Symplectic structures and dynamical symmetry groups
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Velazquez Q, M.P.
2004-01-01
Apart from the total energy, the two-dimensional isotropic harmonic oscillator possesses three independent constants of motion which, with the standard symplectic structure, generates a dynamical symmetry group isomorphic to SU (2). We show that, by suitably redefining the symplectic structure, any of these three constants of motion can be used as a Hamiltonian, and that the remaining two, together with the total energy, generate a dynamical symmetry group isomorphic to SU (1,1). We also show that the standard energy levels of the quantum two-dimensional isotropic harmonic oscillator and their degeneracies are obtained making use of the appropriate representations of SU(1,1), provided that the canonical commutation relations are modified according to the new symplectic structure. Whereas in classical mechanics the different symplectic structures lead to equivalent formulations of the equations of motion, in quantum mechanics the modifications of the commutation relations should be accompanied by modifications in the interpretation of the formalism in order to obtain results equivalent to those found with the common relations. (Author) 12 refs
Fan, Hong-Yi; Chen, Jun-Hua
2002-08-01
We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived. The project supported by National Natural Science Foundation of China under Grant No. 10575057 and the President Foundation of the Chinese Academy of Sciences
Introduction to orthogonal, symplectic and unitary representations of finite groups
Riehm, Carl R
2011-01-01
Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics-linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms-and thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the "classical" fields-algebraically closed, rea
The endoscopic classification of representations orthogonal and symplectic groups
Arthur, James
2013-01-01
Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups G. The representations are shown to occur in families (known as global L-packets and A-packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group GL(N). The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of G
Symplectic S5 action on symplectic homotopy K3 surfaces
Indian Academy of Sciences (India)
HONGXIA LI
Introduction. Let X be a symplectic homotopy K3 surface, namely X is a closed, oriented smooth. 4-manifold homeomorphic to the standard K3 surface and admits an orientation-compatible symplectic structure. A finite group G is called a symplectic K3 group if G can be real- ized as a subgroup of the symplectic ...
Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group
International Nuclear Information System (INIS)
Morariu, B.
1997-01-01
The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin
The real symplectic groups quantum mechanics and optics
International Nuclear Information System (INIS)
Arvind; Mukunda, N.
1995-01-01
We present a utilitarian review of the family of matrix groups Sp(2n,R), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n,R). Global decomposition theorems, interesting subgroups and their generators are described. Turning to n-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and developed a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n,R) action are delineated. (author). 22 refs
Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis
Fan, Hong-Yi; Chen, Jun-Hua
2003-11-01
We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed. The project supported by National Natural Science Foundation of China under Grant No. 10575057
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Classical mechanics and symplectic geometry
International Nuclear Information System (INIS)
Souriau, J.M.
1984-11-01
The author analyzes some classical or more recent mechanics notions (force, impulse, momentum, energy, mass, action and reaction, electric charge, spin, magnetic moment, etc..) which give physical examples of various mathematical structures: symplectic and pre-symplectic varieties, groups and Lie algebra cohomology, homotopy, homology, etc.. [fr
Function theory on symplectic manifolds
Polterovich, Leonid
2014-01-01
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...
Energy Technology Data Exchange (ETDEWEB)
Voit, Kay-Michael
2008-06-16
In the first part we considered the quantum phase space in terms of noncommutative differential geometry. Following relevant literature, a short introduction to vector fields and differential forms on the differential vector space M{sub N}(C) was given. Special emphasis has been laid on the construction of a canonical symplectic form analogous to the one known from classical mechanics. The canonical choice of this form has been shown to be just the (scaled) commutator of two matrices. Using the Schwinger basis, the symplectic form derived in the first sections has been further examined by calculating concrete expressions for products of general matrices and their commutators which are, as we remember, just the symplectic form. Subsequently, a discrete analog to the continuous theory has been developed, in which the lattice of the quantum phase space forms the base space, and the Heisenberg group including the Schwinger elements is identified with the fiber space. In the continuum limit it could be shown that the discrete theory seamlessly passed into the commonly known continuous theory of connection forms on fiber bundles. The connection form and its exterior covariant derivation, the curvature form, have been calculated. It has been found that the curvature form can even be pulled back to the symplectic form by the section defined by the Schwinger elements. (orig.)
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
Hamiltonian systems (especially in increasing the stability region). Furthermore, the norm can also serve as a measure to compute the 'distance' between two symplectic maps. Now the symmetry group for the linear part ˆM for n degrees of freedom is the finite dimensional non-compact real symplectic group Sp(2n, R).
Modular geometry of the symplectic group attached to a q-level system and to multiple q-dit mixtures
Energy Technology Data Exchange (ETDEWEB)
Planat, Michel, E-mail: michel.planat@femto-st.fr [Institut FEMTO-ST, CNRS, 32 Avenue de l' Observatoire, F-25044 Besancon (France)
2011-03-01
We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors. Illustrative low dimensional examples are the quartit (q = 4) and two-qubit (q = 2{sup 2}) systems, the octit (q = 8), qubit/quartit (q = 2x4) and three-qubit (q = 2{sup 3}) systems, and so on. In the single qudit case, e.g. q = 4, 8, 12,..., one defines a bijection between the {sigma}(q) maximal commuting sets [with {sigma}[q)the sum of divisors of q] of Pauli observables and the maximal submodules of the modular ring Z{sub q}{sup 2}, that arrange into the projective line P{sub 1}(Z{sub q}) and a independent set of size {sigma}(q) - {psi}(q) [with {psi}(q) the Dedekind psi function]. In the multiple qudit case, e.g. q = 2{sup 2}, 2{sup 3}, 3{sup 2},..., the Pauli graphs rely on symplectic polar spaces such as the generalized quadrangles GQ(2,2) (if q = 2{sup 2}) and GQ(3,3) (if q = 3{sup 2}). More precisely, in dimension p{sup n} (p a prime) of the Hilbert space, the observables of the Pauli group (modulo the center) are seen as the elements of the 2n-dimensional vector space over the field F{sub p}. In this space, one makes use of the commutator to define a symplectic polar space W{sub 2n-1}(p) of cardinality {sigma}(p{sup 2n-1}), that encodes the maximal commuting sets of the Pauli group by its totally isotropic subspaces. Building blocks of W{sub 2n-1}(p) are punctured polar spaces (i.e. a observable and all maximum cliques passing to it are removed) of size given by the Dedekind psi function {psi}(p{sup 2N-1}). For multiple qudit mixtures (e.g. qubit/quartit, qubit/octit and so on), one finds multiple copies of polar spaces, ponctured polar spaces, hypercube geometries and other intricate structures. Such structures play a role in the science of quantum information.
Symplectic and hyperkähler implosion
DEFF Research Database (Denmark)
Dancer, Andrew; Doran, Brent; Kirwan, Frances
2016-01-01
We review the quiver descriptions of symplectic and hyperkähler implosion in the case of SU(n) actions. We give quiver descriptions of symplectic implosion for other classical groups, and discuss some of the issues involved in obtaining a similar description for hyperkähler implosion....
Collective coordinates on symplectic manifolds
International Nuclear Information System (INIS)
Razumov, A.V.; Taranov, A.Yu.
1981-01-01
For an arbitrary Lie group of canonical transformations on a symplectic manifold collective coordinates are introduced. They describe a motion of the dynamical system as a whole under the group transformations. Some properties of Lie group of canonical transformations are considered [ru
Classical Mechanics and Symplectic Integration
DEFF Research Database (Denmark)
Nordkvist, Nikolaj; Hjorth, Poul G.
2005-01-01
Content: Classical mechanics: Calculus of variations, Lagrange’s equations, Symmetries and Noether’s theorem, Hamilton’s equations, cannonical transformations, integrable systems, pertubation theory. Symplectic integration: Numerical integrators, symplectic integrators, main theorem on symplectic...
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Symplectic S5 action on symplectic homotopy K3 surfaces
Indian Academy of Sciences (India)
HONGXIA LI
Let X be a symplectic homotopy K3 surface and G = S5 act on X symplectically. In this paper, we give a weak classification of the G action on X by discussing the fixed-point set structure. Besides, we analyse the exoticness of smooth structures of X under the action of G. Keywords. K3 surfaces; symplectic actions; exotic ...
Isotropic isotopy and symplectic null sets
Tokieda, Tadashi F.
1997-01-01
Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups. PMID:9391037
Isotropic isotopy and symplectic null sets.
Tokieda, T F
1997-12-09
Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups.
Energy Technology Data Exchange (ETDEWEB)
Chuang, Wu-yen; Kachru, Shamit; /Stanford U., ITP /SLAC; Tomasiello, Alessandro; /Stanford U., ITP
2005-10-28
We construct a class of symplectic non-Kaehler and complex non-Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten-dimensional supergravity and KK reduction on SU(3)-structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds.
Symplectic integrators for spin systems
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
2014-06-01
We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R3. Unlike splitting methods, it is defined for all Hamiltonians and is O (3)-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretization of the spinning top.
Bianchi type A hyper-symplectic and hyper-Kaehler metrics in 4D
International Nuclear Information System (INIS)
De Andrés, L C; Fernández, M; Ivanov, S; Santisteban, J A; Ugarte, L; Vassilev, D
2012-01-01
We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-para-Kaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures of dimension 4. (paper)
Bianchi type A hyper-symplectic and hyper-K\\"ahler metrics in 4D
de Andrés, Luis C.; Fernández, Marisa; Ivanov, Stefan; Santisteban, José A.; Ugarte, Luis; Vassilev, Dimiter
2011-01-01
We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures in dimension four.
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.
On orbifold criteria for symplectic toric quotients
DEFF Research Database (Denmark)
Farsi, Carla; Herbig, Hans-Christian; Seaton, Christopher
2013-01-01
We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic...
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
Webb, G. M.; Anco, S. C.
2016-02-01
The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.
On Non-Abelian Symplectic Cutting
DEFF Research Database (Denmark)
Martens, Johan; Thaddeus, Michael
2012-01-01
We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro......-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors....
Elementary symplectic topology and mechanics
Cardin, Franco
2015-01-01
This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in...
Symplecticity in Beam Dynamics: An Introduction
Energy Technology Data Exchange (ETDEWEB)
Rees, John R
2003-06-10
A particle in a particle accelerator can often be considered a Hamiltonian system, and when that is the case, its motion obeys the constraints of the Symplectic Condition. This tutorial monograph derives the condition from the requirement that a canonical transformation must yield a new Hamiltonian system from an old one. It then explains some of the consequences of symplecticity and discusses examples of its applications, touching on symplectic matrices, phase space and Liouville's Theorem, Lagrange and Poisson brackets, Lie algebra, Lie operators and Lie transformations, symplectic maps and symplectic integrators.
Examples and counter-examples of log-symplectic manifolds
Cavalcanti, Gil R.
We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably, we show that several symplectic manifolds do not admit bona fide log-symplectic structures and several bona fide log-symplectic manifolds do not admit symplectic
Symplectic and trigonometrically fitted symplectic methods of second and third order
International Nuclear Information System (INIS)
Monovasilis, Th.; Simos, T.E.
2006-01-01
The numerical integration of Hamiltonian systems by symplectic and trigonometrically symplectic method is considered in this Letter. We construct new symplectic and trigonometrically symplectic methods of second and third order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis
Symplectic maps for accelerator lattices
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.; Gabella, W.
1988-05-01
We describe a method for numerical construction of a symplectic map for particle propagation in a general accelerator lattice. The generating function of the map is obtained by integrating the Hamilton-Jacobi equation as an initial-value problem on a finite time interval. Given the generating function, the map is put in explicit form by means of a Fourier inversion technique. We give an example which suggests that the method has promise. 9 refs., 9 figs
Symplectic and semiclassical aspects of the Schläfli identity
Hedeman, Austin; Kur, Eugene; Littlejohn, Robert G.; Haggard, Hal M.
2015-03-01
The Schläfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, three-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian manifolds related to the Schläfli identity, including several versions of a Lagrangian manifold of tetrahedra, are discussed. Semiclassical interpretations of the various steps are provided. Possible generalizations to three-dimensional spaces of constant (nonzero) curvature, involving Poisson-Lie groups and q-deformed spin networks, are discussed.
Gravitational descendants in symplectic field theory
Fabert, O.
2011-01-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic
A homotopy classification of symplectic immersions
International Nuclear Information System (INIS)
Datta, M.
1995-11-01
The principal result of this paper is a theorem on the C 0 dense parametric h-principle of symplectic immersions. In particular, it is shown that symplectic immersions satisfy this principle in the space of continuous maps f of (M,ω) onto (N,σ) which pull back the cohomology class of σ onto that of ω. 5 refs
The Maslov index in symplectic Banach spaces
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces...
Symplectic geometry of constrained optimization
Agrachev, Andrey A.; Beschastnyi, Ivan Yu.
2017-11-01
In this paper, we discuss geometric structures related to the Lagrange multipliers rule. The practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows one to effectively do it even for very degenerate problems with complicated constraints. The main geometric and analytic tool is an appropriately rearranged Maslov index. We try to emphasize the geometric framework and omit analytic routine. Proofs are often replaced with informal explanations, but a well-trained mathematician will easily rewrite them in a conventional way. We believe that Vladimir Arnold would approve of such an attitude.
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
Generalized reciprocity principle for discrete symplectic systems
Directory of Open Access Journals (Sweden)
Julia Elyseeva
2015-12-01
Full Text Available This paper studies transformations for conjoined bases of symplectic difference systems $Y_{i+1}=\\mathcal S_{i}Y_{i}$ with the symplectic coefficient matrices $\\mathcal S_i.$ For an arbitrary symplectic transformation matrix $P_{i}$ we formulate most general sufficient conditions for $\\mathcal S_{i},\\, P_{i}$ which guarantee that $P_{i}$ preserves oscillatory properties of conjoined bases $Y_{i}.$ We present examples which show that our new results extend the applicability of the discrete transformation theory.
Multiparametric quantum symplectic phase space
International Nuclear Information System (INIS)
Parashar, P.; Soni, S.K.
1992-07-01
We formulate a consistent multiparametric differential calculus on the quadratic coordinate algebra of the quantum vector space and use this as a tool to obtain a deformation of the associated symplectic phase space involving n(n-1)/2+1 deformation parameters. A consistent calculus on the relation subspace is also constructed. This is achieved with the help of a restricted ansatz and solving the consistency conditions to directly arrive at the main commutation structures without any reference to the R-matrix. However, the non-standard R-matrices for GL r,qij (n) and Sp r,qij (2n) can be easily read off from the commutation relations involving coordinates and derivatives. (author). 9 refs
Symplectic topology of integrable Hamiltonian systems
International Nuclear Information System (INIS)
Nguyen Tien Zung.
1993-08-01
We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs
How Wigner functions transform under symplectic maps
International Nuclear Information System (INIS)
Dragt, A.J.; Habib, S.
1998-01-01
It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are quantum corrections whose ℎ → 0 limit may be very complicated. Examples of the behavior of Wigner functions in the ℎ → 0 limit are given in order to examine to what extent the corresponding Liouville densities are recovered
How Wigner functions transform under symplectic maps
Energy Technology Data Exchange (ETDEWEB)
Dragt, A.J. [Univ. of Maryland, College Park, MD (United States). Center for Theoretical Physics; Habib, S. [Los Alamos National Lab., NM (United States). Theoretical Div.
1998-05-16
It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are quantum corrections whose {Dirac_h} {r_arrow} 0 limit may be very complicated. Examples of the behavior of Wigner functions in the {Dirac_h} {r_arrow} 0 limit are given in order to examine to what extent the corresponding Liouville densities are recovered.
Symplectic Yang-Mills theory, Ricci tensor, and connections
Habermann, Katharina; Habermann, Lutz; Rosenthal, Paul
2006-01-01
A Yang-Mills theory in a purely symplectic framework is developed. The corresponding Euler-Lagrange equations are derived and first integrals are given. We relate the results to the work of Bourgeois and Cahen on preferred symplectic connections.
Symplectic method in quantum cosmology
International Nuclear Information System (INIS)
Silva, E. V. Correa; Monerat, G. A.; Oliveira-Neto, G.; Neves, C.; Ferreira Filho, L. G.
2009-01-01
In the present work, we study the quantum cosmology description of Friedmann-Robertson-Walker models in the presence of a generic perfect fluid and a cosmological constant, which may be positive or negative. We work in Schutz's variational formalism and the three-dimensional spatial sections may have positive, negative, or zero constant curvature. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we follow references [Edesio M. Barbosa, Jr. and Nivaldo A. Lemos, Gen. Relativ. Gravit. 38, 1609 (2006).][Edesio M. Barbosa, Jr. and Nivaldo A. Lemos, Phys. Rev. D 78, 023504 (2008).] and introduce new phase space variables. We explicitly demonstrate, using the symplectic method, that the transformation leading from the old set of variables to the new one is canonical.
Symplectic method in quantum cosmology
Silva, E. V. Corrêa; Monerat, G. A.; Oliveira-Neto, G.; Neves, C.; Filho, L. G. Ferreira
2009-08-01
In the present work, we study the quantum cosmology description of Friedmann-Robertson-Walker models in the presence of a generic perfect fluid and a cosmological constant, which may be positive or negative. We work in Schutz’s variational formalism and the three-dimensional spatial sections may have positive, negative, or zero constant curvature. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we follow references [Edésio M. Barbosa, Jr. and Nivaldo A. Lemos, Gen. Relativ. Gravit. 38, 1609 (2006).GRGVA80001-770110.1007/s10714-006-0333-y][Edésio M. Barbosa, Jr. and Nivaldo A. Lemos, Phys. Rev. DPRVDAQ1550-7998 78, 023504 (2008).10.1103/PhysRevD.78.023504] and introduce new phase space variables. We explicitly demonstrate, using the symplectic method, that the transformation leading from the old set of variables to the new one is canonical.
An algorithm for symplectic implicit Taylor-map tracking
International Nuclear Information System (INIS)
Yan, Y.; Channell, P.; Syphers, M.
1992-10-01
An algorithm has been developed for converting an ''order-by-order symplectic'' Taylor map that is truncated to an arbitrary order (thus not exactly symplectic) into a Courant-Snyder matrix and a symplectic implicit Taylor map for symplectic tracking. This algorithm is implemented using differential algebras, and it is numerically stable and fast. Thus, lifetime charged-particle tracking for large hadron colliders, such as the Superconducting Super Collider, is now made possible
Composite particles and symplectic (Semi-) groups
International Nuclear Information System (INIS)
Kramer, P.
1978-01-01
Nuclear composits particle dynamics is intimately related to the fermion character of nucleons. This property is implemented via the permutational structure of nuclear states, leading to the concept of exchange and to the quantum number of the orbital partition. We review Weyl operators and representations of linear canonical transformations in Bargmann Hilbert space. In section 4 we use canonical transformations to describe the general n-body dynamics. In section 5 we derive the composite particle dynamics and discuss an algorithm to obtain the interaction of composite particles whose constituents are assumed to be in harmonic oscillator states. As a first example we treat in section 6 composite particles with unexcited internal oscillator states. In section 7 we deal with composite particles of internal oscillator shell configurations. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Zhou, Weien, E-mail: weienzhou@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China)
2017-08-01
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.
International Nuclear Information System (INIS)
Cui, Jianbo; Hong, Jialin; Liu, Zhihui; Zhou, Weien
2017-01-01
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.
