les nouveaux outils de la biologie. Il est destiné à un large public, allant du monde de l'aquaculture à ceux de la santé...
Dualizing the Poisson summation formula.
Duffin, R J; Weinberger, H F
1991-01-01
If f(x) and g(x) are a Fourier cosine transform pair, then the Poisson summation formula can be written as 2sumfrominfinityn = 1g(n) + g(0) = 2sumfrominfinityn = 1f(n) + f(0). The concepts of linear transformation theory lead to the following dual of this classical relation. Let phi(x) and gamma(x) = phi(1/x)/x have absolutely convergent integrals over the positive real line. Let F(x) = sumfrominfinityn = 1phi(n/x)/x - integralinfinity0phi(t)dt and G(x) = sumfrominfinityn = 1gamma (n/x)/x - integralinfinity0 gamma(t)dt. Then F(x) and G(x) are a Fourier cosine transform pair. We term F(x) the "discrepancy" of phi because it is the error in estimating the integral phi of by its Riemann sum with the constant mesh spacing 1/x. PMID:11607208
Deficiently extremal Gorenstein algebras
Indian Academy of Sciences (India)
Thus, R/I is a Cohen–. Macaulay algebra of Type 1, and hence R/I is Gorenstein. In view of Theorem 2.1, R/I is a nearly (or 1-deficient) extremal Gorenstein algebra. We now shall describe a result of Bruns and Hibi [1] which characterizes the Stanley–. Reisner rings having 2-pure but not 2-linear resolutions. Theorem 2.3.
Intermediate algebra a textworkbook
McKeague, Charles P
1985-01-01
Intermediate Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in intermediate algebra. The publication first takes a look at basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on properties of exponents, polynomials, sums, and differences, multiplication of polynomials, inequalities involving absolute value, word problems, first-degree inequalities, real numbers, opposites, reciprocals, and absolute value, and addition and subtraction of real numbers. The text then ex
Beginning algebra a textworkbook
McKeague, Charles P
1985-01-01
Beginning Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in algebra. The publication first elaborates on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on solving linear systems by graphing, elimination method, graphing ordered pairs and straight lines, linear and compound inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then examines exponents and polynomials, factoring, and rational expressions. Topics include multiplication and division
International Nuclear Information System (INIS)
Waldron, A.K.; Joshi, G.C.
1992-01-01
By considering representation theory for non-associative algebras the fundamental adjoint representations of the octonion algebra is constructed. It is then shown how these representations by associative matrices allow a consistent octonionic gauge theory to be realized. It was found that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian. 13 refs
Currents on Grassmann algebras
International Nuclear Information System (INIS)
Coquereaux, R.; Ragoucy, E.
1993-09-01
Currents are defined on a Grassmann algebra Gr(N) with N generators as distributions on its exterior algebra (using the symmetric wedge product). The currents are interpreted in terms of Z 2 -graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on Gr(N)). An explicit construction of the vector space of closed currents of degree p on Gr(N) is given by using Berezin integration. (authors). 10 refs
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
The 'golden' algebraic equations
International Nuclear Information System (INIS)
Stakhov, A.; Rozin, B.
2006-01-01
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman
The Boolean algebra of Galois algebras
Directory of Open Access Journals (Sweden)
Lianyong Xue
2003-02-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={bÃ¢ÂˆÂˆB|bx=g(xbÃ¢Â€Â‰for allÃ¢Â€Â‰xÃ¢ÂˆÂˆB} for each gÃ¢ÂˆÂˆG, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|gÃ¢ÂˆÂˆG}, e a nonzero element in Ba, and He={gÃ¢ÂˆÂˆG|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.
Real division algebras and other algebras motivated by physics
Energy Technology Data Exchange (ETDEWEB)
Benkart, G.; Osborn, J.M.
1981-02-01
In this survey we discuss several general techniques which have been productive in the study of real division algebras, flexible Lie-admissible algebras, and other nonassociative algebras, and we summarize results obtained using these methods. The principal method involved in this work is to view an algebra A as a module for a semisimple Lie algebra of derivations of A and to use representation theory to study products in A. In the case of real division algebras, we also discuss the use of isotopy and the use of a generalized Peirce decomposition. Most of the work summarized here has appeared in more detail in various other papers. The exceptions are results on a class of algebras of dimension 15, motivated by physics, which admit the Lie algebra sl(3) as an algebra of derivations.
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
Directory of Open Access Journals (Sweden)
Andrzej Borowiec
2010-10-01
Full Text Available Some classes of Deformed Special Relativity (DSR theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version Quantum Mechanics. On this basis we review some recent results concerning twist realization of κ-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum κ-Poincaré and κ-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called ''q-analog'' version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.
Hecke algebras with unequal parameters
Lusztig, G
2003-01-01
Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives rese...
Algebra II workbook for dummies
Sterling, Mary Jane
2014-01-01
To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebr
Davidson, Kenneth R
1996-01-01
The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of K-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty yea
A Seemingly Unrelated Poisson Regression Model
King, Gary
1989-01-01
This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.
Color stability of ceramic brackets immersed in potentially staining solutions
Directory of Open Access Journals (Sweden)
Bruna Coser Guignone
2015-08-01
Full Text Available OBJECTIVE: To assess the color stability of five types of ceramic brackets after immersion in potentially staining solutions.METHODS: Ninety brackets were divided into 5 groups (n = 18 according to brackets commercial brands and the solutions in which they were immersed (coffee, red wine, coke and artificial saliva. The brackets assessed were Transcend (3M/Unitek, Monrovia, CA, USA, Radiance (American Orthodontics, Sheboygan, WI, USA, Mystique (GAC International Inc., Bohemia, NY, USA and Luxi II (Rocky Mountain Orthodontics, Denver, CO, USA. Chromatic changes were analyzed with the aid of a reflectance spectrophotometer and by visual inspection at five specific time intervals. Assessment periods were as received from the manufacturer (T0, 24 hours (T1, 72 hours (T2, as well as 7 days (T3 and 14 days (T4 of immersion in the aforementioned solutions. Results were submitted to statistical analysis with ANOVA and Bonferroni correction, as well as to a multivariate profile analysis for independent and paired samples with significance level set at 5%.RESULTS: The duration of the immersion period influenced color alteration of all tested brackets, even though these changes could not always be visually observed. Different behaviors were observed for each immersion solution; however, brackets immersed in one solution progressed similarly despite minor variations.CONCLUSIONS: Staining became more intense over time and all brackets underwent color alterations when immersed in the aforementioned solutions.
Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra
Pitsch, Wolfgang; Zarzuela, Santiago
2016-01-01
This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest dev...
Quantum cluster algebra structures on quantum nilpotent algebras
Goodearl, K R
2017-01-01
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.
Reproducibility of bracket positioning in the indirect bonding technique.
Nichols, Dale A; Gardner, Gary; Carballeyra, Alain D
2013-11-01
Current studies have compared indirect bonding with direct placement of orthodontic brackets; many of these have shown that indirect bonding is generally a more accurate technique. However, the reproducibility of an indirect bonding setup by an orthodontist has yet to be described in the literature. Using cone-beam computed tomography and computer-assisted modeling software, we evaluated the consistency of orthodontists in placing orthodontic brackets at different times. Five orthodontists with experience in indirect bonding were selected to place brackets on 10 different casts at 3 time periods (n = 30 per orthodontist). Each participant completed an initial indirect bonding setup on each cast; subsequent bracket placements were completed twice at monthly intervals for comparison with the initial setup. The casts were scanned using an iCAT cone-beam computed tomography scanner (Imaging Sciences International, Hatfield, Pa) and imported into Geomagic Studio software (Geomagic, Research Triangle Park, NC) for superimposition and analysis. The scans for each time period were superimposed on the initial setup in the imaging software, and differences between bracket positions were calculated. For each superimposition, the measurements recorded were the greatest discrepancies between individual brackets as well as the mean discrepancies and standard deviations between all brackets on each cast. Single-factor and repeated-measure analysis of variance showed no statistically significant differences between time points of each orthodontist, or among the orthodontists for the parameters measured. The mean discrepancy was 0.1 mm for each 10-bracket indirect bonding setup. Orthodontists are consistent in selecting bracket positions for an indirect bonding setup at various time periods. Copyright © 2013 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.
Deo, Satya
2018-01-01
This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...
Algebraic quantum field theory
International Nuclear Information System (INIS)
Foroutan, A.
1996-12-01
The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)
Jarvis, Frazer
2014-01-01
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Blyth, T S
2002-01-01
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...
Bloch, Spencer J
2000-01-01
This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.
Wadsworth, A R
2017-01-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Peternell, Thomas; Schneider, Michael; Schreyer, Frank-Olaf
1992-01-01
The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibra...
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
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…
On Associative Conformal Algebras of Linear Growth
Retakh, Alexander
2000-01-01
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We introduce the notions of conformal identity and unital associative conformal algebras and classify finitely generated simple unital associative conformal algebras of linear growth. These are precisely the complete algebras of conformal endomorphisms of finite ...
Computer Program For Linear Algebra
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.
Atomistic and orthoatomistic effect algebras
Tkadlec, Josef
2008-05-01
We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.
Algebra for Gifted Third Graders.
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
Contractions of quantum algebraic structures
International Nuclear Information System (INIS)
Doikou, A.; Sfetsos, K.
2010-01-01
A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Hohn, Franz E
2012-01-01
This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur
Algebra & trigonometry super review
2012-01-01
Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Algebra and Trigonometry Super Review includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much y
Principles of algebraic geometry
Griffiths, Phillip A
1994-01-01
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top
Artin, Emil
2007-01-01
The present text was first published in 1947 by the Courant Institute of Mathematical Sciences of New York University. Published under the title Modern Higher Algebra. Galois Theory, it was based on lectures by Emil Artin and written by Albert A. Blank. This volume became one of the most popular in the series of lecture notes published by Courant. Many instructors used the book as a textbook, and it was popular among students as a supplementary text as well as a primary textbook. Because of its popularity, Courant has republished the volume under the new title Algebra with Galois Theory.
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2010-01-01
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Pseudo Algebraically Closed Extensions
Bary-Soroker, Lior
2009-07-01
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
Hogben, Leslie
2013-01-01
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of
Algebraic curves and cryptography
Murty, V Kumar
2010-01-01
It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \\ell-adic point counting algorithm, the p-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on
Partially ordered algebraic systems
Fuchs, Laszlo
2011-01-01
Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Algebra & trigonometry I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Algebra & Trigonometry I includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, eq
Linear Algebra Thoroughly Explained
Vujičić, Milan
2008-01-01
Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.
Directory of Open Access Journals (Sweden)
Ajith R Pillai
2014-01-01
Full Text Available Background and Objectives: The purpose of this study is to evaluate the frictional resistance generated by conventional stainless steel, radiance ceramic bracket, self-ligating and composite brackets using a 0.019 × 0.025 stainless steel straight length wires in a 022 slot and to select brackets based on their frictional characteristic. Methodology: In order to conduct this study, four different types of bracket system were selected of the mclaughlin-bennet-trevesi (MBT discipline. They are Group 1 - stainless steel, Group 2 - composite bracket Group 3 - (American Orthodontics radiance ceramic bracket Group 4 - self-ligating bracket (SLB (Empower. In this study, five maxillary brackets of an arch of each type were used. All brackets are 0.022 × 0.028" in preadjusted edgewise appliance which simulates the dental arch. Five brackets were bonded to a stainless steel bar of dimension 150 mm × 25 mm × 3 mm. The bracket-arch wire units were submitted to mechanical test with an Instron universal testing machine 3365. A testing apparatus or holding jig was designed to hold the bracket during the mechanical test. Each sample was pulled at a speed of 6 mm for 1 min. Descriptive statistical information including mean and standard deviation of maximum friction force was calculated for each bracket wire combination. Interpretation and Conclusion: The SLB has the least friction among the four groups. The ceramic bracket showed the highest friction followed by stainless steel bracket, composite bracket, and SLB.
A comparative assessment of forces and moments generated by lingual and conventional brackets
Sifakakis, I.; Pandis, N.; Makou, M.; Katsaros, C.; Eliades, T.; Bourauel, C.
2013-01-01
The aim of this study was to assess the effect of bracket type on the labiopalatal forces and moments generated in the sagittal plane. Incognito lingual brackets (3M Unitek), STb lingual brackets (Light Lingual System; ORMCO), and conventional 0.018 inch slot brackets (Gemini; 3M Unitek) were bonded
Homomorphisms between C∗ -algebra extensions
Indian Academy of Sciences (India)
C∗. -algebra extensions, Ext groups do not classify extension algebras. So one has to study the isomorphism equivalence of extensions. In fact, a homomorphism between two extension algebras may not map the essential ideal into the other in general, so we have to consider properties of extension homomorphisms.
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Assessing Elementary Algebra with STACK
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…
M5-brane as a Nambu-Poisson geometry of a multi-D1-brane theory
International Nuclear Information System (INIS)
De Castro, A.; Garcia del Moral, M.P.; Martin, I.; Restuccia, A.
2004-01-01
We introduce a Nambu-Poisson bracket in the geometrical description of the D=11 M5-brane. This procedure allows us, under some assumptions, to eliminate the local degrees of freedom of the antisymmetric field in the M5-brane Hamiltonian and to express it as a D=11 p-brane theory invariant under symplectomorphisms. The explicit expression of the Hamiltonian is obtained. The existence of nontrivial physical configurations annihilating the energy density is shown. Finally, a regularization of the M5-brane in terms of a multi D1-brane theory invariant under the SU(N)xSU(N) group in the limit when N→∞ is constructed
On the optimality of double-bracket flows
Directory of Open Access Journals (Sweden)
Anthony M. Bloch
2004-01-01
Full Text Available We analyze the optimality of the stable fixed point of the double-bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schatten p-norms.
Time-dependent constrained Hamiltonian systems and Dirac brackets
Energy Technology Data Exchange (ETDEWEB)
Leon, Manuel de [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Madrid (Spain); Marrero, Juan C. [Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands (Spain); Martin de Diego, David [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, Madrid (Spain)
1996-11-07
In this paper the canonical Dirac formalism for time-dependent constrained Hamiltonian systems is globalized. A time-dependent Dirac bracket which reduces to the usual one for time-independent systems is introduced. (author)
Bond strengths evaluation of laser ceramic bracket debonding
Dostalová, T.; Jelinková, H.; Šulc, J.; Němec, M.; Fibrich, M.; Jelínek, M.; Michalík, P.; Bučková, M.
2012-09-01
Ceramic brackets often used for an orthodontic treatment can lead to problems such as enamel tear outs because of their low fracture resistance and high bond strengths. Therefore the aim of our study was to investigate the positive laser radiation effect on bracket debonding. Moreover, the influence of the enamel shape surface under the bracket and laser radiation power on the debonding strength was investigated. The source of the radiation was the longitudinally diode-pumped Tm:YAP laser operating at 1997 nm. To eliminate the tooth surface roughness the flat enamel surface was prepared artificially and the bracket was bonded on it. The debonding was accomplished by Tm:YAP laser radiation with different the power value while recording the temperature rise in the pulp. To simulate the debonding process in vivo the actual bond strength was measured by the digital force gauge. The results were analyzed by scanning electron microscope.
Lyapunov stability and Poisson structure of the thermal TDHF and RPA equations
International Nuclear Information System (INIS)
Veneroni, M.; Balian, R.
1989-01-01
The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p.) density ρ behave as classical dynamical variables. By introducing the Lie-Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered
Corrosion behavior of self-ligating and conventional metal brackets
Directory of Open Access Journals (Sweden)
Lúcio Henrique Esmeraldo Gurgel Maia
2014-04-01
Full Text Available Objective: To test the null hypothesis that the aging process in self-ligating brackets is not higher than in conventional brackets. Methods: Twenty-five conventional (GN-3M/Unitek; GE-GAC; VE-Aditek and 25 self-ligating (SCs-3M/Unitek; INs-GAC; ECs-Aditek metal brackets from three manufacturers (n = 150 were submitted to aging process in 0.9% NaCl solution at a constant temperature of 37 ± 1ºC for 21 days. The content of nickel, chromium and iron ions in the solution collected at intervals of 7, 14 and 21 days was quantified by atomic absorption spectrophotometry. After the aging process, the brackets were analyzed by scanning electron microscopy (SEM under 22X and 1,000X magnifications. Results: Comparison of metal release in self-ligating and conventional brackets from the same manufacturer proved that the SCs group released more nickel (p < 0.05 than the GN group after 7 and 14 days, but less chromium (p < 0.05 after 14 days and less iron (p < 0.05 at the three experimental time intervals. The INs group released less iron (p < 0.05 than the GE group after 7 days and less nickel, chromium and iron (p < 0.05 after 14 and 21 days. The ECs group released more nickel, chromium and iron (p < 0.05 than the VE group after 14 days, but released less nickel and chromium (p < 0.05 after 7 days and less chromium and iron (p < 0.05 after 21 days. The SEM analysis revealed alterations on surface topography of conventional and self-ligating brackets. Conclusions: The aging process in self-ligating brackets was not greater than in conventional brackets from the same manufacturer. The null hypothesis was accepted.
Clinical evaluation of the failure rates of metallic brackets
Directory of Open Access Journals (Sweden)
Fábio Lourenço Romano
2012-04-01
Full Text Available OBJECTIVES: The aim of this study was to evaluate in vivo the bonding of metallic orthodontic brackets with different adhesive systems. MATERIAL AND METHODS: Twenty patients (10.5-15.1 years old who had sought corrective orthodontic treatment at a University Orthodontic Clinic were evaluated. Brackets were bonded from the right second premolar to the left second premolar in the upper and lower arches using: Orthodontic Concise, conventional Transbond XT, Transbond XT without primer, and Transbond XT associated with Transbond Plus Self-etching Primer (TPSEP. The 4 adhesive systems were used in all patients using a split-mouth design; each adhesive system was used in one quadrant of each dental arch, so that each group of 5 patients received the same bonding sequence. Initial archwires were inserted 1 week after bracket bonding. The number of bracket failures for each adhesive system was quantified over a 6-month period. RESULTS: The number of debonded brackets was: 8- Orthodontic Concise, 2- conventional Transbond XT, 9- Transbond XT without primer, and 1- Transbond XT + TPSEP. By using the Kaplan-Meier methods, statistically significant differences were found between the materials (p=0.0198, and the Logrank test identified these differences. Conventional Transbond XT and Transbond XT + TPSEP adhesive systems were statistically superior to Orthodontic Concise and Transbond XT without primer (p<0.05. There was no statistically significant difference between the dental arches (upper and lower, between the dental arch sides (right and left, and among the quadrants. CONCLUSIONS: The largest number of bracket failures occurred with Orthodontic Concise and Transbond XT without primer systems and few bracket failures occurred with conventional Transbond XT and Transbond XT+TPSEP. More bracket failures were observed in the posterior region compared with the anterior region.
A comparative study in three methods of bracket placement
Kanako, FUKUYO; Yasushi, NISHII; Kunihiko, NOJIMA; Hideharu, YAMAGUCHI; Imai Orthodontic Clinic; Department of Orthodontics, Tokyo Dental College; Department of Orthodontics, Tokyo Dental College; Department of Orthodontics, Tokyo Dental College
2004-01-01
Results of orthodontic treatment with the straight-wire appliances largely depend on bracket positioning. Forty subjects with individual normal occlusion (20 males, 20 females, mean age 23 years) were selected from Tokyo Dental College student. Their orthodontic diagnostic models were digitized with a laser scanner. Three bracket placement methods were compared : the FA Method, which bisects the clinical crown into the gingival and occlusal portions, the Height Method, which measures from the...
In vitro tooth cleaning efficacy of electric toothbrushes around brackets
Schätzle, M.; Sener, B.; Schmidlin, P R.; Imfeld, T.; Attin, T.
2017-01-01
This in vitro study assessed the cleaning efficacy of different electric toothbrushes around upper incisor brackets. Standard and Mini Diamond™ brackets were fixed on black-stained teeth. The teeth were coated with white titanium oxide and brushed in a machine twice for 1 minute each. Twelve different brush heads with either a wiping or an oscillating-rotating action were tested. After brushing, the teeth were scanned, the black surfaces were assessed planimetrically and a modified plaque ind...
Commutative algebra with a view toward algebraic geometry
Eisenbud, David
1995-01-01
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...
Quantitative Algebraic Reasoning
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon
2016-01-01
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We deﬁne an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...
Fan, Yun; Zheng, Y L
2000-01-01
This volume is based on the lectures given by the authors at Wuhan University and Hubei University in courses on abstract algebra. It presents the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them and other mathematical branches and applied aspects.
Indian Academy of Sciences (India)
from India, I will describe mainly some work in four topics with which I am familiar: Moduli problem of vector bundles (and the related geometric invariant theory), the work of. CPRamanujam, Frobenius split varieties and algebraic .... One important series of works, by Seshadri in collaboration with V Lakshmibai, C Musili, and.
Indian Academy of Sciences (India)
To the Indian reader, the word discourse, evokes a respected figure interpreting divine wisdom to common folk in an accessible fash- ion. I dug a bit deeper with Google trans- late, and found that the original Russian ti- tle of Shafarevich's book was more like Se- lected Chapters of Algebra and that it was first published in a ...
Bergstra, J.A.; Middelburg, C.A.
2015-01-01
We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution
Gudder, Stan
2004-08-01
We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J( a) ≤ a for all a ɛ E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.
Thinking Visually about Algebra
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,…
Algebraic Thinking through Origami.
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
Pasha, Azam; Vishwakarma, Swati; Narayan, Anjali; Vinay, K; Shetty, Smitha V; Roy, Partha Pratim
2015-09-01
Fixed orthodontic mechanotherapy is associated with friction between the bracket - wire - ligature interfaces during the sliding mechanics. A sound knowledge of the various factors affecting the magnitude of friction is of paramount importance. The present study was done to analyze and compare the frictional forces generated by a new ceramic (Clarity Advanced) bracket with the conventional, (metal and ceramic) brackets using unconventional and conventional ligation system, and the self-ligating (metal and ceramic) brackets in the dry condition. The various bracket wire ligation combinations were tested in dry condition. The brackets used were of 0.022″ × 0.028″ nominal slot dimension of MBT prescription: Stainless steel (SS) self-ligating bracket (SLB) of (SmartClip), SS Conventional bracket (CB) (Victory series), Ceramic SLB (Clarity SL), Conventional Ceramic bracket with metal slot (Clarity Bracket), Clarity Advanced Ceramic Brackets (Clarity(™) ADVANCED, 3M Unitek). These brackets were used with two types of elastomeric ligatures: Conventional Elastomeric Ligatures (CEL) (Clear medium mini modules) and Unconventional Elastomeric Ligatures (UEL) (Clear medium slide ligatures, Leone orthodontic products). The aligning and the retraction wires were used, i.e., 0.014″ nickel titanium (NiTi) wires and 0.019″ × 0.025″ SS wires, respectively. A universal strength testing machine was used to measure the friction produced between the different bracket, archwires, and ligation combination. This was done with the use of a custom-made jig being in position. Mean, standard deviation, and range were computed for the frictional values obtained. Results were subjected to statistical analysis through ANOVA. The frictional resistance observed in the new Clarity Advanced bracket with a conventional elastomeric ligature was almost similar with the Clarity metal slot bracket with a conventional elastomeric ligature. When using the UEL, the Clarity Advanced bracket
Operator algebras and topology
International Nuclear Information System (INIS)
Schick, T.