Characterization and solvability of quasipolynomial symplectic mappings
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito [ESCET (Edificio Departamental II), Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933-Mostoles-Madrid (Spain); Brenig, Leon [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles, Campus Plaine, CP 231, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2004-02-13
Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, physics, chemistry or economy. In addition, QP mappings are a natural discrete-time analogue of the continuous QP systems, which have been extensively used in different pure and applied domains. After presenting the basic definitions and properties of QP mappings in a previous paper, the purpose of this work is to focus on their characterization by considering the existence of symplectic QP mappings. In what follows such QP symplectic maps are completely characterized. Moreover, use of the QP formalism can be made in order to demonstrate that all QP symplectic mappings have an analytical solution that is explicitly and generally constructed. Examples are given.
DEFF Research Database (Denmark)
Nest, Ryszard; Tsygan, Boris
2001-01-01
Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids......, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem....
Cohomology theories on locally conformal symplectic manifolds
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van; Vanžura, Jiří
2015-01-01
Roč. 19, č. 1 (2015), s. 45-82 ISSN 1093-6106 Institutional support: RVO:67985840 Keywords : locally conformal symplectic manifold * Lichnerowicz-Novikov cohomology * primitive cohomology Subject RIV: BA - General Mathematics Impact factor: 0.722, year: 2015 http://www.intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0019/0001/a003/
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced. Keywords. Invariant metric; symplectic maps; performance optimization. PACS Nos 05.45. ...... [7] A Nijenhuis and H S Wilf, Computational algorithms for computers and calculators (Academic. Press, New ...
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we ...
Symplectic symmetry in the nuclear shell model
French, J.B.
The nature of the general two-particle interaction which is compatible with symplectic symmetry in the jj coupling shell model is investigated. The essential result is that, to within an additive constant and an additive multiple of T2, the interaction should have the form of a sum of scalar
Symplectic integrators with adaptive time steps
Richardson, A. S.; Finn, J. M.
2012-01-01
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper, we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, Δ = Δ(t). In this case, backward error analysis shows that while the algorithms remain symplectic, parametric instabilities may arise because of resonance between oscillations of Δ(t) and the orbital motion. In the second category the time step is a function of phase space variables Δ = Δ(q, p). In this case, the system of equations to be solved is analyzed by introducing a new time variable τ with dt = Δ(q, p) dτ. The transformed equations are no longer in Hamiltonian form, and thus do not benefit from integration methods which would be symplectic for Hamiltonian systems. We analyze two methods for integrating the transformed equations which do, however, preserve the structure of the original equations. The first is an extended phase space method, which has been successfully used in previous studies of adaptive time step symplectic integrators. The second, novel, method is based on a non-canonical mixed-variable generating function. Numerical trials for both of these methods show good results, without parametric instabilities or spurious growth or damping. It is then shown how to adapt the time step to an error estimate found by backward error analysis, in order to optimize the time-stepping scheme. Numerical results are obtained using this formulation and compared with other time-stepping schemes for the extended phase space symplectic method.
Directory of Open Access Journals (Sweden)
Shangdi Chen
2014-01-01
Full Text Available Multisender authentication codes allow a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message. In this paper, we construct multisender authentication codes with sequential model from symplectic geometry over finite fields, and the parameters and the maximum probabilities of deceptions are also calculated.
QCD gauge symmetries through Faddeev-Jackiw symplectic method
International Nuclear Information System (INIS)
Abreu, E.M.C.; Mendes, A.C.R.; Neves, C.; Oliveira, W.; Silva, R.C.N.
2013-01-01
Full text: The FJ method is an approach that is geometrically motivated. It is based on the symplectic structure of the phase space. The first-order characteristic allows to obtain the Hamiltonian equations of motion from a variational principle. Its geometric structure of the Hamiltonian phase-space will be carried out directly from the equations of motion via the inverse of the so-called symplectic two-form, if the inverse exists. Few years after its publication, the FJ formalism was extended and through the years it has been applied to different systems. Gauge invariance is one of the most well established concepts in theoretical physics and it is one of the main ingredients in Standard Model theory. However, we can ask if it could have an alternative origin connected to another theory or principle. With this motivation in mind we will show in this paper that gauge invariance could be considered an emergent concept having its origin in the algebraic formalism of a well known method that deals with constrained systems, namely, the Faddeev-Jackiw (FJ) technique. Of course the gauge invariance idea is older than FJ's, but the results obtained here will show that the connection between both will prove that SU(3) and SU(3) X SU(2) X U(1) gauge groups, which are fundamental to important theories like QCD and Standard Model, can be obtained through FJ formalism. (author)
Symplectic models for general insertion devices
International Nuclear Information System (INIS)
Wu, Y.; Forest, E.; Robin, D. S.; Nishimura, H.; Wolski, A.; Litvinenko, V. N.
2001-01-01
A variety of insertion devices (IDs), wigglers and undulators, linearly or elliptically polarized,are widely used as high brightness radiation sources at the modern light source rings. Long and high-field wigglers have also been proposed as the main source of radiation damping at next generation damping rings. As a result, it becomes increasingly important to understand the impact of IDs on the charged particle dynamics in the storage ring. In this paper, we report our recent development of a general explicit symplectic model for IDs with the paraxial ray approximation. High-order explicit symplectic integrators are developed to study real-world insertion devices with a number of wiggler harmonics and arbitrary polarizations
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 ...
The Maslov index in weak symplectic functional analysis
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
2013-01-01
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach...... spaces. We derive basic properties of this Maslov index and emphasize the new features appearing....
Lorentz covariant canonical symplectic algorithms for dynamics of charged particles
Wang, Yulei; Liu, Jian; Qin, Hong
2016-12-01
In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSAs) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of a discrete symplectic structure and the Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which are difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when the Lorentz factor varies.
A symplectic framework for field theories
International Nuclear Information System (INIS)
Kijowski, J.; Tulczyjew, W.M.
1979-01-01
These notes are concerned with the formulation of a new conceptual framework for classical field theories. Although the formulation is based on fairly advanced concepts of symplectic geometry these notes cannot be viewed as a reformulation of known structures in more rigorous and elegant torns. Our intention is rather to communicate to theoretical physicists a set of new physical ideas. We have chosen for this purpose the language of local coordinates which is more elementary and more widely known than the abstract language of modern differntial geometry. Our emphasis is directed more to physical intentions than to mathematical vigour. We start with a symplectic analysis of staties. Both discrete and continuous systems are considered on a largely intuitive level. The notion of reciprocity and potentiality of the theory is discussed. Chapter II is a presentation of particle dynamics together with more rigorous definitions of the geometric structure. Lagrangian-Submanifolds and their generating function 3 are defined and the time evolution of particle states is studied. Chapter II form the main part of these notes. Here we describe the construction of canonical momenta and discuss the field dynamics in finite domains of space-time. We also establish the relation between our symplectic framework and the geometric formulation of the calculus of variations of multiple integrals. In the following chapter we give a few examples of field theories selected to illustrate various features of the new approach. A new formulation of the theory of gravity consists of using the affine connection in space-time as the field configuration. In the past section we present an analysis of hydrodynamics within our framework which reveals a formal analogy with electrodynamics. The discovery of potentials for hydrodynamics and the subsequent formulation of a variational principle provides an excellent example for the fruitfulness of the new approach to field theory. A short review of
A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS
International Nuclear Information System (INIS)
Quinn, Thomas; Barnes, Rory; Perrine, Randall P.; Richardson, Derek C.
2010-01-01
Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV, and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of particle positions.
J-holomorphic curves and symplectic topology
McDuff, Dusa
2012-01-01
The theory of J-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was also one of the main inspirations for the creation of Floer homology. In mathematical physics, it provides a natural context in which to define Gromov-Witten invariants and quantum cohomology, two important ingredients of the mirror symmetry conjecture. The main goal of this book is to establish the fundamental theorems of the subject in full and rigorous detail. In particular, the book contains comple
The GL(1 vertical stroke 1)-symplectic fermion correspondence
Energy Technology Data Exchange (ETDEWEB)
Creutzig, Thomas; Roenne, Peter B.
2008-12-15
In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)
Transversity results and computations in symplectic field theory
Energy Technology Data Exchange (ETDEWEB)
Fabert, Oliver
2008-02-21
Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M{sub {phi}} of symplectic manifolds (M,{omega}{sub M}) with symplectomorphisms {phi}. While the cylindrical contact homology of M{sub {phi}} is given by the Floer homologies of powers of {phi}, the other algebraic invariants of symplectic field theory for M{sub {phi}} provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian {phi} we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M{sub {phi}} {approx_equal} S{sup 1} x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic
Transversity results and computations in symplectic field theory
International Nuclear Information System (INIS)
Fabert, Oliver
2008-01-01
Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M φ of symplectic manifolds (M,ω M ) with symplectomorphisms φ. While the cylindrical contact homology of M φ is given by the Floer homologies of powers of φ, the other algebraic invariants of symplectic field theory for M φ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian φ we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M φ ≅ S 1 x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic field theory are established, our result implies that the
Symplectic and multisymplectic schemes with the simple finite element method
International Nuclear Information System (INIS)
Zhen Liu; Bai Yongqiang; Li Qisheng; Wu Ke
2003-01-01
We study the numerical scheme of elliptic equations by the finite element method. With the special finite element domain, we can find that the scheme can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case. Then we consider the discrete variational principle with the finite element method in the corresponding Lagrangian formalism for classical mechanics and field theory and get the symplectic or multisymplectic scheme of the Euler-Lagrangian equation
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.
Light Nuclei in the Framework of the Symplectic No-Core Shell Model
Energy Technology Data Exchange (ETDEWEB)
Draayer, Jerry P.; Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; /Louisiana State U.; Vary, James P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-04-02
A symplectic no-core shell model (Sp-NCSM) is constructed with the goal of extending the ab-initio NCSM to include strongly deformed higher-oscillator-shell configurations and to reach heavier nuclei that cannot be studied currently because the spaces encountered are too large to handle, even with the best of modern-day computers. This goal is achieved by integrating two powerful concepts: the ab-initio NCSM with that of the Sp(3,R) {contains} SU(3) group-theoretical approach. The NCSM uses modern realistic nuclear interactions in model spaces that consists of many-body configurations up to a given number of {h_bar}{Upsilon} excitations together with modern high-performance parallel computing techniques. The symplectic theory extends this picture by recognizing that when deformed configurations dominate, which they often do, the model space can be better selected so less relevant low-lying {h_bar}{Upsilon} configurations yield to more relevant high-lying {h_bar}{Upsilon} configurations, ones that respect a near symplectic symmetry found in the Hamiltonian. Results from an application of the Sp-NCSM to light nuclei are compared with those for the NCSM and with experiment.
Energy conservation with non-symplectic methods: examples and counter-examples
Faou, Erwan; Hairer, Ernst; Pham, Truong-Linh
2004-01-01
Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented.
Generalized Zeros of Symplectic Difference System and of Its Reciprocal System
Directory of Open Access Journals (Sweden)
Pechancová Šárka
2011-01-01
Full Text Available Abstract We establish a conjugacy criterion for a symplectic difference system by means of the concept of a phase of any basis of this symplectic system. We also describe a construction of a symplectic difference system whose recessive solution has the prescribed number of generalized zeros in .
Symplectic ab initio no-core shell model
Energy Technology Data Exchange (ETDEWEB)
Draayer, J. P.; Dytrych, T.; Sviratcheva, K. D.; Bahri, C. [Department of Physics and Astronomy, Lousiana State University, Baton Rouge, 70803 Lousiana (United States); Vary, J. P. [Department of Physics and Astronomy, Iowa State University, Ames, 50011 Iowa (United States)
2008-12-15
The present study confirms the significance of the symplectic Sp(3,R) symmetry in nuclear dynamics as unveiled, for the first time, by examinations of realistic nucleon-nucleon interactions as well as of eigenstates calculated in the framework of the ab initio No-Core Shell Model (NCSM). The results reveal that the NCSM wave functions for light nuclei highly overlap (at the {approx} 90% level) with only a few of the most deformed Sp(3,R)-symmetric basis states. This points to the possibility of achieving convergence of higher-lying collective modes and reaching heavier nuclei by expanding the NCSM basis space beyond its current limits through Sp(3,R) basis states. Furthermore the symplectic symmetry is found to be favored by the JISP 16 and CD-Bonn realistic nucleon-nucleon interactions, which points to a more fundamental origin of the symplectic symmetry. (Author)
Canonical and symplectic analysis for three dimensional gravity without dynamics
International Nuclear Information System (INIS)
Escalante, Alberto; Osmart Ochoa-Gutiérrez, H.
2017-01-01
In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev–Jackiw symplectic approach is developed; we report the complete set of Faddeev–Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev–Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw and Dirac’s formalism are briefly discussed. - Highlights: • We report the symplectic analysis for three dimensional gravity without dynamics. • We report the Faddeev–Jackiw constraints. • A pure Dirac’s analysis is performed. • The complete structure of Dirac’s constraints is reported. • We show that symplectic and Dirac’s brackets coincide to each other.
Canonical and symplectic analysis for three dimensional gravity without dynamics
Energy Technology Data Exchange (ETDEWEB)
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48 72570, Puebla, Pue. (Mexico); Osmart Ochoa-Gutiérrez, H. [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado postal 1152, 72001 Puebla, Pue. (Mexico)
2017-03-15
In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev–Jackiw symplectic approach is developed; we report the complete set of Faddeev–Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev–Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw and Dirac’s formalism are briefly discussed. - Highlights: • We report the symplectic analysis for three dimensional gravity without dynamics. • We report the Faddeev–Jackiw constraints. • A pure Dirac’s analysis is performed. • The complete structure of Dirac’s constraints is reported. • We show that symplectic and Dirac’s brackets coincide to each other.
Explicit K-symplectic algorithms for charged particle dynamics
International Nuclear Information System (INIS)
He, Yang; Zhou, Zhaoqi; Sun, Yajuan; Liu, Jian; Qin, Hong
2017-01-01
We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.
Proton spin tracking with symplectic integration of orbit motion
Energy Technology Data Exchange (ETDEWEB)
Luo, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States); Dutheil, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States); Huang, H. [Brookhaven National Lab. (BNL), Upton, NY (United States); Meot, F. [Brookhaven National Lab. (BNL), Upton, NY (United States); Ranjbar, V. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2015-05-03
Symplectic integration had been adopted for orbital motion tracking in code SimTrack. SimTrack has been extensively used for dynamic aperture calculation with beam-beam interaction for the Relativistic Heavy Ion Collider (RHIC). Recently proton spin tracking has been implemented on top of symplectic orbital motion in this code. In this article, we will explain the implementation of spin motion based on Thomas-BMT equation, and the benchmarking with other spin tracking codes currently used for RHIC. Examples to calculate spin closed orbit and spin tunes are presented too.
Major shell centroids in the symplectic collective model
International Nuclear Information System (INIS)
Draayer, J.P.; Rosensteel, G.; Tulane Univ., New Orleans, LA
1983-01-01
Analytic expressions are given for the major shell centroids of the collective potential V(#betta#, #betta#) and the shape observable #betta# 2 in the Sp(3,R) symplectic model. The tools of statistical spectroscopy are shown to be useful, firstly, in translating a requirement that the underlying shell structure be preserved into constraints on the parameters of the collective potential and, secondly, in giving a reasonable estimate for a truncation of the infinite dimensional symplectic model space from experimental B(E2) transition strengths. Results based on the centroid information are shown to compare favorably with results from exact calculations in the case of 20 Ne. (orig.)
The shallow water equations: conservation laws and symplectic geometry
Akyildiz, Yilmaz
1987-01-01
We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relative to a symplectic form introduced by Manin.
Relative symplectic caps, 4-genus and fibered knots
Indian Academy of Sciences (India)
Bowden uses Gay's symplectic 2-handles (see. [10]) to ... book. For a curve γ on , we denote the positive (right handed) Dehn twist along γ by. Dγ . Let ξst denote the unique (up to isotopy) tight contact structure on S3 and ωst denote ... If K is a quasipositive fibered knot such that the corresponding open book has monodromy.
Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices
Ran, A.C.M.; Mehl, Ch.; Mehrmann, V.; Rodman, L.
2009-01-01
Lagrangian invariant subspaces for symplectic matrices play an important role in the numerical solution of discrete time, robust and optimal control problems. The sensitivity (perturbation) analysis of these subspaces, however, is a difficult problem, in particular, when the eigenvalues are on or
Relative symplectic caps, 4-genus and fibered knots
Indian Academy of Sciences (India)
need to take care of the following two issues. (1) Firstly, the resulting manifold should have ... complex structure on the fiber given by multiplication by i. Let ω denote the symplectic form on the total space given ... We construct the function φ by solving the Dirichlet problem φ = f on with boundary value 1, so that f is a positive ...
A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed Flow
Dai, Song
2013-01-01
Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.
Deformations of coisotropic submanifolds in locally conformal symplectic manifolds
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van; Oh, Y.-G.
2016-01-01
Roč. 20, č. 3 (2016), s. 553-596 ISSN 1093-6106 Institutional support: RVO:67985840 Keywords : locally conformal symplectic manifold * coisotropic submanifold * b-twisted differential * bulk deformation Subject RIV: BA - General Mathematics Impact factor: 0.895, year: 2016 http://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0020/0003/a007/index.html
Associated quantum vector bundles and symplectic structure on a quantum space
International Nuclear Information System (INIS)
Coquereaux, R.; Garcia, A.O.; Trinchero, R.
2000-01-01
We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a Hopf algebra H are particular instances of these extensions, and in these cases we are able to define a differential calculus over their associated vector bundles without requiring the use of a (bicovariant) differential structure over H. Moreover, if H is coquasitriangular, it coacts naturally on the associated bundle, and the differential structure is covariant. We apply this construction to the case of the finite quotient of the SL q (2) function Hopf algebra at a root of unity (q 3 = 1) as the structure group, and a reduced 2-dimensional quantum plane as both the 'base manifold' and fibre, getting an algebra which generalizes the notion of classical phase space for this quantum space. We also build explicitly a differential complex for this phase space algebra, and find that levels 0 and 2 support a (co)representation of the quantum symplectic group. On this phase space we define vector fields, and with the help of the Sp q structure we introduce a symplectic form relating 1-forms to vector fields. This leads naturally to the introduction of Poisson brackets, a necessary step to do 'classical' mechanics on a quantum space, the quantum plane. (author)
Period mappings with applications to symplectic complex spaces
Kirschner, Tim
2015-01-01
Extending Griffiths’ classical theory of period mappings for compact Kähler manifolds, this book develops and applies a theory of period mappings of “Hodge-de Rham type” for families of open complex manifolds. The text consists of three parts. The first part develops the theory. The second part investigates the degeneration behavior of the relative Frölicher spectral sequence associated to a submersive morphism of complex manifolds. The third part applies the preceding material to the study of irreducible symplectic complex spaces. The latter notion generalizes the idea of an irreducible symplectic manifold, dubbed an irreducible hyperkähler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicely.
Symplectic manifolds with no Kähler structure
Tralle, Aleksy
1997-01-01
This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.
Symplectic tomography of nonclassical states of trapped ion
International Nuclear Information System (INIS)
Man'ko, O.