2002-01-01
These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)
Advanced modern algebra part 2
Rotman, Joseph J
2017-01-01
This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
The Poisson equation on Klein surfaces
Directory of Open Access Journals (Sweden)
Monica Rosiu
2016-04-01
Full Text Available We obtain a formula for the solution of the Poisson equation with Dirichlet boundary condition on a region of a Klein surface. This formula reveals the symmetric character of the solution.
Poisson point processes imaging, tracking, and sensing
Streit, Roy L
2010-01-01
This overview of non-homogeneous and multidimensional Poisson point processes and their applications features mathematical tools and applications from emission- and transmission-computed tomography to multiple target tracking and distributed sensor detection.
Energy Technology Data Exchange (ETDEWEB)
Clark, Michael A. [Harvard; Joo, Balint [JLAB; Kennedy, Anthony D. [Edinburgh; Silva, Paolo J. [Coimbra
2011-10-01
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian H but conserve exactly a nearby shadow Hamiltonian H~. This property allows for a new tuning method of the molecular dynamics integrator and also allows for a new class of integrators (force-gradient integrators) which is expected to reduce significantly the computational cost of future large-scale gauge field ensemble generation.
Kusy, R P; Whitley, J Q
2001-10-01
The frictional resistances of 2 metal-lined ceramic brackets (Luxi and Clarity) were compared with 2 conventional stainless steel brackets (Mini-Taurus and Mini-Twin) in vitro. In method 1, we varied the second-order angulation from 0 degrees to 12 degrees while maintaining the normal or ligature force constant at 0.3 kg; in method 2, we varied the ligature force from 0.1 kg to 0.9 kg while maintaining the angulation at theta = 0 degrees or theta = 11 degrees. The hardware simulated a 3-bracket system in which the interbracket distances were always 18 mm. All couples were evaluated at 34 degrees C using the same size stainless steel archwire (19 x 26 mil) and ligature wire (10 mil). In the passive region, the static and kinetic frictional forces and coefficients of friction were key parameters; in the active region, the static and kinetic binding forces and coefficients of binding were critical parameters. From outcomes of methods 1 and 2, the 4 aforementioned parameters, and a knowledge of the critical contact angle for binding, 3-dimensional friction maps were constructed in the dry and wet states from which the frictional resistances could be determined at any ligature force or second-order angulation. Those 3-dimensional maps show that metal-lined ceramic brackets can function comparably to conventional stainless steel brackets and that 18-kt gold inserts appear superior to stainless steel inserts. As the morphologies of metal inserts are improved, these metal-lined ceramic brackets will provide not only good esthetics among ceramic brackets but also minimal friction among conventionally ligated brackets.
On Dunkl angular momenta algebra
Energy Technology Data Exchange (ETDEWEB)
Feigin, Misha [School of Mathematics and Statistics, University of Glasgow,15 University Gardens, Glasgow G12 8QW (United Kingdom); Hakobyan, Tigran [Yerevan State University,1 Alex Manoogian, 0025 Yerevan (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)
2015-11-17
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 subalgebra 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.
Free Malcev algebra of rank three
Kornev, Alexandr
2011-01-01
We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated by a simple seven-dimensional Malcev algebra.
In vitro tooth cleaning efficacy of manual toothbrushes around brackets.
Schätzle, Marc; Imfeld, Thomas; Sener, Beatrice; Schmidlin, Patrick R
2009-02-01
The purpose of this laboratory study was to assess the potential cleaning efficacy of nine different toothbrushes around brackets in vitro. Standard and Mini Diamond brackets were fixed on coloured teeth in a special model, coated with white titanium oxide, brushed in a machine with different manual toothbrushes (three different types: planar, staged, and v-shaped bristle field), and tested with a horizontal motion for 1 minute. After brushing, the teeth were scanned and the black surfaces were planimetrically assessed using a grey scale. Tooth areas which were black again after brushing indicated tooth surface contact of the filaments. The remaining white tooth areas around the brackets indicated 'plaque-retentive' niches. Statistical analysis was carried out using the Kruskal-Wallis one-way test of variance for individual comparison. Bonferroni adjustment was used for multiple testing, and comparison of bracket size with Wilcoxon signed rank test. In the most critical area of 2 mm around the brackets, there was no statistically significant difference between the different toothbrushes evaluated. The untouched area ranged from 11 to 26 per cent of the initially whitened tooth surface. By pooling the toothbrushes according to their design, the median cleaning efficacy of the v-shaped (73.1 per cent) and staged (75.6 per cent) toothbrushes resulted in significantly superior cleaning efficacy than planar toothbrushes (60.7 per cent) for standard brackets. For mini bracket type, staged toothbrushes showed a significantly better mean cleaning efficacy (77.8 per cent) than planar (65 per cent) and v-shaped (72.4 per cent) toothbrushes. Staged and v-shaped brush designs resulted in superior cleaning efficacy of teeth with fixed orthodontic attachments than toothbrushes with a planar bristle field. None of the tested toothbrushes showed a consistent, significantly higher cleaning efficacy than the others in this in vitro experiment.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Jacobson-Witt algebras and Lie-admissible algebras
International Nuclear Information System (INIS)
Tomber, M.L.
1981-01-01
For any field PHI of characteristics p > 0 and integer m greater than or equal to 1, there is a Jacobson-Witt algebra which is a Lie algebra. In this paper, all flexible Lie-admissible algebras U, such that U - is a Jacobson-Witt algebra W/sub m/(p), are determined. For any W/sub m/(p), p > 2 there is exactly one such U and it is isomorphic to W/sub m/(p). There are two non-isomorphic algebras U such that U - is isomorphic to W 1 (2), and there are no algebras U with U - isomorphic to W/sub m/(2), m > 1
Ozturk Ortan, Yildiz; Yurdakuloglu Arslan, Tugce; Aydemir, Bulent
2012-02-01
Friction between archwires and labial brackets has received considerable attention; however, information on the frictional behaviour of commercially available lingual brackets is limited. The aim of this study was to investigate the frictional resistance resulting from a combination of lingual orthodontic brackets (7th Generation, STb, Magic, and In-Ovation L) and stainless steel archwires at 0, 5, and 10 degrees of second-order angulation. Each bracket type (n = 30) was tested with three different sizes of archwires. Static and kinetic frictional forces were evaluated with a universal testing machine. Statistical analysis of the data was performed with non-parametric Kruskal-Wallis and Dunn's multiple comparison tests. All tested brackets showed higher frictional forces as the wire size and second-order angulation increased. The lowest friction was found with In-Ovation L brackets and 0.016 inch archwires at 0 degrees angulation, and the greatest friction with a combination of STb brackets and 0.017 × 0.025 inch archwires at 10 degrees angulation. For all combinations, Magic and In-Ovation L brackets showed lower frictional resistance when compared with 7th Generation and STb brackets. The slot width (occluso-gingival dimension) of the brackets, measured using the optics of a microhardness machine, showed that all brackets were oversized and that Magic brackets had the largest slot width. Surface roughness of the brackets investigated using atomic force microscopy and scanning electron microscopy, demonstrated that the 7th Generation brackets had the greatest surface roughness.
Algebras of Information States
Czech Academy of Sciences Publication Activity Database
Punčochář, Vít
2017-01-01
Roč. 27, č. 5 (2017), s. 1643-1675 ISSN 0955-792X R&D Projects: GA ČR(CZ) GC16-07954J Institutional support: RVO:67985955 Keywords : information states * relational semantics * algebraic semantics * intuitionistic logic * inquisitive disjunction Subject RIV: AA - Philosophy ; Religion OBOR OECD: Philosophy, History and Philosophy of science and technology Impact factor: 0.909, year: 2016
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Indian Academy of Sciences (India)
project of the Spanish Ministerio de Educación y Ciencia MTM2007-60333. References. [1] Calderón A J, On split Lie algebras with symmetric root systems, Proc. Indian. Acad. Sci (Math. Sci.) 118(2008) 351–356. [2] Calderón A J, On split Lie triple systems, Proc. Indian. Acad. Sci (Math. Sci.) 119(2009). 165–177.
Fundamentals of linear algebra
Dash, Rajani Ballav
2008-01-01
FUNDAMENTALS OF LINEAR ALGEBRA is a comprehensive Text Book, which can be used by students and teachers of All Indian Universities. The Text has easy, understandable form and covers all topics of UGC Curriculum. There are lots of worked out examples which helps the students in solving the problems without anybody's help. The Problem sets have been designed keeping in view of the questions asked in different examinations.
International Nuclear Information System (INIS)
Todorov, Ivan
2010-12-01
Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [M84] and includes historical notes and biographical data on past participants in the story. (author)
Lutfiyya, Lutfi A
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Modern Algebra includes set theory, operations, relations, basic properties of the integers, group theory, and ring theory.
Algebra & trigonometry II essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Algebra & Trigonometry II includes logarithms, sequences and series, permutations, combinations and probability, vectors, matrices, determinants and systems of equations, mathematica
The Kepler problem in the Snyder space
Indian Academy of Sciences (India)
The deformations were characterized in the Poisson bracket algebra under a mimic procedure from quantum standard formulations by taking into account a general recipe to build the noncommutative phase space coordinates (in the sense of Poisson brackets). An expression for the deformed potential was obtained, and ...
Blyth, T S
2002-01-01
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text. Solutions to the ex...
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
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.
Krňávek, Jan; Kühr, Jan
2011-12-01
Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras.
Prototype to measure bracket debonding force in vivo
Directory of Open Access Journals (Sweden)
Jéssika Lagni Tonus
Full Text Available ABSTRACT Introduction: Material biodegradation that occurs in the mouth may interfere in the bonding strength between the bracket and the enamel, causing lower bond strength values in vivo, in comparison with in vitro studies. Objective: To develop a prototype to measure bracket debonding force in vivo and to evaluate, in vitro, the bond strength obtained with the prototype. Methods: A original plier (3M Unitek was modified by adding one strain gauge directly connected to its claw. An electronic circuit performed the reading of the strain gauge, and the software installed in a computer recorded the values of the bracket debonding force, in kgf. Orthodontic brackets were bonded to the facial surface of 30 bovine incisors with adhesive materials. In Group 1 (n = 15, debonding was carried out with the prototype, while tensile bond strength testing was performed in Group 2 (n = 15. A universal testing machine was used for the second group. The adhesive remnant index (ARI was recorded. Results: According to Student’s t test (α = 0.05, Group 1 (2.96 MPa and Group 2 (3.08 MPa were not significantly different. ARI score of 3 was predominant in the two groups. Conclusion: The prototype proved to be reliable for obtaining in vivo bond strength values for orthodontic brackets.
From current algebras for p-branes to topological M-theory
Energy Technology Data Exchange (ETDEWEB)
Bonelli, Giulio [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy); Zabzine, Maxim [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)
2005-09-01
In this note we generalize a result by Alekseev and Strobl for the case of p-branes. We show that there is a relation between anomalous free current algebras and 'isotropic' involutive subbundles of T and {sup p}T* with the Vinogradov bracket, that is a generalization of the Courant bracket. As an application of this construction we go through some interesting examples: topological strings on symplectic manifolds, topological membrane on G{sub 2}-manifolds and topological 3-brane on Spin(7) manifolds. We show that these peculiar topological theories are related to the physical (i.e., Nambu-Goto) brane theories in a specific way. These topological brane theories are proposed as microscopic description of topological M/F-theories.
Assessing Algebraic Solving Ability: A Theoretical Framework
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…
Einstein algebras and general relativity
International Nuclear Information System (INIS)
Heller, M.
1992-01-01
A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs
Fusion rules of chiral algebras
International Nuclear Information System (INIS)
Gaberdiel, M.
1994-01-01
Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)
Categorical Algebra and its Applications
1988-01-01
Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.
Estimation of Poisson noise in spatial domain
Švihlík, Jan; Fliegel, Karel; Vítek, Stanislav; Kukal, Jaromír.; Krbcová, Zuzana
2017-09-01
This paper deals with modeling of astronomical images in the spatial domain. We consider astronomical light images contaminated by the dark current which is modeled by Poisson random process. Dark frame image maps the thermally generated charge of the CCD sensor. In this paper, we solve the problem of an addition of two Poisson random variables. At first, the noise analysis of images obtained from the astronomical camera is performed. It allows estimating parameters of the Poisson probability mass functions in every pixel of the acquired dark frame. Then the resulting distributions of the light image can be found. If the distributions of the light image pixels are identified, then the denoising algorithm can be applied. The performance of the Bayesian approach in the spatial domain is compared with the direct approach based on the method of moments and the dark frame subtraction.
High order Poisson Solver for unbounded flows
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2015-01-01
This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...
Selective Contrast Adjustment by Poisson Equation
Directory of Open Access Journals (Sweden)
Ana-Belen Petro
2013-09-01
Full Text Available Poisson Image Editing is a new technique permitting to modify the gradient vector field of an image, and then to recover an image with a gradient approaching this modified gradient field. This amounts to solve a Poisson equation, an operation which can be efficiently performed by Fast Fourier Transform (FFT. This paper describes an algorithm applying this technique, with two different variants. The first variant enhances the contrast by increasing the gradient in the dark regions of the image. This method is well adapted to images with back light or strong shadows, and reveals details in the shadows. The second variant of the same Poisson technique enhances all small gradients in the image, thus also sometimes revealing details and texture.
The κ-(AdS quantum algebra in (3+1 dimensions
Directory of Open Access Journals (Sweden)
Ángel Ballesteros
2017-03-01
Full Text Available The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(AdS quantum algebra in (3+1 dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a Poisson–Lie group contraction parameter, and the limit Λ→0 leads to the well-known κ-Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this κ-(AdS deformation is sketched.
"Lost chains" in algebraic models
Fortunato, L.; de Graaf, W. A.
2011-03-01
The algebraic structure of some of the simplest algebraic models u(2), u(3) and u(4), widely used in several branches of physics either as toy models or as working instruments, are reanalyzed under a new perspective that releases the requirement that chains should terminate or pass through the angular momentum algebra. Unitary algebras are non-semisimple, therefore we first apply the Levi-Malcev decomposition. Then we use the theory of weighted Dynkin diagrams to identify conjugacy classes of A1 ~ su(2) ~ so(3) subalgebras: a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries follows that we substantiate with examples.
Applications of Computer Algebra Conference
Martínez-Moro, Edgar
2017-01-01
The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.
Introduction to algebraic independence theory
Philippon, Patrice
2001-01-01
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
Chiral algebras for trinion theories
International Nuclear Information System (INIS)
Lemos, Madalena; Peelaers, Wolfger
2015-01-01
It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T n theories. We also explicitly construct the chiral algebra arising from the T 4 theory. Its null relations give rise to new T 4 Higgs branch chiral ring relations.
Computational aspects of algebraic curves
Shaska, Tanush
2005-01-01
The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book cove
Self-ligating brackets in orthodontics. A systematic review.
Fleming, Padhraig S; Johal, Ama
2010-05-01
To evaluate the clinical differences in relation to the use of self-ligating brackets in orthodontics. Electronic databases were searched; no restrictions relating to publication status or language of publication were applied. Randomized controlled trials (RCTs) and controlled clinical trials (CCTs) investigating the influence of bracket type on alignment efficiency, subjective pain experience, bond failure rate, arch dimensional changes, rate of orthodontic space closure, periodontal outcomes, and root resorption were selected. Both authors were involved in study selection, validity assessment, and data extraction. Disagreements were resolved by discussion. Six RCTs and 11 CCTs were identified. Meta-analysis of the influence of bracket type on subjective pain experience failed to demonstrate a significant advantage for either type of appliance. Statistical analysis of other outcomes was unfeasible because of inadequate methodological design and heterogenous designs. At this stage there is insufficient high-quality evidence to support the use of self-ligating fixed orthodontic appliances over conventional appliance systems or vice versa.
Therapeutic accuracy of individualized brackets in lingual orthodontics.
Pauls, Alexander Harry
2010-09-01
Verification of the therapeutic accuracy of the Incognito ® bracket system. The therapeutic set-up casts and final treatment casts were digitalized using a 3D scanner, and the scans were subsequently superimposed. The deviations in rotation and translation of each tooth in the three spatial dimensions were calculated. The front teeth showed deviations in rotations of less than 4.6 ° and in translations under 0.5 mm. In addition, influences such as upper or lower jaw, growth, type of tooth, anterior tooth position, bracket generation, 3D scanner hardware and finishing archwires were analyzed. The clinical impression was confirmed by the measurements taken in this study. The final results following lingual orthodontic treatment using individualized brackets correlate satisfactorily with the therapeutic set-ups.
Evaluating the double Poisson generalized linear model.
Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique
2013-10-01
The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. Copyright © 2013 Elsevier Ltd. All rights reserved.
Force loss in archwire-guided tooth movement of conventional and self-ligating brackets.
Montasser, Mona A; El-Bialy, Tarek; Keilig, Ludger; Reimann, Susanne; Jäger, Andreas; Bourauel, Christoph
2014-02-01
This study aimed to investigate the differences in the force loss during simulated archwire-guided canine retraction between various conventional and self-ligating brackets. Three types of orthodontic brackets have been investigated experimentally using a biomechanical set-up: 1. conventional ligating brackets (Victory Series and Mini-Taurus), 2. self-ligating brackets (SmartClip: passive self-ligating bracket, and Time3 and SPEED: active self-ligating brackets), and 3. a conventional low-friction bracket (Synergy). All brackets had a nominal 0.022″ slot size. The brackets were combined with three rectangular 0.019×0.025″ archwires: 1. Remanium (stainless steel), 2. Nitinol SE (nickel-titanium alloy, NiTi), and 3. Beta III Titanium (titanium-molybdenum alloy). Stainless steel ligatures were used with the conventional brackets. Archwire-guided tooth movement was simulated over a retraction path of up to 4mm using a superelastic NiTi coil spring (force: 1 N). Force loss was lowest for the Victory Series and SmartClip brackets in combination with the steel guiding archwire (35 and 37.6 per cent, respectively) and highest for the SPEED and Mini-Taurus brackets in combination with the titanium wire (73.7 and 64.4 per cent, respectively). Force loss gradually increased by 10 per cent for each bracket type in combination with the different wires in the following sequence: stainless steel, Nitinol, and beta-titanium. Self-ligating brackets did not show improved performance compared with conventional brackets. There was no consistent pattern of force loss when comparing conventional and self-ligating brackets or passive and active self-ligating brackets.
Air-powder polishing on self-ligating brackets after clinical use: effects on debris levels
Directory of Open Access Journals (Sweden)
Mônica L. S. Castro Aragón
Full Text Available ABSTRACT Introduction: Debris buildup on brackets and arch surfaces is one of the main factors that can influence the intensity of friction between bracket and orthodontic wire. Objective: This study sought to evaluate the effect of air-powder polishing cleaning on debris levels of self-ligating ceramic brackets at the end of orthodontic treatment, compared to the behavior of conventional brackets. Methods: Debris levels were evaluated in metal conventional orthodontic brackets (n = 42 and ceramic self-ligating brackets (n = 42 on canines and premolars, arranged in pairs. There were brackets with and without air-powder polishing. At the end of orthodontic treatment, a hemiarch served as control and the contralateral hemiarch underwent prophylaxis with air-powder polishing. Debris buildup in bracket slots was assessed through images, and Wilcoxon test was used to analyze the results. Results: The median debris levels were statistically lower in the conventional metal brackets compared to self-ligating ones (p = 0.02, regarding brackets not submitted to air-powder polishing. Polishing significantly reduced debris buildup to zero in both systems, without differences between groups. Conclusions: Ceramic self-ligating brackets have a higher debris buildup in comparison to conventional metal brackets in vivo, but prophylaxis with sodium bicarbonate jet was effective in reducing debris levels in self-ligating and also in conventional brackets.
Equilibrium stochastic dynamics of Poisson cluster ensembles
Directory of Open Access Journals (Sweden)
L.Bogachev
2008-06-01
Full Text Available The distribution μ of a Poisson cluster process in Χ=Rd (with n-point clusters is studied via the projection of an auxiliary Poisson measure in the space of configurations in Χn, with the intensity measure being the convolution of the background intensity (of cluster centres with the probability distribution of a generic cluster. We show that μ is quasi-invariant with respect to the group of compactly supported diffeomorphisms of Χ, and prove an integration by parts formula for μ. The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms.
White Noise of Poisson Random Measures
Proske, Frank; Øksendal, Bernt
2002-01-01
We develop a white noise theory for Poisson random measures associated with a Lévy process. The starting point of this theory is a chaos expansion with kernels of polynomial type. We use this to construct the white noise of a Poisson random measure, which takes values in a certain distribution space. Then we show, how a Skorohod/Itô integral for point processes can be represented by a Bochner integral in terms of white noise of the random measure and a Wick product. Further, we apply these co...
Bayesian regression of piecewise homogeneous Poisson processes
Directory of Open Access Journals (Sweden)
Diego Sevilla
2015-12-01
Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015
Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes
Fuentealba, Oscar; Matulich, Javier; Pérez, Alfredo; Pino, Miguel; Rodríguez, Pablo; Tempo, David; Troncoso, Ricardo
2018-01-01
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for isl(2,R) , being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the Hirota-Satsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k. Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is then recovered from the corresponding surface integrals in the canonical approach.
The planar algebra of a semisimple and cosemisimple Hopf algebra
Indian Academy of Sciences (India)
M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22
[TngGlk] Etingof Pavel and Gelaki Shlomo, On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic. Int. Math. Res. Notices,. 16 (1998) 851–864. [DasKdy] Das Paramita and Vijay Kodiyalam, Planar algebras and the Ocneanu–. Szymanski theorem, Proc. AMS, 133 (2005) 2751–2759.
Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras
Put, Marius van der
1999-01-01
The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.
Dynamical entropy of C* algebras and Von Neumann algebras
International Nuclear Information System (INIS)
Connes, A.; Narnhofer, H.; Thirring, W.
1986-01-01
The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)
Algebraic K-theory of generalized schemes
DEFF Research Database (Denmark)
Anevski, Stella Victoria Desiree
Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry and ge...
Quantum deformation of the affine transformation algebra
International Nuclear Information System (INIS)
Aizawa, N.; Sato, Haru-Tada
1994-01-01
We discuss a quantum deformation of the affine transformation algebra in one-dimensional space. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. (orig.)
Algebraic K-theory of generalized schemes
DEFF Research Database (Denmark)
Anevski, Stella Victoria Desiree
Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry...
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Algebraic topology and concurrency
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric
2006-01-01
We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...
Hazewinkel, M
2008-01-01
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it i
New examples of continuum graded Lie algebras
International Nuclear Information System (INIS)
Savel'ev, M.V.
1989-01-01
Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs
Fractional supersymmetry and infinite dimensional lie algebras
International Nuclear Information System (INIS)
Rausch de Traubenberg, M.
2001-01-01
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed
21 CFR 872.3750 - Bracket adhesive resin and tooth conditioner.
2010-04-01
... SERVICES (CONTINUED) MEDICAL DEVICES DENTAL DEVICES Prosthetic Devices § 872.3750 Bracket adhesive resin... composed of an adhesive compound, such as polymethylmethacrylate, intended to cement an orthodontic bracket...
Spatial Nonhomogeneous Poisson Process in Corrosion Management
López De La Cruz, J.; Kuniewski, S.P.; Van Noortwijk, J.M.; Guriérrez, M.A.
2008-01-01
A method to test the assumption of nonhomogeneous Poisson point processes is implemented to analyze corrosion pit patterns. The method is calibrated with three artificially generated patterns and manages to accurately assess whether a pattern distribution is random, regular, or clustered. The
Efficient information transfer by Poisson neurons
Czech Academy of Sciences Publication Activity Database
Košťál, Lubomír; Shinomoto, S.
2016-01-01
Roč. 13, č. 3 (2016), s. 509-520 ISSN 1547-1063 R&D Projects: GA ČR(CZ) GA15-08066S Institutional support: RVO:67985823 Keywords : information capacity * Poisson neuron * metabolic cost * decoding error Subject RIV: BD - Theory of Information Impact factor: 1.035, year: 2016
Almost Poisson integration of rigid body systems
International Nuclear Information System (INIS)
Austin, M.A.; Krishnaprasad, P.S.; Li-Sheng Wang
1993-01-01
In this paper we discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by lie group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is an O(h 3 ) error estimate for the Lie-Poisson structure, where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored. 24 refs., 9 figs
Affine Poisson Groups and WZW Model
Directory of Open Access Journals (Sweden)
Ctirad Klimcík
2008-01-01
Full Text Available We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the q → ∞ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.
Graded associative conformal algebras of finite type
Kolesnikov, Pavel
2011-01-01
In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\\simeq \\Gamma $. A classification of simple...
1989-01-01
N Tn FRICTION IN SLIDING ORTHODONTIC MECHANICS: N CERAMIC BRACKETS, TEFLON-COATED WIRES , AND COMPARATIVE RESISTANCES 0 DTICSFLECTED James R. Gill1...obsolete. SECURITY CLASSIFICATION OF THIS PAGE AFIT/CI "OVERPRINT" I FRICTION IN SLIDING ORTHODONTIC MECHANICS: CERAMIC BRACKETS, TEFLON-COATED WIRES ...brackets, arch- wires , and ligations during simulated orthodontic edgewise sliding mechanics. Independent variables and their values were 1) bracket
Galois Connections for Flow Algebras
DEFF Research Database (Denmark)
Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis
2011-01-01
to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...
Ultraproducts of von Neumann algebras
DEFF Research Database (Denmark)
Ando, Hiroshi; Haagerup, Uffe
2014-01-01
We study several notions of ultraproducts of von Neumann algebras from a unified viewpoint. In particular, we show that for a sigma-finite von Neumann algebra M , the ultraproduct MωMω introduced by Ocneanu is a corner of the ultraproduct ∏ωM∏ωM introduced by Groh and Raynaud. Using...
Orthogonal symmetries and Clifford algebras
Indian Academy of Sciences (India)
a universal property of the even Clifford algebra in §3. ..... symmetry if σ2 = id. In the literature, such maps are sometimes also called “orthogonal involutions” (cf. Ch. III, §5 of [4]). We have, however, preferred to use the former ...... [7] Helmstetter J and Micali A, Quadratic mappings and Clifford algebras (Basel: Birkhäuser.
Six Lectures on Commutative Algebra
Elias, J; Miro-Roig, Rosa Maria; Zarzuela, Santiago
2009-01-01
Interest in commutative algebra has surged over the years. In order to survey and highlight the developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. This title offers a synthesis of the lectures presented at the Summer School
Templates for Linear Algebra Problems
Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der
1995-01-01
The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and
Linear Algebra and Image Processing
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.)
Ahadpanah, A.; Borumand Saeid, A.
2011-01-01
In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC -algebras, and then we determine the relationships between these hyper ideals.
The Algebra of Complex Numbers.
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…
Modular specifications in process algebra
R.J. van Glabbeek (Rob); F.W. Vaandrager (Frits)
1987-01-01
textabstractIn recent years a wide variety of process algebras has been proposed in the literature. Often these process algebras are closely related: they can be viewed as homomorphic images, submodels or restrictions of each other. The aim of this paper is to show how the semantical reality,
Linear Algebra and Linear Models
Indian Academy of Sciences (India)
Linear Algebra and Linear. Models. Kalyan Das. Linear Algebra and linear Models. (2nd Edn) by R P Bapat. Hindustan Book Agency, 1999 pp.xiii+180, Price: Rs.135/-. This monograph provides an introduction to the basic aspects of the theory oflinear estima- tion and that of testing linear hypotheses. The primary objective ...
Quantum Observables and Effect Algebras
Dvurečenskij, Anatolij
2017-11-01
We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a monotone σ-complete homogeneous effect algebra using its orthoalgebraic skeleton. In addition, we study compatibility in orthoalgebras and we show that every orthoalgebra satisfying RIP is an orthomodular poset.
Algebraic study of chiral anomalies
Indian Academy of Sciences (India)
2012-06-14
Jun 14, 2012 ... Abstract. The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles ... Editor's Note: †Reproduced with kind permission from Springer Science+Business Media: Algebraic study of chiral anoma- ..... We shall see in the sequel several examples in which this ambiguity helps.
An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families
Leyvraz, F.
2017-07-01
We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such Hamiltonians can be solved explicitly by a separation of variables ansatz. The method leads in particular to a proof that the so-called "goldfish" Hamiltonian is maximally superintegrable and leads to an elementary identification of a full set of integrals of motion. The Hamiltonians in involution with the "goldfish" Hamiltonian are also explicitly integrated. New integrable Hamiltonians are identified, among which some have the property of being isochronous, that is, all their orbits have the same period. Finally, a peculiar structure is identified in the Poisson brackets between the elementary symmetric functions and the set of Hamiltonians commuting with the "goldfish" Hamiltonian: these can be expressed as products between elementary symmetric functions and Hamiltonians. The structure displays an invariance property with respect to one element and has both a symmetry and a closure property. The meaning of this structure is not altogether clear to the author, but it turns out to be a powerful tool.
Practical algebraic renormalization
International Nuclear Information System (INIS)
Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias
2001-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ
Waterloo Workshop on Computer Algebra
Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday
2018-01-01
This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.
Invariants of triangular Lie algebras
International Nuclear Information System (INIS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
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
Elements of algebraic coding systems
Cardoso da Rocha, Jr, Valdemar
2014-01-01
Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...
Representations of affine Hecke algebras
Xi, Nanhua
1994-01-01
Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest
Torque expression of 0.018 and 0.022 inch conventional brackets
Sifakakis, I.; Pandis, N.; Makou, M.; Eliades, T.; Katsaros, C.; Bourauel, C.
2013-01-01
The aim of this study was to assess the effect of the moments generated with low- and high-torque brackets. Four different bracket prescription-slot combinations of the same bracket type (Mini Diamond(R) Twin) were evaluated: high-torque 0.018 and 0.022 inch and low-torque 0.018 and 0.022 inch.
Rheocasting an engine mounting bracket in commercial 7075
CSIR Research Space (South Africa)
Curle, UA
2011-07-01
Full Text Available -1 Light Metals Technology V, the 5th International Conference on Light Metals Technology, July 19- 22, 2011, Luneburg, Germany Rheocasting an engine mounting bracket in commercial 7075 CURLE Ulyate Andries1, a 1Materials Science and Manufacturing...
DEBONDING OF CERAMIC BRACKETS BY ER:YAG LASER
Directory of Open Access Journals (Sweden)
Fidan ALAKUŞ-SABUNCUOĞLU
2016-04-01
Full Text Available Purpose: The objective of the present study is to evaluate the effects of Er:YAG laser debonding of ceramic brackets on the bond strength and the amount of adhesive resin remnant. Materials and Methods: Twenty human mandibular incisors were randomly divided into two groups of 10 and polycrystalline ceramic brackets (Transcend series 6000, 3M Unitek, Monrovia, CA, USA were bonded on enamel surfaces. Group 1 was the control group in which no laser application was performed prior to the shear bond strength (SBS testing. In Group 2, Er:YAG was applied in 3W power for 6 seconds using the scanning method. The brackets were tested for SBS with an Instron universal testing machine and results were expressed in megapascals (MPa. The amount of adhesive remnant was evaluated with Adhesive Remnant Index (ARI. One-way analysis of variance and Tukey’s post-hoc tests were used for statistical analysis. Results: Mean ± standard deviation of SBS values in the control group was 13.42 ±1.23 MPa and 8.47 ±0.71 MPa in the Er:YAG group and this difference was statistically significant (p<0.05. The evaluation of ARI scores demonstrated more adhesive was left on the enamel surface with Er:YAG group. Conclusion: 3W power Er:YAG laser application with the scanning method to polycrystalline ceramic brackets demonstrated lower bond strengths and higher ARI scores during the debonding procedure.
(Modular Effect Algebras are Equivalent to (Frobenius Antispecial Algebras
Directory of Open Access Journals (Sweden)
Dusko Pavlovic
2017-01-01
Full Text Available Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; and both come with their conceptual mysteries. A particularly elegant and mysterious constraint, imposed on Frobenius algebras to characterize a class of tripartite entangled states, is the antispecial law. A particularly contentious issue on the quantum logic side is the modularity law, proposed by von Neumann to mitigate the failure of distributivity of quantum logical connectives. We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements; and that the modularity law corresponds to the Frobenius condition. These correspondences lead to the equivalence announced in the title. Aligning the two formalisms, at the very least, sheds new light on the concepts that are more clearly displayed on one side than on the other (such as e.g. the orthogonality. Beyond that, it may also open up new approaches to deep and important problems of quantum mechanics (such as the classification of complementary observables.
Rota-Baxter algebras and the Hopf algebra of renormalization
International Nuclear Information System (INIS)
Ebrahimi-Fard, K.
2006-06-01
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
Rota-Baxter algebras and the Hopf algebra of renormalization
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi-Fard, K.