1996-03-01
The marginal distribution for two types of nonclassical states of trapped ion - for squeezed and correlated states and for squeezed even and odd coherent states (squeezed Schroedinger cat states) is studied. The obtained marginal distribution for the two types of states is shown to satisfy classical dynamical equation equivalent to standard quantum evolution equation for density matrix (wave function) derived in symplectic tomography scheme. (author). 20 refs
Hydrodynamic Covariant Symplectic Structure from Bilinear Hamiltonian Functions
Directory of Open Access Journals (Sweden)
Capozziello S.
2005-07-01
Full Text Available Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture. This feature is gauge free and it seems a deep link common to all interactions, electromagnetism and gravity included. This scheme could lead toward a full canonical quantization.
Symplectic symmetry and the ab initio no-core shell model
Energy Technology Data Exchange (ETDEWEB)
Draayer, J.P.; Dytrych, T.; Sviratcheva, K.D.; Bahri, C. [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Vary, J.P. [Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 (United States)
2007-12-15
The symplectic symmetry of eigenstates for the O{sub gs}{sup +} in {sup 16}O and the O{sub gs}{sup +}s and lowest 2{sup +} and 4{sup +} configurations of {sup 12}C that are well-converged within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 85-90% level onto very few symplectic representations including the most deformed configuration, which confirms the importance of a symplectic no-core shell model and reaffirms the relevance of the Elliott SU(3) model upon which the symplectic scheme is built. (Author)
Symplectic Symmetry and the Ab Initio No-Core Shell Model
Energy Technology Data Exchange (ETDEWEB)
Draayer, Jerry P.; Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; /Louisiana State U.; Vary, James P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-03-14
The symplectic symmetry of eigenstates for the 0{sub gs}{sup +} in {sup 16}O and the 0{sub gs}{sup +} and lowest 2{sup +} and 4{sup +} configurations of {sup 12}C that are well-converged within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 85-90% level onto very few symplectic representations including the most deformed configuration, which confirms the importance of a symplectic no-core shell model and reaffirms the relevance of the Elliott SU(3) model upon which the symplectic scheme is built.
Symmetric integrable-polynomial factorization for symplectic one-turn-map tracking
International Nuclear Information System (INIS)
Shi, Jicong
1993-01-01
It was found that any homogeneous polynomial can be written as a sum of integrable polynomials of the same degree which Lie transformations can be evaluated exactly. By utilizing symplectic integrators, an integrable-polynomial factorization is developed to convert a symplectic map in the form of Dragt-Finn factorization into a product of Lie transformations associated with integrable polynomials. A small number of factorization bases of integrable polynomials enable one to use high order symplectic integrators so that the high-order spurious terms can be greatly suppressed. A symplectic map can thus be evaluated with desired accuracy
Construction of Large Period Symplectic Maps by Interpolative Methods
Energy Technology Data Exchange (ETDEWEB)
Warnock, Robert; Cai, Yunhai; /SLAC; Ellison, James A.; /New Mexico U.
2009-12-17
The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S, given in terms of interpolatory functions. Two ways to find the generator are considered: (1) Find its gradient from tracking data, then the generator itself as a line integral. (2) Compute the action integral on many orbits. A test of method (1) has been made in a difficult example: a full turn map for an electron ring with strong nonlinearity near the dynamic aperture. The method succeeds at fairly large amplitudes, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. For a generally applicable algorithm we propose method (2), realized with meshless interpolation methods.
Global symplectic structure-preserving integrators for spinning compact binaries
Zhong, Shuang-Ying; Wu, Xin; Liu, San-Qiu; Deng, Xin-Fa
2010-12-01
This paper deals mainly with the application of the second-order symplectic implicit midpoint rule and its symmetric compositions to a post-Newtonian Hamiltonian formulation with canonical spin variables in relativistic compact binaries. The midpoint rule, as a basic algorithm, is directly used to integrate the completely canonical Hamiltonian system. On the other hand, there are symmetric composite methods based on a splitting of the Hamiltonian into two parts: the Newtonian part associated with a Kepler motion, and a perturbation part involving the orbital post-Newtonian and spin contributions, where the Kepler flow has an analytic solution and the perturbation can be calculated by the midpoint rule. An example is the second-order mixed leapfrog symplectic integrator with one stage integration of the perturbation flow and two semistage computations of the Kepler flow at every integration step. Also, higher-order composite methods such as the Forest-Ruth fourth-order symplectic integrator and its optimized algorithm are applicable. Various numerical tests including simulations of chaotic orbits show that the mixed leapfrog integrator is always superior to the midpoint rule in energy accuracy, while both of them are almost equivalent in computational efficiency. Particularly, the optimized fourth-order algorithm compared with the mixed leapfrog scheme provides good precision and needs no expensive additional computational time. As a result, it is worth performing a more detailed and careful examination of the dynamical structure of chaos and order in the parameter windows and phase space of the binary system.
Symplectic potentials and resolved Ricci-flat ACG metrics
International Nuclear Information System (INIS)
Balasubramanian, Aswin K.; Govindarajan, Suresh; Gowdigere, Chethan N.
2007-07-01
We pursue the symplectic description of toric Kaehler manifolds. There exists a general local classification of metrics on toric Kaehler manifolds equipped with Hamiltonian two-forms due to Apostolov, Calderbank and Gauduchon(ACG). We derive the symplectic potential for these metrics. Using a method due to Abreu, we relate the symplectic potential to the canonical potential written by Guillemin. This enables us to recover the moment polytope associated with metrics and we thus obtain global information about the metric. We illustrate these general considerations by focusing on six-dimensional Ricci flat metrics and obtain Ricci-flat metrics associated with real cones over L pqr and Y pq manifolds. The metrics associated with cones over Y pq manifolds turn out to be partially resolved with two blow-up parameters taking special (nonzero) values. For a fixed Y pq manifold, we find explicit metrics for several inequivalent blow-ups parametrised by a natural number k in the range 0 3 /Z 3 also fit the ACG classification. (author)
Examples of integrable and non-integrable systems on singular symplectic manifolds
Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva
2017-05-01
We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.
A Symplectic Beam-Beam Interaction with Energy Change
Energy Technology Data Exchange (ETDEWEB)
Moshammer, Herbert
2003-07-14
The performance of many colliding storage rings is limited by the beam-beam interaction. A particle feels a nonlinear force produced by the encountering bunch at the collision. This beam-beam force acts mainly in the transverse directions so that the longitudinal effects have scarcely been studied, except for the cases of a collision with a crossing angle. Recently, however, high luminosity machines are being considered where the beams are focused extensively at the interaction point (IP) so that the beam sizes can vary significantly within the bunch length. Krishnagopal and Siemann have shown that they should not neglect the bunch length effect in this case. The transverse kick depends on the longitudinal position as well as on the transverse position. If they include this effect, however, from the action-reaction principle, they should expect, at the same time, an energy change which depends on the transverse coordinates. Such an effect is reasonably understood from the fact that the beam-beam force is partly due to the electric field, which can change the energy. The action-reaction principle comes from the symplecticity of the reaction: the electromagnetic influence on a particle is described by a Hamiltonian. The symplecticity is one of the most fundamental requirements when studying the beam dynamics. A nonsymplectic approximation can easily lead to unphysical results. In this paper, they propose a simple, approximately but symplectic mapping for the beam-beam interaction which includes the energy change as well as the bunch-length effect. In the next section, they propose the mapping in a Hamiltonian form, which directly assures its symplecticity. Then in section 3, they study the nature of the mapping by interpreting its consequences. The mapping itself is quite general and can be applied to any distribution function. They show in Section 4 how it appears when the distribution function is a Gaussian in transverse directions. The mapping is applied to the
Differential and symplectic topology of knots and curves
Tabachnikov, S
1999-01-01
This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory (""quantum"" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is
Method to render second order beam optics programs symplectic
International Nuclear Information System (INIS)
Douglas, D.; Servranckx, R.V.
1984-10-01
We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs
Spectra and spectral correlations of microwave graphs with symplectic symmetry
Rehemanjiang, A.; Richter, M.; Kuhl, U.; Stöckmann, H.-J.
2018-02-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014), 10.1209/0295-5075/107/50004], a microwave graph with antiunitary symmetry T obeying T2=-1 has been realized, thus mimicking a spin-1/2 system. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level-spacing distribution of the Kramers doublets agreed with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition, we studied the random matrix equivalents of the used graphs both analytically and numerically. Here small deviations from the GSE level-spacing distribution were found, too small to be seen in the experiment but clearly visible in the simulations. Furthermore, results on the two-point correlation function, the spectral form factor, the number variance, and the spectral rigidity are presented, as well as on the transition from Gaussian symplectic to Gaussian orthogonal statistics by continuously changing T from T2=-1 to T2=1 .
Symplectic Hamiltonian HDG methods for wave propagation phenomena
Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
2017-12-01
We devise the first symplectic Hamiltonian hybridizable discontinuous Galerkin (HDG) methods for the acoustic wave equation. We discretize in space by using a Hamiltonian HDG scheme, that is, an HDG method which preserves the Hamiltonian structure of the wave equation, and in time by using symplectic, diagonally implicit and explicit partitioned Runge-Kutta methods. The fundamental feature of the resulting scheme is that the conservation of a discrete energy, which is nothing but a discrete version of the original Hamiltonian, is guaranteed. We present numerical experiments which indicate that the method achieves optimal approximations of order k + 1 in the L2-norm when polynomials of degree k ≥ 0 and Runge-Kutta time-marching methods of order k + 1 are used. In addition, by means of post-processing techniques and by increasing the order of the Runge-Kutta method to k + 2, we obtain superconvergent approximations of order k + 2 in the L2-norm for the displacement and the velocity. We also present numerical examples that corroborate that the methods conserve energy and that they compare favorably with dissipative HDG schemes, of similar accuracy properties, for long-time simulations.
Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
Mei, Lijie; Wu, Xinyuan
2017-06-01
Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.
International Nuclear Information System (INIS)
Latimer, D. C.
2007-01-01
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase-space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition, the authors investigate how these alternative symplectic forms affect this system's quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent
A symplectic Poisson solver based on Fast Fourier Transformation. The first trial
Energy Technology Data Exchange (ETDEWEB)
Vorobiev, L.G. [Gosudarstvennyj Komitet po Ispol`zovaniyu Atomnoj Ehnergii SSSR, Moscow (Russian Federation). Inst. Teoreticheskoj i Ehksperimental`noj Fiziki; Hirata, Kohji
1995-11-01
A symplectic Poisson solver calculates numerically a potential and fields due to a 2D distribution of particles in a way that the symplecticity and smoothness are assured automatically. Such a code, based on Fast Fourier Transformation combined with Bicubic Interpolation, is developed for the use in multi-turn particle simulation in circular accelerators. Beside that, it may have a number of applications, where computations of space charge forces should obey a symplecticity criterion. Detailed computational schemes of all algorithms will be outlined to facilitate practical programming. (author).
A symplectic Poisson solver based on Fast Fourier Transformation. The first trial
International Nuclear Information System (INIS)
Vorobiev, L.G.; Hirata, Kohji.
1995-11-01
A symplectic Poisson solver calculates numerically a potential and fields due to a 2D distribution of particles in a way that the symplecticity and smoothness are assured automatically. Such a code, based on Fast Fourier Transformation combined with Bicubic Interpolation, is developed for the use in multi-turn particle simulation in circular accelerators. Beside that, it may have a number of applications, where computations of space charge forces should obey a symplecticity criterion. Detailed computational schemes of all algorithms will be outlined to facilitate practical programming. (author)
New results for time reversed symplectic dynamic systems and quadratic functionals
Directory of Open Access Journals (Sweden)
Roman Simon Hilscher
2012-05-01
Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.
Notes on qubit phase space and discrete symplectic structures
International Nuclear Information System (INIS)
Livine, Etera R
2010-01-01
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.
Integrals of motion for critical dense polymers and symplectic fermions
International Nuclear Information System (INIS)
Nigro, Alessandro
2009-01-01
We consider critical dense polymers L(1,2). We obtain for this model the eigenvalues of the local integrals of motion of the underlying conformal field theory by means of a thermodynamic Bethe ansatz. We give a detailed description of the relation between this model and symplectic fermions including some examples of the indecomposable structure of the transfer matrix in the continuum limit. Integrals of motion are defined directly on the lattice in terms of the Temperley–Lieb algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained, thus providing a reason for their introduction
Integrals of motion for critical dense polymers and symplectic fermions
Nigro, Alessandro
2009-10-01
We consider critical dense polymers \\mathcal {L}(1,2) . We obtain for this model the eigenvalues of the local integrals of motion of the underlying conformal field theory by means of a thermodynamic Bethe ansatz. We give a detailed description of the relation between this model and symplectic fermions including some examples of the indecomposable structure of the transfer matrix in the continuum limit. Integrals of motion are defined directly on the lattice in terms of the Temperley-Lieb algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained, thus providing a reason for their introduction.
Notes on qubit phase space and discrete symplectic structures
Energy Technology Data Exchange (ETDEWEB)
Livine, Etera R, E-mail: etera.livine@ens-lyon.f [Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d' Italie, 69364 Lyon (France)
2010-02-19
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.
Existence and equivalence of twisted products on a symplectic manifold
International Nuclear Information System (INIS)
Lichnerowicz, A.
1979-01-01
The twisted products play an important role in Quantum Mechanics. A distinction is introduced between Vey *sub(γ) products and strong Vey *sub(γ) products and it is proved that each *sub(γ) product is equivalent to a Vey *sub(γ) product. If b 3 (W) = 0, the symplectic manifold (W,F) admits strong Vey *sub(Gn) products. If b 2 (W) = 0, all *sub(γ) products are equivalent as well as the Vey Lie algebras. In the general case the formal Lie algebras are characterized which are generated by a *sub(γ) product and it proved that the existance of a *sub(γ)-product is equivalent to the existance of a formal Lie algebra infinitesimally equivalent to a Vey Lie algebra at the first order. (Auth.)
Stabilizing constrained chaotic system using a symplectic psuedospectral method
Peng, Haijun; Wang, Xinwei; Shi, Boyang; Zhang, Sheng; Chen, Biaosong
2018-03-01
The problem of controlling chaotic systems has drawn much attention in the last two decades. However, the controlled system may be subjected to complicated constraints and few researches on controlling chaos take constraints into consideration. Therefore, the stabilization of constrained chaotic system is solved under the frame of nonlinear optimal control in this paper. A symplectic pseudospectral method based on qusilinearizaiton techniques and the parametric variational principle is developed to solve constrained nonlinear optimal control problems with arbitrary Lagrange-type cost functional. At the beginning of the proposed method, the original nonlinear optimal control problem is converted into a series of linear-quadratic constrained optimal control problems. Then each of the converted linear quadratic problems is transformed into a standard linear complementarity problem. The proposed method is successfully applied to stabilizing constrained chaotic systems around an unstable equilibrium point or an unstable periodic orbit. Numerical simulations demonstrate that the developed method is effective and efficient, and constraints are strictly satisfied.
Partial dynamical symmetry in the symplectic shell model
Energy Technology Data Exchange (ETDEWEB)
Escher, J. [TRIUMF, Vancouver, British Columbia (Canada); Leviatan, A. [Hebrew Univ., Racah Inst. of Physics, Jerusalem (Israel)
2000-08-01
We present an example of a partial dynamical symmetry (PDS) in an interacting fermion system and demonstrate the close relationship of the associated Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding light on this important interaction. Specifically, in the framework of the symplectic shell model of nuclei, we prove the existence of a family of fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction process for the PDS eigenstates with good symmetry and give analytic expressions for the energies of these states and E2 transition strengths between them. Characteristics of both pure and mixed-symmetry PDS eigenstates are discussed and the resulting spectra and transition strengths are compared to those of real nuclei. The PDS concept is shown to be relevant to the description of prolate, oblate, as well as triaxially deformed nuclei. Similarities and differences between the fermion case and the previously established partial SU(3) symmetry in the interacting boson model are considered. (author)
Partial dynamical symmetry in the symplectic shell model
International Nuclear Information System (INIS)
Escher, Jutta; Leviatan, Amiram
2002-01-01
We present an example of a partial dynamical symmetry (PDS) in an interacting fermion system and demonstrate the close relationship of the associated Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding light on this important interaction. Specifically, in the framework of the symplectic shell model of nuclei, we prove the existence of a family of fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction process for the PDS eigenstates with good symmetry and give analytic expressions for the energies of these states and E2 transition strengths between them. Characteristics of both pure and mixed-symmetry PDS eigenstates are discussed and the resulting spectra and transition strengths are compared to those of real nuclei. The PDS concept is shown to be relevant to the description of prolate, oblate, as well as triaxially deformed nuclei. Similarities and differences between the fermion case and the previously established partial SU(3) symmetry in the interacting boson model are considered
Exact symplectic structures and a classical model for the Dirac electron
International Nuclear Information System (INIS)
Rawnsley, J.
1992-01-01
We show how the classical model for the Dirac electron of Barut and coworkers can be obtained as a Hamiltonian theory by constructing an exact symplectic form on the total space of the spin bundle over spacetime. (orig.)
Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei
Energy Technology Data Exchange (ETDEWEB)
Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; Draayer, Jerry P.; /Louisiana State U.; Vary, James P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-04-24
Clear evidence for symplectic symmetry in low-lying states of {sup 12}C and {sup 16}O is reported. Eigenstates of {sup 12}C and {sup 16}O, determined within the framework of the no-core shell model using the JISP16 NN realistic interaction, typically project at the 85-90% level onto a few of the most deformed symplectic basis states that span only a small fraction of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome confirms Elliott's SU(3) model which underpins the symplectic scheme, and above all, points to the relevance of a symplectic no-core shell model that can reproduce experimental B(E2) values without effective charges as well as deformed spatial modes associated with clustering phenomena in nuclei.
Symplectic matrix, gauge invariance and Dirac brackets for super-QED
Energy Technology Data Exchange (ETDEWEB)
Alves, D.T. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Cheb-Terrab, E.S. [British Columbia Univ., Vancouver, BC (Canada). Dept. of Mathematics
1999-08-01
The calculation of Dirac brackets (DB) using a symplectic matrix approach but in a Hamiltonian framework is discussed, and the calculation of the DB for the supersymmetric extension of QED (super-QED) is shown. The relation between the zero-mode of the pre-symplectic matrix and the gauge transformations admitted by the model is verified. A general description to construct Lagrangians linear in the velocities is also presented. (author)
International Nuclear Information System (INIS)
Wang Hua; Alatancang; Huang Jun-Jie
2011-01-01
This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates. (general)
Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
Hosono, Shinobu
2004-01-01
We study a cohomology-valued hypergeometric series which naturally arises in the description of (local) mirror symmetry. We identify it as a central charge formula for BPS states and study its monodromy property from the viewpoint of Kontsevich's homological mirror symmetry. In the case of local mirror symmetry, we will identify a symplectic form, and will conjecture an integral and symplectic monodromy property of a relevant hypergeometric series of Gel'fand-Kapranov-Zelevinski type.
Highly accurate symplectic element based on two variational principles
Qing, Guanghui; Tian, Jia
2018-02-01
For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.
Highly accurate symplectic element based on two variational principles
Qing, Guanghui; Tian, Jia
2017-11-01
For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.
Analytical and numerical manifolds in a symplectic 4-D map
Delis, N.; Contopoulos, G.