2006-06-15
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
Universal enveloping Lie Rota-Baxter algebra of preLie and post-Lie algebras
Gubarev, Vsevolod
2017-01-01
Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras are constructed. It is proved that the pairs of varieties (Lie Rota-Baxter algebras of zero weight,preLie algebras) and (Lie Rota-Baxter algebras of nonzero weight,post-Lie algebras) are PBW-pairs and the variety of Lie Rota-Baxter algebras is not Schreier.
Lie algebra in quantum physics by means of computer algebra
Kikuchi, Ichio; Kikuchi, Akihito
2017-01-01
This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...
Head First Algebra A Learner's Guide to Algebra I
Pilone, Tracey
2008-01-01
Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials. Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive i
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
International Nuclear Information System (INIS)
Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-01
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes
Directory of Open Access Journals (Sweden)
Andrea Scribante
2013-01-01
Full Text Available Objective. The aim of this study was to compare the shear bond strength (SBS and adhesive remnant index (ARI scores of no-primer adhesives tested with two different bracket bases. Materials and Methods. 120 bovine permanent mandibular incisors were divided into 6 groups of 20 specimens. Two brackets (ODP with different bracket bases (anchor pylons and 80-gauge mesh were bonded to the teeth using a conventional adhesive (Transbond XT and two different no-primer adhesive (Ortho Cem; Heliosit systems. Groups were tested using an instron universal testing machine. SBS values were recorded. ARI scores were measured. SEM microphotographs were taken to evaluate the pattern of bracket bases. Statistical analysis was performed. ANOVA and Tukey tests were carried out for SBS values, whereas a chi-squared test was applied for ARI scores. Results. Highest bond strength values were reported with Transbond XT (with both pad designs, Ortho Cem bonded on anchor pylons and Heliosit on 80-gauge mesh. A higher frequency of ARI score of “3” was reported for Transbond XT groups. Other groups showed a higher frequency of ARI score “2” and “1.” Conclusion. Transbond XT showed the highest shear bond strength values with both pad designs.
Directory of Open Access Journals (Sweden)
Biken Shrestha
2014-01-01
Conclusion: The use of SLBs or the conventionally ligated brackets have no difference in the periodontal response in early orthodontic patients. Oral hygiene prophylaxis before the start of the orthodontic treatment and its maintenance throughout the treatment duration is of prime importance.
Ozcan, M.; Finnema, K.; Ybema, A.
The objectives of this study were to evaluate the effect of silanization on the failure type and shear-peel bond strength (SBS) of ceramic and polycarbonate brackets, and to determine the type of failure when debonded with either a universal testing machine or orthodontic pliers. Silanized and
Current algebra for parafields
International Nuclear Information System (INIS)
Palev, Ch.D.
1976-01-01
Within the framework of the Lagrangean QFT a generalization of canonical commutation and anticommutation relations in terms of three-linear commutation relations, corresponding to the parastatistics, s discussed. A detailed derivation of these three-linear relations for a set of parafermi fields is presented. Then for a Lagrangean, depending of a family of parabose fields and a family of paraferm fields, is shown that the fundamental hypothesis of current algebra is valid. In other words, the currents corresponding to the linear gauge transformations are found to meet the commutation relation: [Jsub(f)sup(0)(x), Jsub(g)sup(0)]sub(x 0 =y 0 ) = -idelta(x vector - y vector)Jsub([f,g])sup(0) (x), where Jsub(f)sup(0) is a time component of the current, corresponding to transformation f. (S.P.)
Meijer, Alko R
2016-01-01
This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his o...
Hestenes, David
2015-01-01
This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, a...
Energy Technology Data Exchange (ETDEWEB)
2017-08-01
AMG is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the BoomerAMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL and is very similar to the AMG2013 benchmark with additional optimizations. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem with a 27-point stencil, which can be scaled up and is designed to solve a very large problem. A second problem simulates a time dependent problem, in which successively various smnllcr systems are solved.
Applications of computer algebra
1985-01-01
Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed for...
Macdonald index and chiral algebra
Song, Jaewon
2017-08-01
For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.
Quantum algebra of N superspace
International Nuclear Information System (INIS)
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-01-01
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 κ-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
Vertex algebras and mirror symmetry
International Nuclear Information System (INIS)
Borisov, L.A.
2001-01-01
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)
Semiprojectivity of universal -algebras generated by algebraic elements
DEFF Research Database (Denmark)
Shulman, Tatiana
2012-01-01
Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given....
Topological Ã-algebras with CÃ-enveloping algebras II
Indian Academy of Sciences (India)
subalgebra and contained in the crossed product *-algebra *(, , ) satisfies ()=*(, , ). If G = R , if is an -invariant dense Frechet ∗-subalgebra of such that () = , and if the action on is -tempered, smooth and by continuous ...
Poisson/Superfish codes for personal computers
International Nuclear Information System (INIS)
Humphries, S.
1992-01-01
The Poisson/Superfish codes calculate static E or B fields in two-dimensions and electromagnetic fields in resonant structures. New versions for 386/486 PCs and Macintosh computers have capabilities that exceed the mainframe versions. Notable improvements are interactive graphical post-processors, improved field calculation routines, and a new program for charged particle orbit tracking. (author). 4 refs., 1 tab., figs
Coxeter groups and Hopf algebras
Aguiar, Marcelo
2011-01-01
An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary backgrou
Linear operators in Clifford algebras
International Nuclear Information System (INIS)
Laoues, M.
1991-01-01
We consider the real vector space structure of the algebra of linear endomorphisms of a finite-dimensional real Clifford algebra (2, 4, 5, 6, 7, 8). A basis of that space is constructed in terms of the operators M eI,eJ defined by x→e I .x.e J , where the e I are the generators of the Clifford algebra and I is a multi-index (3, 7). In particular, it is shown that the family (M eI,eJ ) is exactly a basis in the even case. (orig.)
Homology theory on algebraic varieties
Wallace, Andrew H
1958-01-01
Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The n
Clifford algebraic symmetries in physics
International Nuclear Information System (INIS)
Salingaros, N.
1986-01-01
This paper reviews the following appearances of Clifford algebras in theoretical physics: statistical mechanics; general relativity; quantum electrodynamics; internal symmetries; the vee product; classical electrodynamics; charged-particle motion; and the Lorentz group. It is concluded that the power of the Clifford-algebraic description resides in its ability to perform representation-free calculations which are generalizations of the traditional vector algebra and that this considerable computational asset, in combination with the intrinsic symmetry, provides a practical framework for much of theoretical physics. 5 references
Kolman, Bernard; Levitan, Michael L
1985-01-01
Test Bank for College Algebra, Second Edition is a supplementary material for the text, College Algebra, Second Edition. The book is intended for use by mathematics teachers.The book contains standard tests for each chapter in the textbook. Each set of test aims to evaluate the level of understanding the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book.Mathematics teachers teaching college algebra will find the book very useful.
Algebraic and stochastic coding theory
Kythe, Dave K
2012-01-01
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.
Introduction to applied algebraic systems
Reilly, Norman R
2009-01-01
This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as
Introduction to algebra and trigonometry
Kolman, Bernard
1981-01-01
Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry.This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are
Study guide for college algebra
Snow, James W; Shapiro, Arnold
1981-01-01
Study Guide for College Algebra is a supplemental material for the basic text, College Algebra. Its purpose is to make the learning of college algebra and trigonometry easier and enjoyable.The book provides detailed solutions to exercises found in the text. Students are encouraged to use the study guide as a learning tool during the duration of the course, a reviewer prior to an exam, a reference book, and as a quick overview before studying a section of the text. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what
Planar algebra of the subgroup-subfactor
Indian Academy of Sciences (India)
G in terms of operator matrices. We also obtain an identification between the planar algebra of the fixed algebra sub- factor RG ⊂ RH and the G-invariant planar subalgebra of the planar algebra of the 'flip' of ⋆n. Keywords. Planar algebras; subfactors; standard invariant. 1. Introduction. For every pair H ⊂ G of finite groups, ...
Abstract algebra an introduction with applications
Robinson, Derek JS
2015-01-01
This is the second edition of the introduction to abstract algebra. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. There is ample material here for a two semester course in abstract algebra.
Homomorphisms of certain Banach function algebras
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
. } < ∞ is denoted by Lipα(X, d). These algebras are called Lipschitz algebras of order α and were first studied by Sherbert. The Lipschitz algebras Lipα(X, d) for α ≤ 1 are natural. Banach function algebras on X under the norm f α = f X + pα(f ) ...
Particle-like structure of Lie algebras
Vinogradov, A. M.
2017-07-01
If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.
Contraction of graded su(2) algebra
International Nuclear Information System (INIS)
Patra, M.K.; Tripathy, K.C.
1989-01-01
The Inoenu-Wigner contraction scheme is extended to Lie superalgebras. The structure and representations of extended BRS algebra are obtained from contraction of the graded su(2) algebra. From cohomological consideration, we demonstrate that the graded su(2) algebra is the only superalgebra which, on contraction, yields the full BRS algebra. (orig.)
Elementary derivation of Poisson structures for fluid dynamics and electrodynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
The canonical Poisson structure of the microscopic Lagrangian is used to deduce the noncanonical Poisson structure for the macroscopic Hamiltonian dynamics of a compressible neutral fluid and of fluid electrodynamics
Poisson Plus Quantification for Digital PCR Systems.
Majumdar, Nivedita; Banerjee, Swapnonil; Pallas, Michael; Wessel, Thomas; Hegerich, Patricia
2017-08-29
Digital PCR, a state-of-the-art nucleic acid quantification technique, works by spreading the target material across a large number of partitions. The average number of molecules per partition is estimated using Poisson statistics, and then converted into concentration by dividing by partition volume. In this standard approach, identical partition sizing is assumed. Violations of this assumption result in underestimation of target quantity, when using Poisson modeling, especially at higher concentrations. The Poisson-Plus Model accommodates for this underestimation, if statistics of the volume variation are well characterized. The volume variation was measured on the chip array based QuantStudio 3D Digital PCR System using the ROX fluorescence level as a proxy for effective load volume per through-hole. Monte Carlo simulations demonstrate the efficacy of the proposed correction. Empirical measurement of model parameters characterizing the effective load volume on QuantStudio 3D Digital PCR chips is presented. The model was used to analyze digital PCR experiments and showed improved accuracy in quantification. At the higher concentrations, the modeling must take effective fill volume variation into account to produce accurate estimates. The extent of the difference from the standard to the new modeling is positively correlated to the extent of fill volume variation in the effective load of your reactions.
Self-ligating vs conventional twin brackets during en-masse space closure with sliding mechanics.
Miles, Peter G
2007-08-01
The aim of this study was to compare the rate of en-masse space closure with sliding mechanics between passive self-ligating SmartClip brackets (3M Unitek, Monrovia, Calif) and conventional twin brackets ligated with stainless steel ligatures. Nineteen patients including 20 arches participated in this prospective trial with 0.018-in slot brackets. All patients had first premolar extractions in at least 1 arch, with the second premolar and the first molar distal to the extraction site bonded with SmartClip brackets on 1 side and conventional twin brackets on the other. The sides were alternated with each consecutive patient. Space closure was achieved on 0.016 x 0.022-in stainless steel wires with nickel-titanium coil springs activated 6 to 9 mm. The patients were recalled every 5 weeks until 1 side had closed. The distances from the mesial aspect of the canine bracket to the distal aspect of the first molar bracket were recorded before and after space closure, and an average rate of space closure per month was calculated. Thirteen patients completed the trial (14 arches); the median rates of tooth movement for the SmartClip bracket side (1.1 mm per month) and the conventional twin bracket side (1.2 mm per month) were not significantly different (P = .86). There was no significant difference in the rate of en-masse space closure between passive SmartClip brackets and conventional twin brackets tied with stainless steel ligatures.