2016-05-01
We study analytically the orbits along the asymptotic manifolds from a complex unstable periodic orbit in a symplectic 4-D Froeschlé map. The orbits are given as convergent series. We compare the analytic results by truncating the series at various orders with the corresponding numerical results and we find agreement along a more extended length, as the order of truncation increases. The agreement is improved when the parameters approach those of the stability domain. Along the manifolds no terms with small divisors appear in the series. The same result is found if we use a parametrization method along the asymptotic curves. In the case of orbits starting close to the manifolds small divisors appear, but the orbits remain close to the manifolds for an extended period of time. If the parameters of the map are close to the stable domain the orbits recede and approach the origin several times and remain confined in a certain volume around the origin for a long time before escaping to large distances. For special sets of parameters we see resonance phenomena and the orbits take particular forms near every resonance.
Submaximal Riemann-Roch expected curves and symplectic packing.
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Wioletta Syzdek
2007-06-01
Full Text Available We study Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ in the context of the Nagata-Biran conjecture. This conjecture predicts that for sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$. We construct examples verifying to the effect that the assertions of the Nagata-Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $mathbb{P}^1 imes mathbb{P}^1$ and a relatively smallnumber of points. The solutions geometrically correspond to Riemann-Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of mathbb{P}^1 imes mathbb{P}^1. In fact we conjecture that it can be replaced by a lower number and we provide evidence justifying this conjecture.
Full-turn symplectic map from a generator in a Fourier-spline basis
International Nuclear Information System (INIS)
Berg, J.S.; Warnock, R.L.; Ruth, R.D.; Forest, E.
1993-04-01
Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton's method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been appliedto a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10 7 turns on an IBM RS6000 model 320 workstation, in a run of about one day
Sheikh-Jabbari, M. M.
2016-09-01
General covariance is the cornerstone of Einstein’s general relativity (GR) and implies that any two metrics related by diffeomorphisms are physically equivalent. There are, however, many examples pointing to the fact that this strict statement of general covariance needs refinement. There are a very special (measure-zero) subset of diffeomorphisms, the residual diffeomorphisms, to which one can associate well-defined conserved charges. This would hence render these diffeomorphic geometries physically distinct. We discuss that these symmetries may be appropriately called “symplectic symmetries”. Existence of residual diffeomorphisms and symplectic symmetries can be a quite general feature and not limited to the examples discussed so far in the literature. We propose that, in the context of black holes, these diffeomorphic, but distinct, geometries may be viewed as “symplectic soft hair” on black holes. We comment on how this may remedy black hole microstate problem, which in this context are dubbed as “horizon fluffs”.
Vlasov and drift kinetic simulation methods based on the symplectic integrator
International Nuclear Information System (INIS)
Watanabe, T.-H.; Sugama, H.
2004-02-01
Vlasov and drift kinetic simulation methods based on the symplectic integrators are benchmarked for test problems on the linear and nonlinear Landau dampings and the Kelvin-Helmholtz (K-H) instability. The explicit symplectic integrator for the separable Hamiltonian straightforwardly leads to generalization of the splitting scheme for the Vlasov-Poisson system. The Nth-order version improves the total energy conservation decreasing the error as ∝ Δt N where Δt denotes the time step size. An Eulerian drift kinetic simulation scheme derived from the implicit symplectic integrator for the non-separable Hamiltonian exactly satisfies the conservation of the energy and the enstrophy in the K-H instability, and results in successful application to the plasma echo. (author)
International Nuclear Information System (INIS)
Liao Cui-Cui; Cui Jin-Chao; Liang Jiu-Zhen; Ding Xiao-Hua
2016-01-01
In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. (paper)
Directory of Open Access Journals (Sweden)
You-Wei Zhang
Full Text Available A general symplectic method for the random response analysis of infinitely periodic structures subjected to stationary/non-stationary random excitations is developed using symplectic mathematics in conjunction with variable separation and the pseudo-excitation method (PEM. Starting from the equation of motion for a single loaded substructure, symplectic analysis is firstly used to eliminate the dependent degrees of the freedom through condensation. A Fourier expansion of the condensed equation of motion is then applied to separate the variables of time and wave number, thus enabling the necessary recurrence scheme to be developed. The random response is finally determined by implementing PEM. The proposed method is justified by comparison with results available in the literature and is then applied to a more complicated time-dependent coupled system.
International Nuclear Information System (INIS)
Chang, P.; Lee, S.Y.; Yan, Y.T.
2006-01-01
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders
Chen, Qiang; Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei
2017-11-01
An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schrödinger-Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.
International Nuclear Information System (INIS)
Chang, P
2004-01-01
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders
Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds
International Nuclear Information System (INIS)
Krouglikov, B.S.
1994-10-01
Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs
Odd invariant semidensity and divergence-like operators on an odd symplectic superspace
International Nuclear Information System (INIS)
Khudaverdyan, O.M.
1998-01-01
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The formula for this semidensity is similar to the formula of the mean curvature of hypersurfaces in Euclidean space
Principal and nonprincipal solutions of symplectic dynamic systems on time scales
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Ondrej Dosly
2000-01-01
Full Text Available We establish the concept of the principal and nonprincipal solution for the so-called symplectic dynamic systems on time scales. We also present a brief survey of the history of these concept for differential and difference equations.
Linear PDEs and numerical methods that preserve a multi-symplectic conservation law
J.E. Frank (Jason); B.E. Moore; S. Reich
2006-01-01
textabstractMultisymplectic methods have recently been proposed as a generalization of symplectic ODE methods to the case of Hamiltonian PDEs. Their excellent long time behavior for a variety of Hamiltonian wave equations has been demonstrated in a number of numerical studies. A theoretical
An optimized formulation for Deprit-type Lie transformations of Taylor maps for symplectic systems
International Nuclear Information System (INIS)
Shi, Jicong
1993-01-01
An optimized iterative formulation is presented for directly transforming a Taylor map of a symplectic system into a Deprit-type Lie transformation, which is a composition of a linear transfer matrix and a single Lie transformation, to an arbitrary order
A formula for the Chern classes of symplectic blow-ups
Geiges, H.; Pasquotto, F.
2007-01-01
It is shown that the formula for the Chern classes (in the Chow ring) of blow-ups of algebraic varieties, due to Porteous and Lascu-Scott, also holds (in the singular cohomology ring) for blow-ups of symplectic and complex manifolds. This was used by the second author in her solution of the
The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies
Kersten, P.H.M.; Krasil'shchik, I.; Verbovetsky, A.V.
2004-01-01
Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as recursion operators for this equation in its
International Nuclear Information System (INIS)
Zhang, Ruili; Tang, Yifa; Zhu, Beibei; Liu, Jian; Xiao, Jianyuan; Qin, Hong
2014-01-01
The gyrocenter dynamics of charged particles in time-independent magnetic fields is a non-canonical Hamiltonian system. The canonical description of the gyrocenter has both theoretical and practical importance. We provide a general procedure of the gyrocenter canonicalization, which is expressed by the series of a small variable ϵ depending only on the parallel velocity u and can be expressed in a recursive manner. We prove that the truncation of the series to any given order generates a set of exact canonical coordinates for a system, whose Lagrangian approximates to that of the original gyrocenter system in the same order. If flux surfaces exist for the magnetic field, the series stops simply at the second order and an exact canonical form of the gyrocenter system is obtained. With the canonicalization schemes, the canonical symplectic simulation of gyrocenter dynamics is realized for the first time. The canonical symplectic algorithm has the advantage of good conservation properties and long-term numerical accuracy, while avoiding numerical instability. It is worth mentioning that explicitly expressing the canonical Hamiltonian in new coordinates is usually difficult and impractical. We give an iteration procedure that is easy to implement in the original coordinates associated with the coordinate transformation. This is crucial for modern large-scale simulation studies in plasma physics. The dynamics of gyrocenters in the dipole magnetic field and in the toroidal geometry are simulated using the canonical symplectic algorithm by comparison with the higher-order non symplectic Runge-Kutta scheme. The overwhelming superiorities of the symplectic method for the gyrocenter system are evidently exhibited
Zhang, Ruili; Wang, Yulei; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa
2018-02-01
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. The numerical simulation of relativistic dynamics is often multi-scale and requires accurate long-term numerical simulations. Therefore, explicit symplectic algorithms are much more preferable than non-symplectic methods and implicit symplectic algorithms. In this paper, we employ the proper time and express the Hamiltonian as the sum of exactly solvable terms and product-separable terms in space-time coordinates. Then, we give the explicit symplectic algorithms based on the generating functions of orders 2 and 3 for relativistic dynamics of a charged particle. The methodology is not new, which has been applied to non-relativistic dynamics of charged particles, but the algorithm for relativistic dynamics has much significance in practical simulations, such as the secular simulation of runaway electrons in tokamaks.
Directory of Open Access Journals (Sweden)
Xiao-Chuan Li
2011-01-01
Full Text Available The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as their duality variables—lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-eigenvalue, the eigensolutions of nonzero-eigenvalues are also obtained. The former are the basic solutions of Saint-Venant problem, and the latter are the solutions which have the local effect, decay drastically with respect to distance, and are covered in the Saint-Venant principle. So the complete solution of the problem is given out by the symplectic eigensolutions expansion. Finally, a few examples are selected and their analytical solutions are presented.
An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Karlsson, Peer Jesper
2015-01-07
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
International Nuclear Information System (INIS)
Hong Jialin; Li Chun
2006-01-01
In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law
An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Karlsson, Jesper
2015-01-01
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.
Symplectic deformations of integrable field theories and AdS/CFT
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Timothy J. Hollowood
2014-12-01
Full Text Available Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical level. The latter hierarchy admits a family of symplectic structures which we argue can be viewed as deformations of the relativistic sine-Gordon symplectic structure. These deformed theories are integrable but no longer relativistic and the basic excitations of the theory, the solitons, have an interesting non-relativistic dispersion relation that in a certain limit becomes the dispersion relation of dyonic giant magnons of string theory in the AdS/CFT correspondence. We argue that the deformed classical theories can be lifted to quantum theories when the sine-Gordon theory is embedded in a larger theory that describes the string world-sheet sigma model in AdS5×S5.
On the Faddeev-Jackiw symplectic framework for topologically massive gravity
Energy Technology Data Exchange (ETDEWEB)
Escalante, Alberto [Benemerita Universidad Autonoma de Puebla, Instituto de Fisica, Puebla (Mexico); Rodriguez-Tzompantzi, Omar [Benemerita Universidad Autonoma de Puebla, Facultad de Ciencias Fisico Matematicas, Puebla (Mexico)
2016-10-15
The dynamical structure of topologically massive gravity in the context of the Faddeev-Jackiw symplectic approach is studied. It is shown that this method allows us to avoid some ambiguities arising in the study of the gauge structure via the Dirac formalism. In particular, the complete set of constraints and the generators of the gauge symmetry of the theory are obtained straightforwardly via the zero modes of the symplectic matrix. In order to obtain the generalized Faddeev-Jackiw brackets and calculate the local physical degrees of freedom of this model, an appropriate gauge-fixing procedure is introduced. Finally, the similarities and relative advantages between the Faddeev-Jackiw method and Dirac's formalism are briefly discussed. (orig.)
Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy
Andrianopoli, Laura; Ferrara, Sergio
1998-01-01
In these lectures we give a geometrical formulation of N-extended supergravities which generalizes N=2 special geometry of N=2 theories. In all these theories duality symmetries are related to the notion of "flat symplectic bundles" and central charges may be defined as "sections" over these bundles. Attractor points giving rise to "fixed scalars" of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.
Reduction of locally conformal symplectic manifolds with examples of non-Kähler manifolds
Noda, Tomonori
2004-01-01
Let $(M, \\Omega)$ be a locally conformal symplectic manifold. $\\Omega$ is a non-degenerate 2-form on $M$ such that there is a closed 1-form $\\omega$, called the Lee form, satisfing $ d\\Omega=\\omega\\wedge\\Omega$. In this paper we consider Marsden-Weinstein reduction theorem which induces Jacobi-Liouville theorem as a special case. For locally conformal Kähler manifolds, this reduction theorem gives a construction of non-Kähler manifolds in general dimension.
Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces
Khesin, Boris; Rosly, Alexei
2000-01-01
We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves of the latter are classified by restrictions of the bundles to certain divisors. This can be regarded as fixing a "complex analogue of the holonomy" of a connection along a "complex analogue of the boundary" in analogy with the real case.
Stochastic multi-symplectic Runge-Kutta methods for stochastic Hamiltonian PDEs
Zhang, Liying; Ji, Lihai
2018-01-01
In this paper, we consider stochastic Runge-Kutta methods for stochastic Hamiltonian partial differential equations and present some sufficient conditions for multisymplecticity of stochastic Runge-Kutta methods of stochastic Hamiltonian partial differential equations. Particularly, we apply these ideas to stochastic Maxwell equations with multiplicative noise, possessing the stochastic multi-symplectic conservation law and energy conservation law. Theoretical analysis shows that the methods ...
Disconjugacy, transformations and quadratic functionals for symplectic dynamicsystems on time scales
Czech Academy of Sciences Publication Activity Database
Došlý, Ondřej; Hilscher, R.
2001-01-01
Roč. 7, č. 2 (2001), s. 265-295 ISSN 1023-6198 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Keywords : symplectic dynamic system%time scale% quadratic functional Subject RIV: BA - General Mathematics Impact factor: 0.325, year: 2001 http://www.tandfonline.com/doi/abs/10.1080/10236190108808273
Symplectic tracking using point magnets in the presence of a longitudinal magnetic field
International Nuclear Information System (INIS)
Parzen, G.
1993-09-01
In the absence of a longitudinal magnetic field, symplectic tracking can be achieved by replacing the magnets by a series of point magnets and drift spaces. To treat the case when a longitudinal magnetic field is also present, this procedure is modified in this paper by replacing the drift space by a solenoidal drift, which is defined as the motion of a particle in a uniform longitudinal magnetic field. A symplectic integrator can be obtained by subdividing each magnet into pieces and replacing each magnet piece by point magnets, with only transverse fields, and solenoidal drift spaces. The reference orbit used here is made up of arcs of circles and straight lines which join smoothly with each other. For this choice of reference orbit, the required results are obtained to track particles, which are the transfer functions, and the transfer time for the different elements. It is shown that these results provide a symplectic integrator, and they are exact in the sense that as the number of magnet pieces is increased, the particle motion will converge to the particle motion of the exact equations of motion
International Nuclear Information System (INIS)
Le Van Hop.
1989-12-01
The combinatorics computation is used to describe the Casimir operators of the symplectic Lie Algebra. This result is applied for determining the Center of the enveloping Algebra of the semidirect Product of the Heisenberg Lie Algebra and the symplectic Lie Algebra. (author). 10 refs
International Nuclear Information System (INIS)
Wang, Zhong-Min; Liu, Yan-Zhuang
2016-01-01
Highlights: • We investigate the transverse vibration of FGM pipe conveying fluid. • The FGM pipe conveying fluid can be classified into two cases. • The variations between the frequency and the power law exponent are obtained. • “Case 1” is relatively more reasonable than “case 2”. - Abstract: Problems related to the transverse vibration of pipe conveying fluid made of functionally graded material (FGM) are addressed. Based on inside and outside surface material compositions of the pipe, FGM pipe conveying fluid can be classified into two cases. It is hypothesized that the physical parameters of the material along the direction of the pipe wall thickness change in the simple power law. A differential equation of motion expressed in non-dimensional quantities is derived by using Hamilton's principle for systems of changing mass. Using the assuming modal method, the pipe deflection function is expanded into a series, in which each term is expressed to admissible function multiplied by generalized coordinate. Then, the differential equation of motion is discretized into the two order differential equations expressed in the generalized coordinates. Based on symplectic elastic theory and the introduction of dual system and dual variable, Hamilton's dual equations are derived, and the original problem is reduced to eigenvalue and eigenvector problem in the symplectic space. Finally, a symplectic method is employed to analyze the vibration and stability of FGM pipe conveying fluid. For a clamped–clamped FGM pipe conveying fluid in “case 1” and “case 2”, the dimensionless critical flow velocity for first-mode divergence and the critical coupled-mode flutter flow velocity are obtained, and the variations between the real part and imaginary part of dimensionless complex frequency and fluid velocity, mass ratio and the power law exponent (or graded index, volume fraction) for FGM pipe conveying fluid are analyzed.
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
From Stein to Weinstein and back symplectic geometry of affine complex manifolds
Cieliebak, Kai
2013-01-01
A beautiful and comprehensive introduction to this important field. -Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment of the interplay between the world of Stein manifolds and the more topological and flexible world of Weinstein manifolds. Devoted to this subject with a long history, the book serves as a superb introduction to this area and also contains the authors' new results. -Tomasz Mrowka, MIT This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine co
The symplectic algorithm for use in a model of laser field
International Nuclear Information System (INIS)
Liu Xiaoyan; Liu Xueshen; Ding Peizhu; Zhou Zhongyuan
2002-01-01
Using the asymptotic boundary condition the time-dependent Schroedinger equations with initial conditions in the infinite space can be transformed into the problem with initial and boundary conditions, and it can further be discrected into the inhomogeneous canonic equations. The symplectic algorithms to solve the inhomogeneous canonic equations have been developed and adopted to compute the high-order harmonics of one-dimensional Hydrogen in the laser field. We noticed that there is saturation intensity for generating high-order harmonics, which are agree with previous results, and there is a relationship between harmonics and bound state probabilities
τ-function evaluation of gap probabilities in orthogonal and symplectic matrix ensembles
International Nuclear Information System (INIS)
Forrester, P.J.; Witte, N.S.
2001-01-01
It has recently been emphasized that all known exact evaluations of gap probabilities for classical unitary matrix ensembles are in fact τ-functions for certain Painleve systems. We show that all known exact evaluations of gap probabilities for classical orthogonal matrix ensembles are likewise τ-functions for certain Painleve systems. In the case of symplectic matrix ensembles all known exact evaluations are identified as the mean of two τ-functions, both of which correspond to Hamiltonians satisfying the same differential equation, differing only in the boundary condition
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
Quantization of a symplectic manifold associated to a manifold with projective structure
International Nuclear Information System (INIS)
Biswas, Indranil
2009-01-01
Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L P ' over X associated with P. We show that the holomorphic cotangent bundle of the total space of L P ' equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim C X=1.
Ikeda, Noriaki; Xu, Xiaomeng
2014-11-01
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structures, we introduce a generalization of differential graded symplectic manifolds, called twisted QP manifolds, in terms of graded symplectic geometry, canonical functions, and QP pairs. We generalize the AKSZ construction of topological sigma models to sigma models with Wess-Zumino terms and show that all the twisted Poisson-like structures known in the literature can actually be naturally realized as boundary conditions for AKSZ sigma models.
Strict deformation quantization for actions of a class of symplectic lie groups
International Nuclear Information System (INIS)
Bieliavsky, Pierre; Massar, Marc
2002-01-01
We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SN(1, n). This answers a question raised by Rieffel in [Contemp. Math. 228 (1998), 315]. (author)
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
0 in the foliated cohomology group. H2(F ). Now, there exists a neighbourhood Y of Image g0 such that Image g0 is a strong deformation retract of Y; further the deformation retraction is foliation preserving. Con- sequently, ˆω is a foliated exact form on (Y, ˆF). Hence there exists a 1-form τ on Y such that ˆω = dτ on T ˆF.
Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
2017-05-01
A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Fault Detection for Vibration Signals on Rolling Bearings Based on the Symplectic Entropy Method
Directory of Open Access Journals (Sweden)
Min Lei
2017-11-01
Full Text Available Bearing vibration response studies are crucial for the condition monitoring of bearings and the quality inspection of rotating machinery systems. However, it is still very difficult to diagnose bearing faults, especially rolling element faults, due to the complex, high-dimensional and nonlinear characteristics of vibration signals as well as the strong background noise. A novel nonlinear analysis method—the symplectic entropy (SymEn measure—is proposed to analyze the measured signals for fault monitoring of rolling bearings. The core technique of the SymEn approach is the entropy analysis based on the symplectic principal components. The dynamical characteristics of the rolling bearing data are analyzed using the SymEn method. Unlike other techniques consisting of high-dimensional features in the time-domain, frequency-domain and the empirical mode decomposition (EMD/wavelet-domain, the SymEn approach constructs low-dimensional (i.e., two-dimensional features based on the SymEn estimate. The vibration signals from our experiments and the Case Western Reserve University Bearing Data Center are applied to verify the effectiveness of the proposed method. Meanwhile, it is found that faulty bearings have a great influence on the other normal bearings. To sum up, the results indicate that the proposed method can be used to detect rolling bearing faults.
Ran, A.C.M.; Mehl, Chr.; Mehrmann, V.; Rodman, L.
2014-01-01
We study the perturbation theory of structured matrices under structured rank one perturbations, with emphasis on matrices that are unitary, orthogonal, or symplectic with respect to an indefinite inner product. The rank one perturbations are not necessarily of arbitrary small size (in the sense of
International Nuclear Information System (INIS)
Qin, H.; Guan, X.
2008-01-01
A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.
Symplectic structures in the chirally gauged Wess-Zumino-Witten model
International Nuclear Information System (INIS)
Inamoto, T.
1992-01-01
The algebraic structure of the chirally gauged Wess-Zumino-Witten model is studied from the Hamiltonian point of view. The consistent chiral anomaly, which is reproduced at the tree level in this model, is related to the Schwinger term of the Gauss-law algebra through descent equations constructed with phase-space differential forms. The descent equations express the effects of the consistent anomaly upon the symplectic structure of the theory, and provide the Hamiltonian analogue of the Wess-Zumino consistency condition in the Weyl gauge. We also clarify the canonical structure of the ungauged Wess-Zumino-Witten model, and the algebra associated with the global Noether symmetry is derived
Symplectic finite element scheme: application to a driven problem with a regular singularity
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.
Explicit higher order symplectic integrator for s-dependent magnetic field
International Nuclear Information System (INIS)
Wu, Y.; Forest, E.; Robin, D.S.
2001-01-01
We derive second and higher order explicit symplectic integrators for the charged particle motion in an s-dependent magnetic field with the paraxial approximation. The Hamiltonian of such a system takes the form of H (summation) k (p k - a k (rvec q), s) 2 + V((rvec q), s). This work solves a long-standing problem for modeling s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with strong field wigglers, arbitrarily polarized insertion devices,and super-conducting magnets with strong fringe fields. Consequently, this work will have a significant impact on the optimal use of the above magnetic devices in the light source rings as well as in next generation linear collider damping rings
Okumura, Hisashi; Itoh, Satoru G; Okamoto, Yuko
2007-02-28
The authors propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isobaric-isothermal ensembles. They also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, they can perform a MD simulation more stably than by conventional nonsymplectic algorithms. They applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. They found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.
Black holes and groups of type E7
Indian Academy of Sciences (India)
We report some results on the relation between extremal black holes in locally supersymmetric theories of gravity and groups of type 7, appearing as generalized electric-magnetic duality symmetries in such theories. Some basics on the covariant approach to the stratiﬁcation of the relevant symplectic representation are ...
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
McCoy, Anna E.; Caprio, Mark A.; Dytrych, Tomas
2017-09-01
A major challenge in quantitatively predicting nuclear structure ab initio, directly from realistic nucleon-nucleon interactions, arises due to an explosion in the dimension of the traditional configuration interaction basis as the number of nucleons and included shells increases. The need for including highly excited configurations exists, in large part, because the kinetic energy induces strong coupling across shells. However, the kinetic energy conserves symplectic symmetry. Combining symplectic symmetry with the no-core configuration interaction (NCCI) framework provides a means of identifying and restricting the basis to include only the highly excited configurations which dominantly contribute to the nuclear wavefunction, thereby reducing the size of basis necessary to obtain accurate results. We present a framework for ab initio symplectic no-core configuration interaction (SpNCCI) calculations of the nuclear problem and explore convergence behavior of calculations of p-shell nuclei in this framework. Supported by the US DOE under Award No. DE-FG02-95ER-40934 and the Czech Science Foundation under Grant No. 16-16772S.
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
Energy Technology Data Exchange (ETDEWEB)
Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China
2015-11-01
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
International Nuclear Information System (INIS)
Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Qin, Hong; Sun, Yajuan
2015-01-01
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave
Endoscopic classification of representations of quasi-split unitary groups
Mok, Chung Pang
2015-01-01
In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.
Ni, Xiao-Ting; Wu, Xin
2014-10-01
The time-transformed leapfrog scheme of Mikkola & Aarseth was specifically designed for a second-order differential equation with two individually separable forms of positions and velocities. It can have good numerical accuracy for extremely close two-body encounters in gravitating few-body systems with large mass ratios, but the non-time-transformed one does not work well. Following this idea, we develop a new explicit symplectic integrator with an adaptive time step that can be applied to a time-dependent Hamiltonian. Our method relies on a time step function having two distinct but equivalent forms and on the inclusion of two pairs of new canonical conjugate variables in the extended phase space. In addition, the Hamiltonian must be modified to be a new time-transformed Hamiltonian with three integrable parts. When this method is applied to the elliptic restricted three-body problem, its numerical precision is explicitly higher by several orders of magnitude than the nonadaptive one's, and its numerical stability is also better. In particular, it can eliminate the overestimation of Lyapunov exponents and suppress the spurious rapid growth of fast Lyapunov indicators for high-eccentricity orbits of a massless third body. The present technique will be useful for conservative systems including N-body problems in the Jacobian coordinates in the the field of solar system dynamics, and nonconservative systems such as a time-dependent barred galaxy model in a rotating coordinate system.
Energy Technology Data Exchange (ETDEWEB)
Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)
2014-05-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.
International Nuclear Information System (INIS)
Skokos, Ch.; Gerlach, E.; Bodyfelt, J.D.; Papamikos, G.; Eggl, S.
2014-01-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.
A direct link between the Lie group SU (3) and the singular ...
Indian Academy of Sciences (India)
A classical phase space with a suitable symplectic structure is constructed together with functions which have Poisson brackets algebraically identical to the Lie algebra structure of the Lie group SU(3). It is shown that in this phase space there are two spheres which intersect at one point. Such a system has a representation ...
Black Holes and Groups of Type E7
Ferrara, Sergio
2012-01-01
We report some results on the relation between extremal black holes in locally supersymmetric theories of gravity and groups of type E7, appearing as generalized electric-magnetic duality symmetries in such theories. Some basics on the covariant approach to the stratification of the relevant symplectic representation are reviewed, along with a connection between special Kaehler geometry and a "generalization" of groups of type E7.
Group theoretical construction of planar noncommutative phase spaces
Energy Technology Data Exchange (ETDEWEB)
Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)
2014-01-15
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.
Group and representation theory
Vergados, J D
2017-01-01
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...
Symplectic orbit and spin tracking code for all-electric storage rings
Talman, Richard M.; Talman, John D.
2015-07-01
Proposed methods for measuring the electric dipole moment (EDM) of the proton use an intense, polarized proton beam stored in an all-electric storage ring "trap." At the "magic" kinetic energy of 232.792 MeV, proton spins are "frozen," for example always parallel to the instantaneous particle momentum. Energy deviation from the magic value causes in-plane precession of the spin relative to the momentum. Any nonzero EDM value will cause out-of-plane precession—measuring this precession is the basis for the EDM determination. A proposed implementation of this measurement shows that a proton EDM value of 10-29e -cm or greater will produce a statistically significant, measurable precession after multiply repeated runs, assuming small beam depolarization during 1000 s runs, with high enough precision to test models of the early universe developed to account for the present day particle/antiparticle population imbalance. This paper describes an accelerator simulation code, eteapot, a new component of the Unified Accelerator Libraries (ual), to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the nonconstant particle velocity in electric rings gives them significantly different properties, especially in weak focusing rings. Like the earlier code teapot (for magnetic ring simulation) this code performs exact tracking in an idealized (approximate) lattice rather than the more conventional approach, which is approximate tracking in a more nearly exact lattice. The Bargmann-Michel-Telegdi (BMT) equation describing the evolution of spin vectors through idealized bend elements is also solved exactly—original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial "symplectification"). Any residual spurious damping or antidamping is sufficiently small to permit reliable tracking for the
Integrable systems on semidirect product Lie groups
Capriotti, S.; Montani, H.
2014-05-01
We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler-Kostant-Symes sense) are naturally built through collective dynamics. In doing so, we address other issues such as factorization, Poisson-Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.
Symplectic orbit and spin tracking code for all-electric storage rings
Directory of Open Access Journals (Sweden)
Richard M. Talman
2015-07-01
Full Text Available Proposed methods for measuring the electric dipole moment (EDM of the proton use an intense, polarized proton beam stored in an all-electric storage ring “trap.” At the “magic” kinetic energy of 232.792 MeV, proton spins are “frozen,” for example always parallel to the instantaneous particle momentum. Energy deviation from the magic value causes in-plane precession of the spin relative to the momentum. Any nonzero EDM value will cause out-of-plane precession—measuring this precession is the basis for the EDM determination. A proposed implementation of this measurement shows that a proton EDM value of 10^{-29}e-cm or greater will produce a statistically significant, measurable precession after multiply repeated runs, assuming small beam depolarization during 1000 s runs, with high enough precision to test models of the early universe developed to account for the present day particle/antiparticle population imbalance. This paper describes an accelerator simulation code, eteapot, a new component of the Unified Accelerator Libraries (ual, to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the nonconstant particle velocity in electric rings gives them significantly different properties, especially in weak focusing rings. Like the earlier code teapot (for magnetic ring simulation this code performs exact tracking in an idealized (approximate lattice rather than the more conventional approach, which is approximate tracking in a more nearly exact lattice. The Bargmann-Michel-Telegdi (BMT equation describing the evolution of spin vectors through idealized bend elements is also solved exactly—original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial “symplectification”. Any residual spurious damping or antidamping is sufficiently small to
Prykarpatsky, Yarema A.; Artemovych, Orest D.; Pavlov, Maxim V.; Prykarpatski, Anatolij K.
2013-06-01
A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.
The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
Energy Technology Data Exchange (ETDEWEB)
Farsad, Vanda
2017-06-14
This thesis is concerned with ''N pairs of symplectic fermions'' which are examples of logarithmic conformal field theories in two dimensions. The mathematical language of two-dimensional conformal field theories (on Riemannian surfaces of genus zero) are vertex operator algebras. The representation category of the even part of the symplectic fermion vertex operator super-algebra Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category. This determines an isomorphism of projective representations between two SL(2,Z)-actions associated to V{sub ev}. The first action is obtained by modular transformations on the space of so-called pseudo-trace functions of a vertex operator algebra. For V{sub ev} this was developed by A.M.Gaberdiel and I. Runkel. For the action one uses that Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category and thus carries a projective SL(2,Z)-action on a certain Hom-space [Ly1,Ly2,KL]. To do so we calculate the SL(2,Z)-action on the representation category of a general factorisable quasi-Hopf algebras. Then we show that Rep V{sub ev} is conjecturally ribbon equivalent to Rep Q, for Q a factorisable quasi-Hopf algebra, and calculate the SL(2,Z)-action explicitly on Rep Q. The result is that the two SL(2,Z)-action indeed agree. This poses the first example of such comparison for logarithmic conformal field theories.
The Poincare group as the symmetry group of canonical general relativity
International Nuclear Information System (INIS)
Beig, R.; Murchadha, N. o
1986-01-01
This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to General Relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincare group acts as a symmetry group on the phase space of G.R. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained. (Author)
Energy Technology Data Exchange (ETDEWEB)
Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei; Sun, Yajuan; Burby, Joshua W.; Ellison, Leland; Zhou, Yao
2015-12-14
Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. 10(9), degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.
The Hopf algebra structure of the character rings of classical groups
International Nuclear Information System (INIS)
Fauser, Bertfried; Jarvis, Peter D; King, Ronald C
2013-01-01
The character ring Char-GL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra Symm-Λ of symmetric functions. Here we study the character rings Char-O and Char-Sp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that Char-O and Char-Sp also admit natural Hopf algebra structures that are isomorphic to that of Char-GL, and hence to Symm-Λ. The isomorphisms are determined explicitly, along with the specification of standard bases for Char-O and Char-Sp analogous to those used for Symm-Λ. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur–Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the Char-GL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras Char-O and Char-Sp are not self-dual. The dual Hopf algebras Char-O * and Char-Sp are identified. Finally, the Hopf algebra of the universal rational character ring Char-GLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified. (paper)
Energy Technology Data Exchange (ETDEWEB)
Abreu, Everton M.C. [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil); Mendes, R.; Oliveira, Wilson; Xavier, Luciana M.V. [Universidade Federal de Juiz de Fora (UFJF), MG (Brazil); Neves, Clifford [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil); Wostzasek, Clovis [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil)
2009-07-01
Full text. The interest in the dual mapping between two different theories that show the same physical properties has been increased in the last years motivated by its success in both field theory as well as string theory. At the same time, the interest in the study of theories involving higher-order derivatives is by now well appreciated and remains intense. Within the context of Maxwell theory, generalizations involving higher-order derivatives can be found in the literature. We know that in D=3+1 massive gauge fields are introduced by the Higgs Mechanism through the spontaneous breaking of symmetry. However, in the Abelian case, it is possible to introduce a massive gauge field without having to accomplish a spontaneous breaking of symmetry. So, the gauge symmetry does not forbid the appearance of the massive gauge fields. We can fall back to a topological term of mass like Chern-Simons, that in D=2+1 preserve the gauge and Lorentz symmetries. However, in D=3+1 the Lorentz symmetry is broken for the Chern-Simons theory. We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained, a Maxwell-Podolsky-like theory, includes a higher-order derivative term and preserve the gauge symmetry. We also furnish an investigation of the pole structure of the vector propagator by the residue matrix which considers the eventual existence of the negative-norm of the theory. (author)
Differential Geometry and Lie Groups for Physicists
Fecko, Marián.
2011-03-01
Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.
Dey, Rukmini
2002-12-01
In this paper we show that the dimensionally reduced Seiberg-Witten equations lead to a Higgs field and we study the resulting moduli spaces. The moduli space arising out of a subset of the equations, shown to be non-empty for a compact Riemann surface of genus g ≥ 1, gives rise to a family of moduli spaces carrying a hyperkähler structure. For the full set of equations the corresponding moduli space does not have the aforementioned hyperkähler structure but has a natural symplectic structure. For the case of the torus, g = 1, we show that the full set of equations has a solution, different from the "vortex solutions".
Harmonic and applied analysis from groups to signals
Mari, Filippo; Grohs, Philipp; Labate, Demetrio
2015-01-01
This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction ...
International Nuclear Information System (INIS)
Okubo, S.
1978-01-01
Assuming that all quarks have only electric charges 2/3 and - 1/3, we classify all possible representations and all admissible gauge groups G underlying the unified weak and electromagnetic interactions. In particular, the group G cannot contain any exceptional Lie groups G 2 , F 4 , E 6 , E 7 , and E 8 as its factor. Moreover, the underlying irreducible representation for quark multiplets to be used must be one of fundamental representations for each component of simple Lie groups contained as a factor of G. For example, only the spinor representation is allowed for the SO(2n + 1) group, while only the basic representation is admissible for the symplectic groups. If G is semisimple in addition, then G must be a product of SU(3l) groups
Convexity properties of Hamiltonian group actions
Guillemin, Victor
2005-01-01
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic&rdquo case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel sub...
Energy Technology Data Exchange (ETDEWEB)
Fields, Susannah
2007-08-16
This project is currently under contract for research through the Department of Homeland Security until 2011. The group I was responsible for studying has to remain confidential so as not to affect the current project. All dates, reference links and authors, and other distinguishing characteristics of the original group have been removed from this report. All references to the name of this group or the individual splinter groups has been changed to 'Group X'. I have been collecting texts from a variety of sources intended for the use of recruiting and radicalizing members for Group X splinter groups for the purpose of researching the motivation and intent of leaders of those groups and their influence over the likelihood of group radicalization. This work included visiting many Group X websites to find information on splinter group leaders and finding their statements to new and old members. This proved difficult because the splinter groups of Group X are united in beliefs, but differ in public opinion. They are eager to tear each other down, prove their superiority, and yet remain anonymous. After a few weeks of intense searching, a list of eight recruiting texts and eight radicalizing texts from a variety of Group X leaders were compiled.
Sawyer, Keith
2015-01-01
Keith Sawyer views the spontaneous collaboration of group creativity and improvisation actions as "group flow," which organizations can use to function at optimum levels. Sawyer establishes ideal conditions for group flow: group goals, close listening, complete concentration, being in control, blending egos, equal participation, knowing…
Energy Technology Data Exchange (ETDEWEB)
Muktibodh, A. S. [Department of Mathematics, Mohota College of Science, NAGPUR-440009 India E-mail: amukti2000@yahoo.com (India)
2015-03-10
The concept of ‘Isotopy’ as formulated by Ruggero Maria Santilli [1, 2, 3] plays a vital role in the development of Iso mathematics. Santilli defined iso-fields of characteristic zero. In this paper we extend this definition to define Iso-Galois fields [4] which are essentially of non-zero characteristic. Isotopically isomorphic realizations of a group define isopermutation group which gives a clear cut distinction between automorphic groups and isotopic groups.
Passman, Donald S
2012-01-01
This volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter feature
International Nuclear Information System (INIS)
Eggermont, G.
2006-01-01
In 2005, PISA organised proactive meetings of reflection groups on involvement in decision making, expert culture and ethical aspects of radiation protection.All reflection group meetings address particular targeted audiences while the output publication in book form is put forward
Clark, Brian
The group interpretation approach to theatre production is defined as a method that will lead to production of plays that will appeal to "all the layers of the conscious and unconscious mind." In practice, it means that the group will develop and use resources of the theatre that orthodox companies too often ignore. The first two chapters of this…
Paldus, Josef
The well known symmetry (invariance, degeneracy) dynamical groups or algebras of quantum mechanical Hamiltonians provide quantum numbers (conservation laws, integrals of motion) for state labeling and the associated selection rules. In addition, it is often advantageous to employ much larger groups, referred to as the dynamical groups (noninvariance groups, dynamical algebras, spectrum generating algebras), which may or may not be the invariance groups of the studied system [4.1,2,3,4,5,6,7]. In all known cases, they are Lie groups (LGs), or rather corresponding Lie algebras (LAs), and one usually requires that all states of interest of a system be contained in a single irreducible representation (irrep). Likewise, one may require that the Hamiltonian be expressible in terms of the Casimir operators of the corresponding universal enveloping algebra [4.8,9]. In a weaker sense, one regards any group (or corresponding algebra) as a dynamical group if the Hamiltonian can be expressed in terms of its generators [4.10,11,12]. In nuclear physics, one sometimes distinguishes exact (baryon number preserving), almost exact (e.g., total isospin), approximate (e.g., SU(3) of the "eightfold way") and model (e.g., nuclear shell model) dynamical symmetries [4.13]. The dynamical groups of interest in atomic and molecular physics can be conveniently classified by their topological characteristic of compactness. Noncompact LGs (LAs) generally arise in simple problems involving an infinite number of bound states, while those involving a finite number of bound states (e.g., molecular vibrations or ab initio models of electronic structure) exploit compact LG's.