A study to compare the effects of simulated torquing forces on pre-adjusted orthodontic brackets.
McKnight, M M; Jones, S P; Davies, E H
1994-11-01
The transmission of torquing forces between three types of preadjusted bracket was investigated. 0.022-inch Roth prescription 'A'-Company (stainless steel), Silkon (reinforced polycarbonate), and Allure III (polycrystalline ceramic) brackets were used. A selection of stainless steel archwires were chosen, 0.018 x 0.025, 0.019 x 0.025, and 0.021 x 0.025 inch. The brackets were torqued with respect to the archwire and force v. angular deflection was recorded on an Instron machine. The dimension of angular change was in part dependent on the ability of the bracket to elastically or plastically deform. There were no significant differences between bracket types with the 0.018 x 0.025-inch archwire. 'A'-Company brackets demonstrated a significantly lower resistance to loading compared to Silkon brackets in the 0.019 x 0.025-inch group. The greatest amount of distortion was seen in Silkon brackets with an 0.021 x 0.025-inch archwire. Allure III brackets demonstrated the greatest resistance to loading in all groups. As no apparent distortion under loading is seen in Allure III brackets, it is assumed that the load is largely transmitted to the tooth. Full thickness stainless steel rectangular wires should be avoided with these brackets, in order to prevent overloading.
AT -algebras and extensions of AT-algebras
Indian Academy of Sciences (India)
and E has real rank zero, then E is an AT-algebra if and only if the index maps are both zero. Accordingly, in this ... It is well-known that two extensions with the same index are isomorphic as C. ∗. -algebras. We call these .... where each Bi = I (Ei) is a direct sum of K. By Lemma 2.3, I (E) = B. Without loss of generality, we may ...
Lectures on algebraic quantum field theory and operator algebras
International Nuclear Information System (INIS)
Schroer, Bert
2001-04-01
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)
Topological أ-algebras with Cأ-enveloping algebras II
Indian Academy of Sciences (India)
A with the locally convex inductive limit topology t is a locally m-convex Q-algebra satisfying EًKnc. A ق ¼ EًKAق ¼ A. (3) If A has a countable bounded approximate identity, then ًKnc. A ; tق is an LFQ-algebra. In general KA 6¼ Knc. A , though KA Knc. A . Now KA has been interpreted as a non- commutative analogue of CcًXق.
Incompressible SPH (ISPH) with fast Poisson solver on a GPU
Chow, Alex D.; Rogers, Benedict D.; Lind, Steven J.; Stansby, Peter K.
2018-05-01
This paper presents a fast incompressible SPH (ISPH) solver implemented to run entirely on a graphics processing unit (GPU) capable of simulating several millions of particles in three dimensions on a single GPU. The ISPH algorithm is implemented by converting the highly optimised open-source weakly-compressible SPH (WCSPH) code DualSPHysics to run ISPH on the GPU, combining it with the open-source linear algebra library ViennaCL for fast solutions of the pressure Poisson equation (PPE). Several challenges are addressed with this research: constructing a PPE matrix every timestep on the GPU for moving particles, optimising the limited GPU memory, and exploiting fast matrix solvers. The ISPH pressure projection algorithm is implemented as 4 separate stages, each with a particle sweep, including an algorithm for the population of the PPE matrix suitable for the GPU, and mixed precision storage methods. An accurate and robust ISPH boundary condition ideal for parallel processing is also established by adapting an existing WCSPH boundary condition for ISPH. A variety of validation cases are presented: an impulsively started plate, incompressible flow around a moving square in a box, and dambreaks (2-D and 3-D) which demonstrate the accuracy, flexibility, and speed of the methodology. Fragmentation of the free surface is shown to influence the performance of matrix preconditioners and therefore the PPE matrix solution time. The Jacobi preconditioner demonstrates robustness and reliability in the presence of fragmented flows. For a dambreak simulation, GPU speed ups demonstrate up to 10-18 times and 1.1-4.5 times compared to single-threaded and 16-threaded CPU run times respectively.
Finite Element Analysis Design of a Split Rotor Bracket for a Bulb Turbine Generator
Directory of Open Access Journals (Sweden)
Yongyao Luo
2013-01-01
Full Text Available The rotor bracket is a key component of the generator rotor with cracks in the rotor bracket leading to rubbing between the rotor and stator, which threatens safe operation of the unit. The rotor rim is so complicated that the equivalent radial stiffness of rim was determined by numerical simulation other than engineering experience. A comprehensive numerical method including finite element analyses and the contact method for multibody dynamics has been used to design the split rotor bracket. The com-putational results showed that cracks would occur in the initial design of the bracket when the turbine operated at the runaway speed, and the bracket design should be improved. The improved design of the bracket was strong enough to avoid cracks and rub between the rotor and stator. This design experience will help improve the design of split rotor brackets for bulb turbine generators.
Pre-Algebra Essentials For Dummies
Zegarelli, Mark
2010-01-01
Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra
Reduction of Nambu-Poisson Manifolds by Regular Distributions
Das, Apurba
2018-03-01
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.
Connections between algebra, combinatorics, and geometry
Sather-Wagstaff, Sean
2014-01-01
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...
Evaluation of friction produced by self-ligating, conventional and Barbosa Versatile brackets
Directory of Open Access Journals (Sweden)
Jurandir Antonio BARBOSA
Full Text Available Abstract Introduction The Barbosa Versatile bracket design may provide lower frictional force and greater sliding. However, no in vitro studies have shown its sliding mechanisms and frictional resistance, particularly in comparison with other self-ligating or conventional brackets. Objective To compare the frictional resistance among self-ligating brackets (EasyClip/ Aditek, Damon MX/ Ormco and In Ovation R/ GAC; conventional brackets (Balance Roth/ GAC, and Roth Monobloc/ Morelli; and Barbosa Versatile bracket (Barbosa Versatile/ GAC with different angles and arch wires. Material and method Brackets were tested with the 0.014", 0.018", 0.019"×0.025" and 0.021"×0.025" stainless steel wires, with 0, 5, 10, 15 and 20 degree angulations. Tying was performed with elastomeric ligature for conventional and Barbosa Versatile brackets, or with a built-in clip system of the self-ligating brackets. A universal testing machine was used to obtain sliding strength and friction value readouts between brackets and wires. Result Three-way factorial ANOVA 4×5×6 (brackets × angulation × wire and Tukey tests showed statistically significant differences for all factors and all interactions (p<0.0001. Static frictional resistance showed a lower rate for Barbosa Versatile bracket and higher rates for Roth Monobloc and Balance brackets. Conclusion The lowest frictional resistance was obtained with the Barbosa Versatile bracket and self-ligating brackets in comparison with the conventional type. Increasing the diameter of the wires increased the frictional resistance. Smaller angles produced less frictional resistance.
Frictional and mechanical properties of diamond-like carbon-coated orthodontic brackets.
Muguruma, Takeshi; Iijima, Masahiro; Brantley, William A; Nakagaki, Susumu; Endo, Kazuhiko; Mizoguchi, Itaru
2013-04-01
This study investigated the effects of a diamond-like carbon (DLC) coating on frictional and mechanical properties of orthodontic brackets. DLC films were deposited on stainless steel brackets using the plasma-based ion implantation/deposition (PBIID) method under two different atmospheric conditions. As-received metal brackets served as the control. Two sizes of stainless steel archwires, 0.018 inch diameter and 0.017 × 0.025 inch cross-section dimensions, were used for measuring static and kinetic friction by drawing the archwires through the bracket slots, using a mechanical testing machine (n = 10). The DLC-coated brackets were observed with a scanning electron microscope (SEM). Values of hardness and elastic modulus were obtained by nanoindentation testing (n = 10). Friction forces were compared by one-way analysis of variance and the Scheffé test. The hardness and elastic modulus of the brackets were compared using Kruskal-Wallis and Mann-Whitney U-tests. SEM photomicrographs showed DLC layers on the bracket surfaces with thickness of approximately 5-7 μm. DLC-coated brackets deposited under condition 2 showed significantly less static frictional force for the stainless steel wire with 0.017 × 0.025 inch cross-section dimensions than as-received brackets and DLC-coated brackets deposited under condition 1, although both DLC-coated brackets showed significantly less kinetic frictional force than as-received brackets. The hardness of the DLC layers was much higher than that of the as-received bracket surfaces. In conclusion, the surfaces of metal brackets can be successfully modified by the PBIID method to create a DLC layer, and the DLC-coating process significantly reduces frictional forces.
Directory of Open Access Journals (Sweden)
Aravind S Raju
2013-01-01
Conclusion: This study highlights that higher retention of plaque in ceramic brackets ligated with elastomeric ring followed with metal brackets ligated with steel ligatures and comparatively less plaque retention in self-ligating brackets. Excess composite around the bracket base is the critical site of plaque accumulation associated with fixed appliances due to its rough surface texture.
Fermion current algebras and Schwinger terms in (3+1)-dimensions
International Nuclear Information System (INIS)
Langmann, E.
1994-01-01
We discuss the restricted linear group in infinite dimensions modeled by the Schatten class of rank 2p=4 which contains the (3+1)-dimensional analogs of the loop groups and is closely related to Yang-Mills theory with fermions in (3+1)-dimensions. We give an alternative to the construction of the ''highest weight'' representation of this group found by Mickelsson and Rajeev. Our approach is close to quantum field theory, with the elements of this group regarded as Bogoliubov transformations for fermions in an external Yang-Mills field. Though these cannot be unitarily implemented in the physically relevant representation of the fermion field algebra, we argue that they can be implemented by sesquilinear forms, and that there is a (regularized) product of forms providing an appropriate group structure. On the Lie algebra level, this gives an explicit, non-perturbative construction of fermion current algebras in (3+1) space-time dimensions which explicitly shows that the ''wave function renormalization'' required for a consistent definition of the currents and their Lie bracket naturally leads to the Schwinger term identical with the Mickelsson-Rajeev cocycle. Though the explicit form of the Schwinger term is given only for the case p=2, our arguments apply also to the restricted linear groups modeled by Schatten classes of rank 2p=6, 8, .. corresponding to current algebras in (d+1)-dimensions, d=5, 7, .. (orig.)
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.
Cartooning in Algebra and Calculus
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.
International Nuclear Information System (INIS)
Baeuerle, G.G.A.; Kerf, E.A. de
1990-01-01
The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It gives a thorough mathematical treatment of finite dimensional Lie algebras and Kac-Moody algebras. Concepts such as Cartan matrix, root system, Serre's construction are carefully introduced. Although the book can be read by an undergraduate with only an elementary knowledge of linear algebra, the book will also be of use to the experienced researcher. Experience has shown that students who followed the lectures are well-prepared to take on research in the realms of string-theory, conformal field-theory and integrable systems. 48 refs.; 66 figs.; 3 tabs
Classical theory of algebraic numbers
Ribenboim, Paulo
2001-01-01
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...
Computational linear and commutative algebra
Kreuzer, Martin
2016-01-01
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...