Adams, Karen
2015-01-01
In this article Karen Adams demonstrates how to incorporate group grammar techniques into a classroom activity. In the activity, students practice using the target grammar to do something they naturally enjoy: learning about each other.
International Nuclear Information System (INIS)
Bauer, H.; Black, I.; Heusler, A.; Hoeptner, G.; Krafft, F.; Lang, R.; Moellenkamp, R.; Mueller, W.; Mueller, W.F.; Schati, C.; Schmidt, A.; Schwind, D.; Weber, G.
1983-01-01
The computer groups has been reorganized to take charge for the general purpose computers DEC10 and VAX and the computer network (Dataswitch, DECnet, IBM - connections to GSI and IPP, preparation for Datex-P). (orig.)
International Nuclear Information System (INIS)
Rome, C.P.
1976-01-01
Group Technology has been conceptually applied to the manufacture of batch-lots of 554 machined electromechanical parts which now require 79 different types of metal-removal tools. The products have been grouped into 7 distinct families which require from 8 to 22 machines in each machine-cell. Throughput time can be significantly reduced and savings can be realized from tooling, direct-labor, and indirect-labor costs
Lie groups and algebraic groups
Indian Academy of Sciences (India)
. These fields are interrelated and each of these fields contributes to the other. 2. Examples and classification. We first give some examples of Lie groups. The most frequently occurring ones are the linear classical groups GLn(R), GLn(C), ...
Lie groups and algebraic groups
Indian Academy of Sciences (India)
M S RAGHUNATHAN and T N VENKATARAMANA. ∗. School of Mathematics, Tata Institute of Fundamental ... linear classical groups GLn(R), GLn(C), SOn(R),. SOn(C), Spn(R) and Spn(C). Let us call a con- nected Lie ..... split groups due respectively to C C Moore and. V Deodhar. B Sury solved the congruence subgroup ...
Fuchs, László
2015-01-01
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah’s seminal work on the undecidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, th...
DEFF Research Database (Denmark)
Pimentel, Ricardo; Noguira, Eloy Eros da Silva; Elkjær, Bente
The article presents a study that aims at the apprehension of the group learning in a top management team composed by teachers in a Brazilian Waldorf school whose management is collective. After deciding to extend the school, they had problems recruiting teachers who were already trained based...... with which they coexist. To achieve this, the research adopted phenomenology as a method and ethnography as strategy, using participant observation, in-depth interviews, and interviews-to-the-double. The results show that the collective management practice is a crossroad of other practices......, and they are interrelated to the group learning as the construction, maintenance and reconstruction of the intelligibility of practices. From this perspective, it can be said that learning is a practice and not an exceptional phenomenon. Building, maintaining and rebuilding the intelligibility is the group learning...
L. Taylor
2011-01-01
The CMS Communications Group, established at the start of 2010, has been busy in all three areas of its responsibility: (1) Communications Infrastructure, (2) Information Systems, and (3) Outreach and Education. Communications Infrastructure There are now 55 CMS Centres worldwide that are well used by physicists working on remote CMS shifts, Computing operations, data quality monitoring, data analysis and outreach. The CMS Centre@CERN in Meyrin, is the centre of the CMS offline and computing operations, hosting dedicated analysis efforts such as during the CMS Heavy Ion lead-lead running. With a majority of CMS sub-detectors now operating in a “shifterless” mode, many monitoring operations are now routinely performed from there, rather than in the main Control Room at P5. The CMS Communications Group, CERN IT and the EVO team are providing excellent videoconferencing support for the rapidly-increasing number of CMS meetings. In parallel, CERN IT and ...
Group representations via geometric quantization of the momentum map
International Nuclear Information System (INIS)
Mladenov, I.M.; Tsanov, V.V.
1992-09-01
In this paper, we treat a general method of quantization of Hamiltonian systems whose flow is a subgroup (not necessarily closed) of a torus acting freely and symplectically on the phase space. The quantization of some classes of completely integrable systems as well as the Borel-Weil-Bott version of representation theory are special cases. (author). 14 refs
L. Taylor
2011-01-01
The CMS Communications Group has been busy in all three areas of its responsibility: (1) Communications Infrastructure, (2) Information Systems, and (3) Outreach and Education. Communications Infrastructure The 55 CMS Centres worldwide are well used by physicists working on remote CMS shifts, Computing operations, data quality monitoring, data analysis and outreach. The CMS Centre@CERN in Meyrin, is the centre of the CMS Offline and Computing operations, and a number of subdetector shifts can now take place there, rather than in the main Control Room at P5. A new CMS meeting room has been equipped for videoconferencing in building 42, next to building 40. Our building 28 meeting room and the facilities at P5 will be refurbished soon and plans are underway to steadily upgrade the ageing equipment in all 15 CMS meeting rooms at CERN. The CMS evaluation of the Vidyo tool indicates that it is not yet ready to be considered as a potential replacement for EVO. The Communications Group provides the CMS-TV (web) cha...
L. Taylor
2010-01-01
The CMS Communications Group, established at the start of 2010, has been strengthening the activities in all three areas of its responsibility: (1) Communications Infrastructure, (2) Information Systems, and (3) Outreach and Education. Communications Infrastructure The Communications Group has invested a lot of effort to support the operations needs of CMS. Hence, the CMS Centres where physicists work on remote CMS shifts, Data Quality Monitoring, and Data Analysis are running very smoothly. There are now 55 CMS Centres worldwide, up from just 16 at the start of CMS data-taking. The latest to join are Imperial College London, the University of Iowa, and the Università di Napoli. The CMS Centre@CERN in Meyrin, which is now full repaired after the major flooding at the beginning of the year, has been at the centre of CMS offline and computing operations, most recently hosting a large fraction of the CMS Heavy Ion community during the lead-lead run. A number of sub-detector shifts can now take pla...
DEFF Research Database (Denmark)
Tychsen, Anders; Hitchens, Michael; Brolund, Thea
2008-01-01
Role-playing games (RPGs) are a well-known game form, existing in a number of formats, including tabletop, live action, and various digital forms. Despite their popularity, empirical studies of these games are relatively rare. In particular there have been few examinations of the effects of the v......Role-playing games (RPGs) are a well-known game form, existing in a number of formats, including tabletop, live action, and various digital forms. Despite their popularity, empirical studies of these games are relatively rare. In particular there have been few examinations of the effects...... of the various formats used by RPGs on the gaming experience. This article presents the results of an empirical study, examining how multi-player tabletop RPGs are affected as they are ported to the digital medium. Issues examined include the use of disposition assessments to predict play experience, the effect...... of group dynamics, the influence of the fictional game characters and the comparative play experience between the two formats. The results indicate that group dynamics and the relationship between the players and their digital characters, are integral to the quality of the gaming experience in multiplayer...
Blomqvist, Gunnar
1989-01-01
As a starting point, the group defined a primary goal of maintaining in flight a level of systemic oxygen transport capacity comparable to each individual's preflight upright baseline. The goal of maintaining capacity at preflight levels would seem to be a reasonable objective for several different reasons, including the maintenance of good health in general and the preservation of sufficient cardiovascular reserve capacity to meet operational demands. It is also important not to introduce confounding variables in whatever other physiological studies are being performed. A change in the level of fitness is likely to be a significant confounding variable in the study of many organ systems. The principal component of the in-flight cardiovascular exercise program should be large-muscle activity such as treadmill exercise. It is desirable that at least one session per week be monitored to assure maintenance of proper functional levels and to provide guidance for any adjustments of the exercise prescription. Appropriate measurements include evaluation of the heart-rate/workload or the heart-rate/oxygen-uptake relationship. Respiratory gas analysis is helpful by providing better opportunities to document relative workload levels from analysis of the interrelationships among VO2, VCO2, and ventilation. The committee felt that there is no clear evidence that any particular in-flight exercise regimen is protective against orthostatic hypotension during the early readaptation phase. Some group members suggested that maintenance of the lower body muscle mass and muscle tone may be helpful. There is also evidence that late in-flight interventions to reexpand blood volume to preflight levels are helpful in preventing or minimizing postflight orthostatic hypotension.
Real symplectic formulation of local special geometry
Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar
2006-01-01
We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.
Symplectic Structure of Intrinsic Time Gravity
Directory of Open Access Journals (Sweden)
Eyo Eyo Ita
2016-08-01
Full Text Available The Poisson structure of intrinsic time gravity is analysed. With the starting point comprising a unimodular three-metric with traceless momentum, a trace-induced anomaly results upon quantization. This leads to a revision of the choice of momentum variable to the (mixed index traceless momentric. This latter choice unitarily implements the fundamental commutation relations, which now take on the form of an affine algebra with SU(3 Lie algebra amongst the momentric variables. The resulting relations unitarily implement tracelessness upon quantization. The associated Poisson brackets and Hamiltonian dynamics are studied.
L. Taylor
2010-01-01
The recently established CMS Communications Group, led by Lucas Taylor, has been busy in all three of its main are areas of responsibility: Communications Infrastructure, Information Systems, and Outreach and Education Communications Infrastructure The damage caused by the flooding of the CMS Centre@CERN on 21st December has been completely repaired and all systems are back in operation. Major repairs were made to the roofs, ceilings and one third of the floor had to be completely replaced. Throughout these works, the CMS Centre was kept operating and even hosted a major press event for first 7 TeV collisions, as described below. Incremental work behind the scenes is steadily improving the quality of the CMS communications infrastructure, particularly Webcasting, video conferencing, and meeting rooms at CERN. CERN/IT is also deploying a pilot service of a new videoconference tool called Vidyo, to assess whether it might provide an enhanced service at a lower cost, compared to the EVO tool currently in w...
L. Taylor
2012-01-01
Outreach and Education We are fortunate that our research has captured the public imagination, even though this inevitably puts us under the global media spotlight, as we saw with the Higgs seminar at CERN in December, which had 110,000 distinct webcast viewers. The media interest was huge with 71 media organisations registering to come to CERN to cover the Higgs seminar, which was followed by a press briefing with the DG and Spokespersons. This event resulted in about 2,000 generally positive stories in the global media. For this seminar, the CMS Communications Group prepared up-to-date news and public material, including links to the CMS results, animations and event displays [http://cern.ch/go/Ch8thttp://cern.ch/go/Ch8t]. There were 44,000 page-views on the CMS public website, with the Higgs news article being by far the most popular item. CMS event displays from iSpy are fast becoming the iconic media images, featuring on numerous major news outlets (BBC, CNN, MSN...) as well as in the sci...
L. Taylor
2011-01-01
Communications Infrastructure The 55 CMS Centres worldwide are well used by physicists working on remote CMS shifts, Computing operations, data quality monitoring, data analysis and outreach. The CMS Centre@CERN in Meyrin is particularly busy at the moment, hosting about 50 physicists taking part in the heavy-ion data-taking and analysis. Three new CMS meeting room will be equipped for videoconferencing in early 2012: 40/5B-08, 42/R-031, and 28/S-029. The CMS-TV service showing LHC Page 1, CMS Page 1, etc. (http://cmsdoc.cern.ch/cmscc/projector/index.jsp) is now also available for mobile devices: http://cern.ch/mcmstv. Figure 12: Screenshots of CMS-TV for mobile devices Information Systems CMS has a new web site: (http://cern.ch/cms) using a modern web Content Management System to ensure content and links are managed and updated easily and coherently. It covers all CMS sub-projects and groups, replacing the iCMS internal pages. It also incorporates the existing CMS public web site (http:/...
Deformations of polyhedra and polygons by the unitary group
International Nuclear Information System (INIS)
Livine, Etera R.
2013-01-01
We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C 2N //SU(2). A framed polyhedron is then parametrized by N spinors living in C 2 satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)). We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in a similar
Atum: Scalable Group Communication Using Volatile Groups
Guerraoui, Rachid; Kermarrec, Anne-Marie; Pavlovic, Matej; Seredinschi, Dragos-Adrian
2016-01-01
This paper presents Atum, a group communication middleware for a large, dynamic, and hostile environment. At the heart of Atum lies the novel concept of volatile groups: small, dynamic groups of nodes, each executing a state machine replication protocol, organized in a flexible overlay. Using volatile groups, Atum scatters faulty nodes evenly among groups, and then masks each individual fault inside its group. To broadcast messages among volatile groups, Atum runs a gossip protocol across the...
Which finite simple groups are unit groups?
DEFF Research Database (Denmark)
Davis, Christopher James; Occhipinti, Tommy
2014-01-01
We prove that if G is a finite simple group which is the unit group of a ring, then G is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order 2^k −1 for some k; or (c) a projective special linear group PSLn(F2) for some n ≥ 3. Moreover, these groups do all occur...
Group Cohesion in Experiential Growth Groups
Steen, Sam; Vasserman-Stokes, Elaina; Vannatta, Rachel
2014-01-01
This article explores the effect of web-based journaling on changes in group cohesion within experiential growth groups. Master's students were divided into 2 groups. Both used a web-based platform to journal after each session; however, only 1 of the groups was able to read each other's journals. Quantitative data collected before and…
Probability groups as orbits of groups
International Nuclear Information System (INIS)
Bhattarai, H.N.
2003-11-01
The set of double cosets of a group with respect to a subgroup and the set of orbits of a group with respect to a group of automorphisms have structures which can be studied as multigroups, hypergroups or Pasch geometries. When the subgroup or the group of automorphisms are finite, the multivalued products can be provided with some weightages forming so-called Probability Groups. It is shown in this paper that some abstract probability groups can be realized as orbit spaces of groups. (author)
Group typicality, group loyalty and cognitive development.
Patterson, Meagan M
2014-09-01
Over the course of childhood, children's thinking about social groups changes in a variety of ways. Developmental Subjective Group Dynamics (DSGD) theory emphasizes children's understanding of the importance of conforming to group norms. Abrams et al.'s study, which uses DSGD theory as a framework, demonstrates the social cognitive skills underlying young elementary school children's thinking about group norms. Future research on children's thinking about groups and group norms should explore additional elements of this topic, including aspects of typicality beyond loyalty. © 2014 The British Psychological Society.
AREVA group overview; Presentation du groupe AREVA
Energy Technology Data Exchange (ETDEWEB)
NONE
2002-02-08
This document presents the Group Areva, a world nuclear industry leader, from a financial holding company to an industrial group, operating in two businesses: the nuclear energy and the components. The structure and the market of the group are discussed, as the financial assets. (A.L.B.)
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Introduction to Sporadic Groups
Directory of Open Access Journals (Sweden)
Luis J. Boya
2011-01-01
Full Text Available This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the 1+1+16=18 families of finite simple groups, as an introduction to the sporadic groups. These are described next, in three levels of increasing complexity, plus the six isolated ''pariah'' groups. The (old five Mathieu groups make up the first, smallest order level. The seven groups related to the Leech lattice, including the three Conway groups, constitute the second level. The third and highest level contains the Monster group M, plus seven other related groups. Next a brief mention is made of the remaining six pariah groups, thus completing the 5+7+8+6=26 sporadic groups. The review ends up with a brief discussion of a few of physical applications of finite groups in physics, including a couple of recent examples which use sporadic groups.
Experience with Group Supervision
Chen, Weiqin
2006-01-01
Supervision can take a few different forms. For example, it can be one-to-one supervision and it can also be group supervision. Group supervision is an important process within the scientific community. Many research groups use this form to supervise doctoral- and master students in groups. Some efforts have been made to study this process. For example, Samara (2002) studied the group supervision process in group writing. However, group supervision has not been studied thorough...
Group Work: How to Use Groups Effectively
Burke, Alison
2011-01-01
Many students cringe and groan when told that they will need to work in a group. However, group work has been found to be good for students and good for teachers. Employers want college graduates to have developed teamwork skills. Additionally, students who participate in collaborative learning get better grades, are more satisfied with their…
Free Boolean Topological Groups
Directory of Open Access Journals (Sweden)
Ol’ga Sipacheva
2015-11-01
Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Group purchasing: an overview.
Wetrich, J G
1987-07-01
The various types and operational methods of purchasing groups are described, and evaluation of groups is discussed. Since group purchasing is increasing in popularity as a method of controlling drug costs, community and hospital pharmacy managers may need to evaluate various groups to determine the appropriateness of their services. Groups are categorized as independent, system based, or alliance or association based. Instead of "purchasing," some groups develop contracts for hospitals, which then purchase directly from the vendor. Aside from this basic difference between groups that purchase and groups that contract, comparisons among groups are difficult because of the wide variation in sizes and services. Competition developing from diversification among groups has led to "super groups," formed from local and regional groups. In evaluating groups, advantages and disadvantages germane to accomplishing the member's objectives must be considered. To ensure a group's success, members must be committed and support the group's philosophies; hospital pharmacists must help to establish a strong formulary system. To select vendors, groups should develop formal qualification and selection criteria and should not base a decision solely on price. The method of solicitation (bidding or negotiating), as well as the role of the prime vendor, should be studied. Legal implications of group purchasing, especially in the areas of administrative fees and drug diversion, must also be considered. The most advantageous group for each organization will include members with common missions and will be able to implement strategies for future success.
Ordered groups and infinite permutation groups
1996-01-01
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that t...
International Nuclear Information System (INIS)
Andritzky, W.
1978-01-01
For the first empirical study of citizens' action groups 331 such groups were consulted. Important information was collected on the following aspects of these groups: their self-image, areas and forms of activities, objectives and their extent, how long the group has existed, successes and failures and their forms of organisation. (orig.) [de
Schopler, Janice H.; Galinsky, Maeda J.
1981-01-01
Studied social workers' perceptions of group dimensions that had negative effects on members. Found that group leaders viewed group composition as a major source of harmful interaction while members and observers saw group norms as a more frequent cause of negative effects. (Author/JAC)
Group Psychotherapy in Germany.
Weber, Rainer; Strauss, Bernhard
2015-10-01
This article gives an overview of the development of group psychotherapies in Germany originating from a psychodynamic tradition. The German health system provides access to inpatient and outpatient psychotherapy for all of its citizens. Whereas groups are common in inpatient settings, the provision of outpatient group treatment still could be improved, as it is the case for the general training of group psychotherapists. Group research in Germany largely reflects clinical practice, with more studies coming from the inpatient field. It is stated that the general image of group treatment seems to be largely positive, which could provide a basis for political initiatives to improve the dissemination of group therapy in this country.
Papadopoulos, Athanase; Yau, Shing-Tung
2015-01-01
Groups and group actions are probably the most central objects in mathematics. Comprising volumes 31 and 32 of the ALM series (with further volumes forthcoming), the Handbook of Group Actions presents survey articles on the topic of group actions and how they appear in several mathematical contexts. The general subject matter is organized under the following sections: geometry, mapping class groups, knot groups, topology, representation theory, deformation theory, and discrete groups. The various articles deal with both classical material and modern developments. They are written by specialists in their respective subject areas, and addressed to graduate students who want to learn the theory, as well as to specialists as a reference.
Sharon Belenzon; Tomer Berkovitz
2007-01-01
Using novel data on European firms, this paper investigates the relationship between business groups and innovation. Controlling for various firm characteristics, we find that group affiliates are more innovative than standalones. We examine several hypotheses to explain this finding, focusing on group internal capital markets and knowledge spillovers. We find that group affiliation is particularly important for innovation in industries that rely more on external funding and in groups with mo...
Group Psychotherapy in Iceland.
Ívarsson, Ómar
2015-10-01
In this overview of group psychotherapy in Iceland, an attempt will be made to describe how it is practiced today, give some glimpses into its earlier history, and clarify seven issues: (1) the standing of group psychotherapy in Iceland, its previous history, and the theoretical orientation of dynamic group therapy in the country; (2) the role of group therapy in the health care system; (3) how training in group therapy is organized; (4) the relationship between group psychotherapy research and clinical practice; (5) which issues/processes can be identified as unique to therapy groups in Iceland; and (6) how important are group-related issues within the social background of the country; and (7) what group work holds for the future.
Independent student study groups.
Hendry, Graham D; Hyde, Sarah J; Davy, Peter
2005-07-01
Teachers and students regulate learning to varying degrees in educational programmes in higher education. We present evidence that students in a student-centred medical programme self- and co-regulate their learning in independently formed study groups. We describe the perceived benefits of study groups and the effect of study group membership on student achievement. Years 1-2 of a 4-year, graduate-entry problem-based medical programme. We surveyed 233 year 2 students about features of their study groups and their study group membership in years 1-2. We compared study group membership with students' scores on a written summative assessment held at the end of their second year. For students who joined 1 study group, the length of time their group stayed together was positively related to achievement in the written summative assessment. There were no differences in summative assessment results between students who had been in a study group and students who had not been in a study group. Effective study groups are supportive, socially cohesive groups who generate mutual trust and loyalty, and self- and co-regulate their learning by giving and receiving explanations and summaries and motivating individual study. Teachers can support the formation of study groups by using small-group teaching/learning activities, providing clear learning outcomes and assessment criteria, minimising competition for grades and allocating room space.
Nilpotent -local finite groups
Cantarero, José; Scherer, Jérôme; Viruel, Antonio
2014-10-01
We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
Group Decision Process Support
DEFF Research Database (Denmark)
Gøtze, John; Hijikata, Masao
1997-01-01
Introducing the notion of Group Decision Process Support Systems (GDPSS) to traditional decision-support theorists.......Introducing the notion of Group Decision Process Support Systems (GDPSS) to traditional decision-support theorists....
U.S. Department of Health & Human Services — The Group Unique Physician Identifier Number (UPIN) File is the business entity file that contains the group practice UPIN and descriptive information. It does NOT...
Introduction to topological groups
Husain, Taqdir
2018-01-01
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
Directory of Open Access Journals (Sweden)
Ali Sayed Elfard
2015-10-01
Full Text Available Let FP(X be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X on a $P_\\alpha$-space $X$ where $\\alpha$ is an infinite cardinal and then we prove that the group FP(X is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a~neighborhood base at the identity of the group FP(X when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group FP(X is T_0 if X is T_0, we characterize the spaces X for which the group FP(X is a topological group and then we give a class of spaces $X$ for which the group FP(X has the inductive limit property.
Group B streptococcus - pregnancy
... page: //medlineplus.gov/ency/patientinstructions/000511.htm Group B streptococcus - pregnancy To use the sharing features on this page, please enable JavaScript. Group B streptococcus (GBS) is a type of bacteria that ...
Harman, Robert L.; Franklin, Richard W.
1975-01-01
Gestalt therapy in groups is not limited to individual work in the presence of an audience. Describes several ways to involve gestalt groups interactionally. Interactions described focus on learning by doing and discovering, and are noninterpretive. (Author/EJT)
Hans Nienstaedt; Dean W. Einspahr; J. Douglas Brodie
1973-01-01
Editor's note: The morning's presentations were discussed during the afternoon by three groups, each group discussing one of the morning's three topics. Summaries of the discussions, prepared by the discussion leaders, follow.
DEFF Research Database (Denmark)
Hansen, Annette Skovsted
2014-01-01
Motivation for the activity I use this strategy for forming groups to ensure diverse/multicultural groups that combine a variety of different strengths and resources based on student's academic, disciplinary, linguistic, national, personal and work backgrounds.......Motivation for the activity I use this strategy for forming groups to ensure diverse/multicultural groups that combine a variety of different strengths and resources based on student's academic, disciplinary, linguistic, national, personal and work backgrounds....
International Nuclear Information System (INIS)
2002-01-01
This document presents the Group Areva, a world nuclear industry leader, from a financial holding company to an industrial group, operating in two businesses: the nuclear energy and the components. The structure and the market of the group are discussed, as the financial assets. (A.L.B.)
Indian Academy of Sciences (India)
Jyotishman Bhowmick
2015-11-07
Nov 7, 2015 ... NONcommutative spaces. 2. Banica and Bichon defined quantum symmetry groups for finite metric spaces, finite graphs, etc. 3. Lots of examples computed leading to discovery of completely new kinds of quantum groups. Jyotishman Bhowmick (Indian Statistical Institute). Quantum isometry groups. 07.11.
DEFF Research Database (Denmark)
Gil, J. I. Burgos; Feliu, Elisenda
2012-01-01
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov co...
Asymmetry within social groups
DEFF Research Database (Denmark)
Barker, Jessie; Loope, Kevin J.; Reeve, H. Kern
2016-01-01
Social animals vary in their ability to compete with group members over shared resources and also vary in their cooperative efforts to produce these resources. Competition among groups can promote within-group cooperation, but many existing models of intergroup cooperation do not explicitly account...
Nooteboom, H.P.; Leonardía, A.A.P.
2012-01-01
Holttum, R.E., Tectaria group. Flora Malesiana, Ser. II, 2 (1991) 1–132 defined this group without the genus Arthropteris. Later molecular studies indicated that this genus belongs to Tectariaceae, the Tectaria group of Holttum. The genus contains two species in Malesia. Illustration is by one
McAllan, Les; Friedman, Amy; Spears, Evans
Perhaps the most well known treatment modalities in the field of prevention and treatment of addiction are groups. Group settings serve to bring individuals with addictions together at one time in one place to work on relevant issues together. Groups may serve as a safe environment for learning new social and relationship skills, gaining…
Group Psychotherapy in Denmark.
Jørgensen, Lars Bo; Thygesen, Bente; Aagaard, Søren
2015-10-01
This is a short article on the history and training standards in the Institute of Group Analysis in Copenhagen (IGA-CPH). We describe theoretical orientations and influences in the long-term training program and new initiatives, like courses in mentalization-based group treatment and a dynamic short-term group therapy course, as well as research in group psychotherapy in Denmark. Some group analytic initiatives in relation to social issues and social welfare are presented, as well as initiatives concerning the school system and unemployment.
Milewski, Emil G
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. Group Theory I includes sets and mapping, groupoids and semi-groups, groups, isomorphisms and homomorphisms, cyclic groups, the Sylow theorems, and finite p-groups.
Steinberg, Robert
2016-01-01
Robert Steinberg's Lectures on Chevalley Groups were delivered and written during the author's sabbatical visit to Yale University in the 1967-1968 academic year. The work presents the status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in the subsequent classification of finite groups. This posthumous edition incorporates additions and corrections prepared by the author during his retirement, including a new introductory chapter. A bibliography and editorial notes have also been added. This is a great unsurpassed introduction to the subject of Chevalley groups that influenced generations of mathematicians. I would recommend it to anybody whose interests include group theory. -Efim Zelmanov, University of California, San Diego Robert Steinberg's lectures on Chevalley groups were given at Yale University in 1967. The notes for the lectures contain a wonderful exposition of ...
HR Department
2012-01-01
There will be an e-groups training course on 16 March 2012 which will cover the main e-groups functionalities i.e.: creating and managing e-groups, difference between static and dynamic e-groups, configuring posting restrictions and archives, examples of where e-groups can be used in daily work. Even if you have already worked with e-groups, this may be a good opportunity to learn about the best practices and security related recommendations when using e-groups. You can find more details as well as enrolment form for the training (it’s free) here. The number of places is limited, so enrolling early is recommended. Technical Training Tel. 72844
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Directory of Open Access Journals (Sweden)
Ranadhir Mitra
2014-01-01
Full Text Available International Society of Blood Transfusion has recently recognized 33 blood group systems. Apart from ABO and Rhesus system, many other types of antigens have been noticed on the red cell membranes. Blood grouping and cross-matching is one of the few important tests that the anaesthesiologist orders during perioperative period. Hence, a proper understanding of the blood group system, their clinical significance, typing and cross-matching tests, and current perspective are of paramount importance to prevent transfusion-related complications. Nonetheless, the knowledge on blood group system is necessary to approach blood group-linked diseases which are still at the stage of research. This review addresses all these aspects of the blood groups system.
CLASSIFICATION OF CRIMINAL GROUPS
Natalia Romanova
2013-01-01
New types of criminal groups are emerging in modern society. These types have their special criminal subculture. The research objective is to develop new parameters of classification of modern criminal groups, create a new typology of criminal groups and identify some features of their subculture. Research methodology is based on the system approach that includes using the method of analysis of documentary sources (materials of a criminal case), method of conversations with themembers of the...
Johnson, D L
1997-01-01
The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
Greenberg, M R
1986-01-01
With the advent of acquisitions and mergers of healthcare organizations, it has become necessary for medical group practices to know what they are worth. The traditional balance sheet valuation ignores what is perhaps the most important consideration of all: a group's earning potential. Discussed in this article are the many facets of the complex valuation process, including both tangible and intangible assets, and the author provides a method for adequately determining a range of values for a medical group.
The maximal acceleration group
International Nuclear Information System (INIS)
Brandt, H.E.
1984-01-01
On the basis of the maximal proper acceleration relative to the vacuum, a line element and differential geometry of eight-dimensional phase space are constructed. The maximal acceleration group is defined as the mathematical transformation group under which the eight dimensional line element is invariant. In the classical limit of vanishing Planck's constant, the maximal acceleration group and geometry reduce to those of general relativity
DEFF Research Database (Denmark)
Hjorth, Poul G.
2007-01-01
Since 1998 European Study Groups have been held in Denmark, and Danish companies from LEGO and NOVO to very small high-tech firms have participated. I briefly describe the history, the organisation and the format of the Danish Study Groups, and highlight a few problem solutions.......Since 1998 European Study Groups have been held in Denmark, and Danish companies from LEGO and NOVO to very small high-tech firms have participated. I briefly describe the history, the organisation and the format of the Danish Study Groups, and highlight a few problem solutions....
Federal Laboratory Consortium — The Explosive Technology Group (ETG) provides diverse technical expertise and an agile, integrated approach to solve complex challenges for all classes of energetic...
International Nuclear Information System (INIS)
Olmos, C.
1990-05-01
The restricted holonomy group of a Riemannian manifold is a compact Lie group and its representation on the tangent space is a product of irreducible representations and a trivial one. Each one of the non-trivial factors is either an orthogonal representation of a connected compact Lie group which acts transitively on the unit sphere or it is the isotropy representation of a single Riemannian symmetric space of rank ≥ 2. We prove that, all these properties are also true for the representation on the normal space of the restricted normal holonomy group of any submanifold of a space of constant curvature. 4 refs
Lipkin, Harry J
2002-01-01
According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie group
Environmental groups in politics
International Nuclear Information System (INIS)
Lowe, P.; Goyder, J.
1983-01-01
The subject is covered in chapters, entitled: introduction; (Part I) the environmental movement (environmental groups and the attentive public; the episodic development of the environmental movement; the underlying values of environmentalism; the roots of environmental concern; the social limits to growth; elite manipulation of values); the organisation of environmental groups; environmental groups in national politics; environmental groups in local politics; (Part II) the Henley Society; Friends of the Earth; the National Trust; the Royal Society for Nature Conservation; the European Environmental Bureau. (U.K.)
Directory of Open Access Journals (Sweden)
Maike Buchin
2015-03-01
Full Text Available The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters that allow more global views of the data in group size, group duration, and entity inter-distance. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. We also study how the trajectory grouping structure can be made robust, that is, how brief interruptions of groups can be disregarded in the global structure, adding a notion of persistence to the structure. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. The Starkey data describe the movement of elk, deer, and cattle. Although there is no ground truth for the grouping structure in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial,algorithmic, and experimental results.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 11. Combinatorial Group Theory Group Theory via Generators and Relations. B Sury. General Article Volume 1 Issue 11 November 1996 pp 42-50. Fulltext. Click here to view fulltext PDF. Permanent link:
Peggs, S.
This paper summarizes the activities of the beam dynamics working group of the LHC Collective Effects Workshop that was held in Montreux in 1994. It reviews the presentations that were made to the group, the discussions that ensued, and the consensuses that evolved.
Indian Academy of Sciences (India)
Jyotishman Bhowmick
2015-11-07
Nov 7, 2015 ... Lots of examples computed leading to discovery of completely new kinds of quantum groups. Jyotishman Bhowmick (Indian Statistical Institute). Quantum ... on a noncommutative Riemannian manifold ( given by a spectral data ). Jyotishman Bhowmick (Indian Statistical Institute). Quantum isometry groups.
Laursen, Erik K.; Tate, Thomas F.
2012-01-01
For a century, democratic values have called for abandoning coercive approaches and teaching children and youth to be responsible citizens. The authors explore strategies for creating respectful environments and positive group cultures with challenging youth. They offer suggestions to adult group facilitators to support youth in developing…
Walker, Karen
2010-01-01
According to Johnson and Johnson, group work helps increase student retention and satisfaction, develops strong oral communication and social skills, as well as higher self-esteem (University of Minnesota, n.d.). Group work, when planned and implemented deliberately and thoughtfully helps students develop cognitive and leadership skills as well as…
Supervision and group dynamics
DEFF Research Database (Denmark)
Hansen, Søren; Jensen, Lars Peter
2004-01-01
An important aspect of the problem based and project organized study at Aalborg University is the supervision of the project groups. At the basic education (first year) it is stated in the curriculum that part of the supervisors' job is to deal with group dynamics. This is due to the experience...
Burlingame, Gary M; McClendon, Debra Theobald; Alonso, Jennifer
2011-03-01
Cohesion is the most popular of several relationship constructs in the clinical and empirical group therapy literature. This article reviews the most frequently cited definitions and studied measures of group cohesion. We briefly introduce a new measure, the Group Questionnaire, which elucidates group relationships by suggesting two latent factors of cohesion-relationship quality (positive bond, positive work, and negative relationship) and structure factors (member-leader and member-member). To further understand the literature, we conducted a meta-analysis examining the relationship between cohesion and treatment outcome in 40 studies. Results indicate cohesion that the weighted aggregate correlation was statistically significant with outcome r = .25, k (40), N (3,323), z = 6.54 (p cohesion outcome correlation (age, theoretical orientation, length, and size of group, as well as interventions intended to enhance cohesion). Consideration of measures and practices to improve treatment outcome are highlighted. (PsycINFO Database Record (c) 2011 APA, all rights reserved).
Natural analogue working group
International Nuclear Information System (INIS)
Come, B.; Chapman, N.
1986-01-01
A Natural Analogue Working Group was established by the Commission of the European Communities in 1985. The purpose of this group is to bring together modellers with earth scientists and others, so that maximum benefit can be obtained from natural analogue studies with a view to safe geological disposal of radioactive waste. The first meeting of this group was held in Brussels from November 5 to 7, 1985. The discussions mainly concerned the identification of the modellers' needs and of the earth scientists' capacity to provide for them. Following the debates, a written statement was produced by the Group; this document forms the core of the present Report. Notes and outlines of many of the presentations made are grouped in four appendixes. The valuable contribution of all those involved in the meeting is gratefully acknowledged
Clay, Adam
2016-01-01
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Mazzoni, Sara E; Carter, Ebony B
2017-06-01
Patients participating in group prenatal care gather together with women of similar gestational ages and 2 providers who cofacilitate an educational session after a brief medical assessment. The model was first described in the 1990s by a midwife for low-risk patients and is now practiced by midwives and physicians for both low-risk patients and some high-risk patients, such as those with diabetes. The majority of literature on group prenatal care uses CenteringPregnancy, the most popular model. The first randomized controlled trial of CenteringPregnancy showed that it reduced the risk of preterm birth in low-risk women. However, recent meta-analyses have shown similar rates of preterm birth, low birthweight, and neonatal intensive care unit admission between women participating in group prenatal care and individual prenatal care. There may be subgroups, such as African Americans, who benefit from this type of prenatal care with significantly lower rates of preterm birth. Group prenatal care seems to result in increased patient satisfaction and knowledge and use of postpartum family planning as well as improved weight gain parameters. The literature is inconclusive regarding breast-feeding, stress, depression, and positive health behaviors, although it is theorized that group prenatal care positively affects these outcomes. It is unclear whether group prenatal care results in cost savings, although it may in large-volume practices if each group consists of approximately 8-10 women. Group prenatal care requires a significant paradigm shift. It can be difficult to implement and sustain. More randomized trials are needed to ascertain the true benefits of the model, best practices for implementation, and subgroups who may benefit most from this innovative way to provide prenatal care. In short, group prenatal care is an innovative and promising model with comparable pregnancy outcomes to individual prenatal care in the general population and improved outcomes in some
Bhavnani, Ravi; Miodownik, Dan; Riolo, Rick
Violence can take place along a multitude of cleavages, e.g., (1) between political groups like the Kach Movement, pitting West Bank settlers against Israeli governments supporting the land-for-peace agenda; (2) between religious groups, such as Christians and Muslims in the Nigerian cities of Jos and Kaduna; (3) along class lines, as in India between Dalits and members of the Brahminical upper castes, upwardly mobile intermediate castes, and even other backward castes such as the Thevars; and (4) between ethnic groups such as the Hutu and Tutsi, both within and across state boundaries in Rwanda and neighboring Burundi.
DEFF Research Database (Denmark)
Lindegaard, Laura Bang
2014-01-01
Scholars of ethnomethodologically informed discourse studies are often sceptical of the use of interview data such as focus group data. Some scholars quite simply reject interview data with reference to a general preference for so-called naturally occurring data. Other scholars acknowledge......, not as something that pre-exists or goes beyond the situated interaction. This article, however, challenges not only the first, but also the second position and suggests that it is, after all, possible to do committedly ethnomethodological studies of focus group data that demonstrate how members of a focus group...
Ballester-Bolinches, Adolfo; Asaad, Mohamed
2010-01-01
The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups.
Energy Technology Data Exchange (ETDEWEB)
Dunigan, T.; Cao, C.
1997-08-01
This report describes an architecture and implementation for doing group key management over a data communications network. The architecture describes a protocol for establishing a shared encryption key among an authenticated and authorized collection of network entities. Group access requires one or more authorization certificates. The implementation includes a simple public key and certificate infrastructure. Multicast is used for some of the key management messages. An application programming interface multiplexes key management and user application messages. An implementation using the new IP security protocols is postulated. The architecture is compared with other group key management proposals, and the performance and the limitations of the implementation are described.
Moreau, A
1976-01-01
Kibbouts-group: three therapeutic or growth factors together: manual work, community life and group technics (group dynamic, Gestalt, psychodrama, bio-energetic) during two weeks. The work of growing and therapy is becoming more concrete and facilitated by the absence of difference between members and leader who share the work and the community life. Important and rapid changes are frequent: a particular attention is given to the "unmedicalisation" of symptoms (fatigue) and to the "unpsychiatrisation" of conflicts. A sample and authentical life style, together with a high degree of communication, favor the desinhibition of attitudes, the clarification of conflicts and the reenforcement of the personality.