Completeness of algebraic CPS simulations
Directory of Open Access Journals (Sweden)
Ali Assaf
2012-07-01
Full Text Available The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the differential lambda calculus, the latter is a candidate lambda calculus for quantum computation. They differ in the handling of application arguments and algebraic rules. The two languages can simulate each other using an algebraic extension of the well-known call-by-value and call-by-name CPS translations. These simulations are sound, in that they preserve reductions. In this paper, we prove that the simulations are actually complete, strengthening the connection between the two languages.
A characterisation of algebraic exactness
Garner, Richard
2011-01-01
An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Ad\\'amek, Lawvere and Rosick\\'y: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conject...
Distribution theory of algebraic numbers
Yang, Chung-Chun
2008-01-01
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.
Nineteen papers on algebraic semigroups
Aizenshtat, A Ya; Podran, N E; Ponizovskii, IS; Shain, BM
1988-01-01
This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.
A quantum Goldman bracket in (2 + 1) quantum gravity
International Nuclear Information System (INIS)
Nelson, J E; Picken, R F
2008-01-01
In the context of quantum gravity for spacetimes of dimension (2 + 1), we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R 2 (representing loops on the spatial manifold, i.e. the torus) and a quantum connection with noncommuting components, we review how holonomies and Wilson loops for two homotopic paths are related by phases in terms of the signed area between them. Paths rerouted at intersection points with other paths occur on the rhs of the Goldman bracket. To better understand their nature we introduce the concept of integer points inside the parallelogram spanned by two intersecting paths, and show that the rerouted paths must necessarily pass through these integer points
Femtosecond laser etching of dental enamel for bracket bonding.
Kabas, Ayse Sena; Ersoy, Tansu; Gülsoy, Murat; Akturk, Selcuk
2013-09-01
The aim is to investigate femtosecond laser ablation as an alternative method for enamel etching used before bonding orthodontic brackets. A focused laser beam is scanned over enamel within the area of bonding in a saw tooth pattern with a varying number of lines. After patterning, ceramic brackets are bonded and bonding quality of the proposed technique is measured by a universal testing machine. The results are compared to the conventional acid etching method. Results show that bonding strength is a function of laser average power and the density of the ablated lines. Intrapulpal temperature changes are also recorded and observed minimal effects are observed. Enamel surface of the samples is investigated microscopically and no signs of damage or cracking are observed. In conclusion, femtosecond laser exposure on enamel surface yields controllable patterns that provide efficient bonding strength with less removal of dental tissue than conventional acid-etching technique.
Algebras with actions and automata
Directory of Open Access Journals (Sweden)
W. Kühnel
1982-01-01
Full Text Available In the present paper we want to give a common structure theory of left action, group operations, R-modules and automata of different types defined over various kinds of carrier objects: sets, graphs, presheaves, sheaves, topological spaces (in particular: compactly generated Hausdorff spaces. The first section gives an axiomatic approach to algebraic structures relative to a base category B, slightly more powerful than that of monadic (tripleable functors. In section 2 we generalize Lawveres functorial semantics to many-sorted algebras over cartesian closed categories. In section 3 we treat the structures mentioned in the beginning as many-sorted algebras with fixed scalar or input object and show that they still have an algebraic (or monadic forgetful functor (theorem 3.3 and hence the general theory of algebraic structures applies. These structures were usually treated as one-sorted in the Lawvere-setting, the action being expressed by a family of unary operations indexed over the scalars. But this approach cannot, as the one developed here, describe continuity of the action (more general: the action to be a B-morphism, which is essential for the structures mentioned above, e.g. modules for a sheaf of rings or topological automata. Finally we discuss consequences of theorem 3.3 for the structure theory of various types of automata. The particular case of algebras with fixed natural numbers object has been studied by the authors in [23].
Algebraic Systems and Pushdown Automata
Petre, Ion; Salomaa, Arto
We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.
In vitro tooth cleaning efficacy of electric toothbrushes around brackets.
Schätzle, Marc; Sener, Beatrice; Schmidlin, Patrick R; Imfeld, Thomas; Attin, Thomas
2010-10-01
This in vitro study assessed the cleaning efficacy of different electric toothbrushes around upper incisor brackets. Standard and Mini Diamond brackets were fixed on black-stained teeth. The teeth were coated with white titanium oxide and brushed in a machine twice for 1 minute each. Twelve different brush heads with either a wiping or an oscillating-rotating action were tested. After brushing, the teeth were scanned, the black surfaces were assessed planimetrically and a modified plaque index for orthodontic patients (PIOP) was introduced. Tooth areas, which were black again after brushing indicated tooth surface contact of the filaments and were expressed as a percentage of total area. The remaining white areas around the brackets indicated 'plaque-retentive' niches. Analysis of variance was used for individual comparison of the brush types. Bonferroni/Dunn adjustment was applied for multiple testing. The Sonicare toothbrush handle with the brush head 'Compact ProResults' (81.7 per cent) and the brush head 'Standard ProResults' (80.8 per cent), as well as the sonic Waterpik toothbrush SR 800E with the standard brush head (78.2 per cent), showed statistically significantly better cleaning efficacy than all others. The poorest cleaning efficacy was observed for the oscillating-rotating Braun Oral-B Professional Care with the brush head 'Ortho' (less than 50 per cent). The planimetric findings were in correspondence with the results of the PIOP assessment. Cleaning efficacy of electric toothbrushes around brackets on upper incisors was different between the tested brushes. The PIOP was practicable, effective, and easy to use, although it has to be verified in a clinical study.
Orthodontic bracket bonding to glazed full-contour zirconia
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Ji-Young Kwak
2016-05-01
Full Text Available Objectives This study evaluated the effects of different surface conditioning methods on the bond strength of orthodontic brackets to glazed full-zirconia surfaces. Materials and Methods Glazed zirconia (except for the control, Zirkonzahn Prettau disc surfaces were pre-treated: PO (control, polishing; BR, bur roughening; PP, cleaning with a prophy cup and pumice; HF, hydrofluoric acid etching; AA, air abrasion with aluminum oxide; CJ, CoJet-Sand. The surfaces were examined using profilometry, scanning electron microscopy, and electron dispersive spectroscopy. A zirconia primer (Z-Prime Plus, Z or a silane primer (Monobond-S, S was then applied to the surfaces, yielding 7 groups (PO-Z, BR-Z, PP-S, HF-S, AA-S, AA-Z, and CJ-S. Metal bracket-bonded specimens were stored in water for 24 hr at 37℃, and thermocycled for 1,000 cycles. Their bond strengths were measured using the wire loop method (n = 10. Results Except for BR, the surface pre-treatments failed to expose the zirconia substructure. A significant difference in bond strengths was found between AA-Z (4.60 ± 1.08 MPa and all other groups (13.38 ± 2.57 - 15.78 ± 2.39 MPa, p < 0.05. For AA-Z, most of the adhesive remained on the bracket. Conclusions For bracket bonding to glazed zirconia, a simple application of silane to the cleaned surface is recommended. A zirconia primer should be used only when the zirconia substructure is definitely exposed.
Enamel Resistance to Demineralization After Bracket Debonding Using Fluoride Varnish
Vicente, Ascensión; Ortiz Ruiz, Antonio José; García López, Miriam; Martínez Beneyto, Yolanda; Bravo-González, Luis-Alberto
2017-01-01
The aim of this study was to evaluate the elemental content and morphology of enamel subjected to demineralization cycles after bracket debonding, adhesive remnant removal, and application of a fluoride varnish. 125 bovine teeth were divided into five groups (n = 25): 1) Intact enamel; 2) Intact enamel + demineralization cycles (DC); 3) Enamel after adhesive removal; 4)Enamel after adhesive removal + DC; 5) Enamel after adhesive removal + Profluorid + DC. The weight percentages of calcium (Ca...
SU(2,R)q symmetries of non-Abelian Toda theories
International Nuclear Information System (INIS)
Gomes, J.F.; Zimerman, A.H.; Sotkov, G.M.
1998-03-01
The classical and quantum algebras of a class of conformal NA-Toda models are studied. It is shown that the SL (2,R) q . Poisson brackets algebra generated by certain chiral and antichiral charges of the nonlocal currents and the global U(1) charge appears as an algebra of the symmetries of these models. (author)
Applicative Characteristics of a New Zirconia Bracket with Multiple Slots
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Koutaro Maki
2016-01-01
Full Text Available We have developed a new orthodontic bracket with three slots with lubricative properties on the working surfaces and proposed a new orthodontic treatment system employing 0.012−0.014-inch Ni-Ti arch wires. We recruited 54 patients, of which 27 received treatment with the new zirconia bracket with multiple slots system (M group, and the others received treatment with standard edge-wise appliances (control group [C group]. We compared the (1 tooth movement rate at the early stage of leveling; (2 changes in the dental arch morphology before and after leveling; and (3 pain caused by orthodontic treatment. Student’s t-test was used in all assessments. The tooth movement rate in the maxillomandibular dentition was higher in the M group. The basal arch width, anterior length, and the intercanine width in the maxillary dentition were not significantly different in the two groups; however, the intercanine width in the mandibular dentition was higher in the C group. In assessments of treatment-related pain, the visual analogue pain score was 56.0 mm and 22.6 mm in the C and M groups, respectively. A new zirconia bracket with multiple slots system provided better outcomes with respect to tooth movement rate, treatment period, and postoperative pain, thus indicating its effectiveness over conventional orthodontic systems.
Wörz-Busekros, Angelika
1980-01-01
The purpose of these notes is to give a rather complete presentation of the mathematical theory of algebras in genetics and to discuss in detail many applications to concrete genetic situations. Historically, the subject has its origin in several papers of Etherington in 1939- 1941. Fundamental contributions have been given by Schafer, Gonshor, Holgate, Reiers¢l, Heuch, and Abraham. At the moment there exist about forty papers in this field, one survey article by Monique Bertrand from 1966 based on four papers of Etherington, a paper by Schafer and Gonshor's first paper. Furthermore Ballonoff in the third section of his book "Genetics and Social Structure" has included four papers by Etherington and Reiers¢l's paper. Apparently a complete review, in par ticular one comprising more recent results was lacking, and it was difficult for students to enter this field of research. I started to write these notes in spring 1978. A first german version was finished at the end of that year. Further revision and tran...
Chirivì, Rocco; Dvornicich, Roberto
2017-01-01
Questo libro – primo di due volumi - presenta oltre 250 esercizi scelti di algebra ricavati dai compiti d'esame dei corsi di Aritmetica tenuti dagli autori all'Università di Pisa. Ogni esercizio viene presentato con una o più soluzioni accuratamente redatte con linguaggio e notazioni uniformi. Caratteristica distintiva del libro è che gli esercizi proposti sono tutti diversi uno dall'altro e le soluzioni richiedono sempre una piccola idea originale; ciò rende il libro unico nel genere. Gli argomenti di questo primo volume sono: principio d'induzione, combinatoria, congruenze, gruppi abeliani, anelli commutativi, polinomi, estensioni di campi, campi finiti. Il libro contiene inoltre una dettagliata sezione di richiami teorici e può essere usato come libro di riferimento per lo studio. Una serie di esercizi preliminari introduce le tecniche principali da usare per confrontarsi con i testi d'esame proposti. Il volume è rivolto a tutti gli studenti del primo anno dei corsi di laur ea in Matematica e Inf...