The Military Cooperation Group
National Research Council Canada - National Science Library
Renzi, Jr, Alfred E
2006-01-01
.... This thesis will describe a structure to assist with both those needs. The premise is that an expanded and improved network of US Military Groups is the weapon of choice for the war on terror, and beyond...
International Nuclear Information System (INIS)
Leivo, H.P.
1992-01-01
The algebraic approach to quantum groups is generalized to include what may be called an anyonic symmetry, reflecting the appearance of phases more general than ±1 under transposition. (author). 6 refs
Homogenous finitary symmetric groups
Directory of Open Access Journals (Sweden)
Otto. H. Kegel
2015-03-01
Full Text Available We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let kappa be an infinite cardinal. If G=underseti=1stackrelinftybigcupG i , where G i =FSym(kappan i , (H=underseti=1stackrelinftybigcupH i , where H i =Alt(kappan i , is a group of strictly diagonal type and xi=(p 1 ,p 2 ,ldots is an infinite sequence of primes, then G is isomorphic to the homogenous finitary symmetric group FSym(kappa(xi (H is isomorphic to the homogenous alternating group Alt(kappa(xi , where n 0 =1,n i =p 1 p 2 ldotsp i .
International Nuclear Information System (INIS)
Anon.
1981-01-01
At this meeting, the main tasks of the study group were to discuss their task report with other task groups and to formulate the five-year research program, including next year's plans. A summary of the discussion with other task groups is presented. The general objective of the five-year program is to gather all elements necessary for a decision on the technical feasibility of the subseabed option. In addition, site selection criteria consistent with both radiological assessment and engineering capability will be produced. The task group report discussed radiological assessments, normal or base-case assessments, operational failures, low-probability postdisposal events, engineering studies, radiological criteria, legal aspects, social aspects, institutional aspects, generic comparison with other disposal options, and research priorities. The text of the report is presented along with supporting documents
Homogeneous group, research, institution
Directory of Open Access Journals (Sweden)
Francesca Natascia Vasta
2014-09-01
Full Text Available The work outlines the complex connection among empiric research, therapeutic programs and host institution. It is considered the current research state in Italy. Italian research field is analyzed and critic data are outlined: lack of results regarding both the therapeutic processes and the effectiveness of eating disorders group analytic treatment. The work investigates on an eating disorders homogeneous group, led into an eating disorder outpatient service. First we present the methodological steps the research is based on including the strong connection among theory and clinical tools. Secondly clinical tools are described and the results commented. Finally, our results suggest the necessity of validating some more specifical hypothesis: verifying the relationship between clinical improvement (sense of exclusion and painful emotions reduction and specific group therapeutic processes; verifying the relationship between depressive feelings, relapses and transition trough a more differentiated groupal field.Keywords: Homogeneous group; Eating disorders; Institutional field; Therapeutic outcome
DEFF Research Database (Denmark)
Nielsen, Henrik
2012-01-01
Group I intron ribozymes constitute one of the main classes of ribozymes and have been a particularly important model in the discovery of key concepts in RNA biology as well as in the development of new methods. Compared to other ribozyme classes, group I intron ribozymes display considerable...... variation both in their structure and the reactions they catalyze. The best described pathway is the splicing pathway that results in a spliced out intron and ligated exons. This is paralleled by the circularization pathway that leads to full-length circular intron and un-ligated exons. In addition......, the intronic products of these pathways have the potential to integrate into targets and to form various types of circular RNA molecules. Thus, group I intron ribozymes and associated elements found within group I introns is a rich source of biological phenomena. This chapter provides a strategy and protocols...
Hall, Marshall
2018-01-01
This 1959 text offers an unsurpassed resource for learning and reviewing the basics of a fundamental and ever-expanding area. "This remarkable book undoubtedly will become a standard text on group theory." - American Scientist.
James, D
2002-01-01
The Transport Working Group was formed on The 10th November 1999 to study all means of transport required for the installation of the LHC machine in the existing tunnel infrastructure of the LEP. The Groups' main aim is to assess the feasibility of transport propositions offered for the handling to be carried out in the new LHC environment. The working group is composed of Mechanical Engineers, Physicists and Transport Engineers, as well as specialists who are invited to the meetings for their advice on certain aspects of the forthcoming installation. In May 2001 the group mandate was revised to include all means of transport, including surface transport as well as that required in the tunnel. The installation phase requires the handling of approximately 100,000 tonnes of delicate experimental equipment with very strict limits in terms of acceleration and shock loading. This must be installed via vertical shafts up to 140 meters deep.
Directory of Open Access Journals (Sweden)
S. Nazmul
2014-03-01
Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.
Auslander, Maurice
2014-01-01
This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions
Parton Distributions Working Group
International Nuclear Information System (INIS)
Barbaro, L. de; Keller, S. A.; Kuhlmann, S.; Schellman, H.; Tung, W.-K.
2000-01-01
This report summarizes the activities of the Parton Distributions Working Group of the QCD and Weak Boson Physics workshop held in preparation for Run II at the Fermilab Tevatron. The main focus of this working group was to investigate the different issues associated with the development of quantitative tools to estimate parton distribution functions uncertainties. In the conclusion, the authors introduce a Manifesto that describes an optimal method for reporting data
Parton Distributions Working Group
Energy Technology Data Exchange (ETDEWEB)
de Barbaro, L.; Keller, S. A.; Kuhlmann, S.; Schellman, H.; Tung, W.-K.
2000-07-20
This report summarizes the activities of the Parton Distributions Working Group of the QCD and Weak Boson Physics workshop held in preparation for Run II at the Fermilab Tevatron. The main focus of this working group was to investigate the different issues associated with the development of quantitative tools to estimate parton distribution functions uncertainties. In the conclusion, the authors introduce a Manifesto that describes an optimal method for reporting data.
Olejarski, Michael; Appleton, Amy; Deltorchio, Stephen
2009-01-01
The Group Capability Model (GCM) is a software tool that allows an organization, from first line management to senior executive, to monitor and track the health (capability) of various groups in performing their contractual obligations. GCM calculates a Group Capability Index (GCI) by comparing actual head counts, certifications, and/or skills within a group. The model can also be used to simulate the effects of employee usage, training, and attrition on the GCI. A universal tool and common method was required due to the high risk of losing skills necessary to complete the Space Shuttle Program and meet the needs of the Constellation Program. During this transition from one space vehicle to another, the uncertainty among the critical skilled workforce is high and attrition has the potential to be unmanageable. GCM allows managers to establish requirements for their group in the form of head counts, certification requirements, or skills requirements. GCM then calculates a Group Capability Index (GCI), where a score of 1 indicates that the group is at the appropriate level; anything less than 1 indicates a potential for improvement. This shows the health of a group, both currently and over time. GCM accepts as input head count, certification needs, critical needs, competency needs, and competency critical needs. In addition, team members are categorized by years of experience, percentage of contribution, ex-members and their skills, availability, function, and in-work requirements. Outputs are several reports, including actual vs. required head count, actual vs. required certificates, CGI change over time (by month), and more. The program stores historical data for summary and historical reporting, which is done via an Excel spreadsheet that is color-coded to show health statistics at a glance. GCM has provided the Shuttle Ground Processing team with a quantifiable, repeatable approach to assessing and managing the skills in their organization. They now have a common
Cyclic Soft Groups and Their Applications on Groups
Directory of Open Access Journals (Sweden)
Hacı Aktaş
2014-01-01
Full Text Available In crisp environment the notions of order of group and cyclic group are well known due to many applications. In this paper, we introduce order of the soft groups, power of the soft sets, power of the soft groups, and cyclic soft group on a group. We also investigate the relationship between cyclic soft groups and classical groups.
International Nuclear Information System (INIS)
1994-01-01
In December 1992, western governors and four federal agencies established a Federal Advisory Committee to Develop On-site Innovative Technologies for Environmental Restoration and Waste Management (the DOIT Committee). The purpose of the Committee is to advise the federal government on ways to improve waste cleanup technology development and the cleanup of federal sites in the West. The Committee directed in January 1993 that information be collected from a wide range of potential stakeholders and that innovative technology candidate projects be identified, organized, set in motion, and evaluated to test new partnerships, regulatory approaches, and technologies which will lead to improve site cleanup. Five working groups were organized, one to develop broad project selection and evaluation criteria and four to focus on specific contaminant problems. A Coordinating Group comprised of working group spokesmen and federal and state representatives, was set up to plan and organize the routine functioning of these working groups. The working groups were charged with defining particular contaminant problems; identifying shortcomings in technology development, stakeholder involvement, regulatory review, and commercialization which impede the resolution of these problems; and identifying candidate sites or technologies which could serve as regional innovative demonstration projects to test new approaches to overcome the shortcomings. This report from the Coordinating Group to the DOIT Committee highlights the key findings and opportunities uncovered by these fact-finding working groups. It provides a basis from which recommendations from the DOIT Committee to the federal government can be made. It also includes observations from two public roundtables, one on commercialization and another on regulatory and institutional barriers impeding technology development and cleanup
Matrix groups for undergraduates
Tapp, Kristopher
2016-01-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups. From reviews of the First Edition: This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. … The book combines an intuitive style of writing w...
Summary report: injection group
International Nuclear Information System (INIS)
Simpson, J.; Ankenbrandt, C.; Brown, B.
1984-01-01
The injector group attempted to define and address several problem areas related to the SSC injector as defined in the Reference Design Study (RDS). It also considered the topic of machine utilization, particularly the question of test beam requirements. Details of the work are given in individually contributed papers, but the general concerns and consensus of the group are presented within this note. The group recognized that the injector as outlined in the RDS was developed primarily for costing estimates. As such, it was not necessarily well optimized from the standpoint of insuring the required beam properties for the SSC. On the other hand, considering the extraordinary short time in which the RDS was prepared, it is an impressive document and a good basis from which to work. Because the documented SSC performance goals are ambitious, the group sought an injector solution which would more likely guarantee that SSC performance not be limited by its injectors. As will be seen, this leads to a somewhat different solution than that described in the RDS. Furthermore, it is the consensus of the group that the new, conservative approach represents only a modest cost increase of the overall project well worth the confidence gained and the risks avoided
Pérez-Zepeda, M U; Ávila-Funes, J A; Gutiérrez-Robledo, L M; García-Peña, C
2016-01-01
The implementation of an aging biomarker into clinical practice is under debate. The Frailty Index is a model of deficit accumulation and has shown to accurately capture frailty in older adults, thus bridging biological with clinical practice. To describe the association of socio-demographic characteristics and the Frailty Index in different age groups (from 20 to over one hundred years) in a representative sample of Mexican subjects. Cross-sectional analysis. Nationwide and population-representative survey. Adults 20-years and older interviewed during the last Mexican National Health and Nutrition Survey (2012). A 30-item Frailty Index following standard construction was developed. Multi-level regression models were performed to test the associations of the Frailty Index with multiple socio-demographic characteristics across age groups. A total of 29,504 subjects was analyzed. The 30-item Frailty Index showed the highest scores in the older age groups, especially in women. No sociodemographic variable was associated with the Frailty Index in all the studied age groups. However, employment, economic income, and smoking status were more consistently found across age groups. To our knowledge, this is the first report describing the Frailty Index in a representative large sample of a Latin American country. Increasing age and gender were closely associated with a higher score.
Hennink, Monique M
2014-01-01
The Understanding Research series focuses on the process of writing up social research. The series is broken down into three categories: Understanding Statistics, Understanding Measurement, and Understanding Qualitative Research. The books provide researchers with guides to understanding, writing, and evaluating social research. Each volume demonstrates how research should be represented, including how to write up the methodology as well as the research findings. Each volume also reviews how to appropriately evaluate published research. Focus Group Discussions addresses the challenges associated with conducting and writing focus group research. It provides detailed guidance on the practical and theoretical considerations in conducting focus group discussions including: designing the discussion guide, recruiting participants, training a field team, moderating techniques and ethical considerations. Monique Hennink describes how a methodology section is read and evaluated by others, such as journal reviewers or ...
Energy Technology Data Exchange (ETDEWEB)
David G. Loomis
2012-05-28
The Illinois Wind Working Group (IWWG) was founded in 2006 with about 15 members. It has grown to over 200 members today representing all aspects of the wind industry across the State of Illinois. In 2008, the IWWG developed a strategic plan to give direction to the group and its activities. The strategic plan identifies ways to address critical market barriers to the further penetration of wind. The key to addressing these market barriers is public education and outreach. Since Illinois has a restructured electricity market, utilities no longer have a strong control over the addition of new capacity within the state. Instead, market acceptance depends on willing landowners to lease land and willing county officials to site wind farms. Many times these groups are uninformed about the benefits of wind energy and unfamiliar with the process. Therefore, many of the project objectives focus on conferences, forum, databases and research that will allow these stakeholders to make well-educated decisions.
Directory of Open Access Journals (Sweden)
James N. Druckman
2013-06-01
Full Text Available A randomized experiment was conducted to assess the effectiveness of three forms of e-mail appeals to prospective members of a newly formed professional group. The baseline condition consisted of an impersonal appeal; prospective members were sent a mass e-mail encouraging them to join. Participants in the personal condition received an e-mail with the same content, prefaced by a personal note from the group president. Participants in the social pressure condition received a personal note that called attention to the fact that they had previously signed a petition to form the professional group and urged them to make good on their earlier pledge (i.e., signing of the petition. Personalization is found to generate strong and statistically significant treatment effects. Even stronger are the effects of social pressure.
Internal deformation of Lie algebroids and symplectic realizations
Energy Technology Data Exchange (ETDEWEB)
Carinena, Jose F [Departamento de Fisica Teorica, Universidad de Zara-goza, 50009 Zaragoza (Spain); Costa, Joana M Nunes da [Departamento de Matematica, Universidade de Coimbra, 3001-454 Coimbra (Portugal); Santos, PatrIcia [Departamento de Fisica e Matematica, Instituto Superior de Engenharia de Coimbra, 3030-199 Coimbra (Portugal)
2006-06-02
Given a Lie algebroid and a bundle over its base which is endowed with a localizable Poisson structure and a flat connection, we construct an extended bundle whose dual is endowed with an almost-Poisson structure that is a quadratic Poisson structure when a certain compatibility property is satisfied. This new formalism on Lie algebroids describes systems with internal degrees of freedom.
Even and odd symplectic and Kaehlerian structures on projective superspaces
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersessyan, A.P.
1992-01-01
Supergeneralization of CP(N) provided by even and odd Kaehlerian structures from Hamiltonian reduction are construct. Operator Δ which used in Batalin - Vilkovsky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered. 21 refs
Galilean Duffin-Kemmer-Petiau algebra and symplectic structure
Fernandes, M C B; Vianna, J D M
2003-01-01
We develop the Duffin-Kemmer-Petiau (DKP) approach in the phase-space picture of quantum mechanics by considering DKP algebras in a Galilean covariant context. Specifically, we develop an algebraic calculus based on a tensor algebra defined on a five-dimensional space which plays the role of spacetime background of the non-relativistic DKP equation. The Liouville operator is determined and the Liouville-von Neumann equation is written in two situations: the free particle and a particle in an external electromagnetic field. A comparison between the non-relativistic and the relativistic cases is commented.
Symplectic structure of quantum phase and stochastic simulation of qubits
International Nuclear Information System (INIS)
Rybakov, Yu.P.; Kamalov, T.F.
2009-01-01
Starting from the projective interpretation of the Hilbert space, a special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, another example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-soliton configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling
Internal deformation of Lie algebroids and symplectic realizations
International Nuclear Information System (INIS)
Carinena, Jose F; Costa, Joana M Nunes da; Santos, PatrIcia
2006-01-01
Given a Lie algebroid and a bundle over its base which is endowed with a localizable Poisson structure and a flat connection, we construct an extended bundle whose dual is endowed with an almost-Poisson structure that is a quadratic Poisson structure when a certain compatibility property is satisfied. This new formalism on Lie algebroids describes systems with internal degrees of freedom
A geometric construction of the symplectic form in general relativity
International Nuclear Information System (INIS)
Szczyrba, W.
1977-01-01
The concept of the canonical quantization plays an important role in passing from classical to quantum systems. This procedure, well known in mechanics is based on the Hamilton (canonical) formulation of physical systems with finite degrees of freedom. In recent years an elegant geometric approach to the Hamilton formalism has been found. In this formulation a 2n-dimensional manifold Psub(2n) - the phase space of the system and a closed non-degenerate differential 2-form Ω on Psub(2n). The form Ω defines a Lie algebra structure in the set F of all smooth functions on Psub(2n). In this paper the multisymplectic structure for General Relativity is constructed. (Auth.)
Symplectic symmetry of the neutrino mass for many neutrino flavors
International Nuclear Information System (INIS)
Oeztuerk, N.; Ankara Univ.
2001-01-01
The algebraic structure of the neutrino mass Hamiltonian is presented for two neutrino flavors considering both Dirac and Majorana mass terms. It is shown that the algebra is Sp(8) and also discussed how the algebraic structure generalizes for the case of more than two neutrino flavors. (orig.)
Degenerations of cubic fourfolds and holomorphic symplectic geometry
van den Dries, B.
2012-01-01
In this thesis we study deformations of varieties of lines on smooth cubic hypersurfaces of the 5-dimensional complex projective space. These cubic hypersurfaces are also called cubic fourfolds. Beauville and Donagi proved that the line variety of any cubic fourfold is a polarized holomorphic
Comparing Maps to Symplectic Integrators in a Galactic Type ...
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... Author Affiliations. N. D. Caranicolas1 N. J. Papadopoulos1. Department of Physics, Section of Astrophysics, Astronomy and Mechanics, University of Thessaloniki, 540 06 Thessaloniki, Greece.
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
Author Affiliations. Mahuya Datta1 Md Rabiul Islam2. Statistics and Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India; Department of Pure Mathematics, University College of Science, University of Calcutta, 35, P. Barua Sarani, Kolkata 700 019, India ...
Fast symplectic map tracking for the CERN Large Hadron Collider
Directory of Open Access Journals (Sweden)
Dan T. Abell
2003-06-01
Full Text Available Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion. In the Large Hadron Collider (LHC at CERN, particles circulate at the injection energy, when multipole errors are most significant, for more than 10^{7} turns, but systematic tracking studies are limited to a small fraction of this total time—even on modern computers. A considerable speedup is expected by replacing element-by-element tracking with the use of a symplectified one-turn map. We have applied this method to the realistic LHC lattice, version 6, and report here our results for various map orders, with special emphasis on precision and speed.
Statistical equilibrium and symplectic geometry in general relativity
International Nuclear Information System (INIS)
Iglesias, P.
1981-09-01
A geometrical construction is given of the statistical equilibrium states of a system of particles in the gravitational field in general relativity. By a method of localization variables, the expression of thermodynamic values is given and the compatibility of this description is shown with a macroscopic model of a relativistic continuous medium for a given value of the free-energy function [fr
... feeding Lethargy (the baby is tired, hard to wake up, limp, or inactive) Difficulty breathing (with severe breathing problems, the baby’s skin, lips, or nails may turn blue) Diagnosis & Tests How will I know I have group B strep? If you’re ...
Indian Academy of Sciences (India)
The gamma gamma community are concerned that in the rush to prepare for the e+e− machine, allowance is not being made for a future upgrade of the photon linear collider. References. [1] ECFA/DESY Photon Collider Working Group: B Badelek et al, TESLA Technical. Design Report, Part VI, Chapter 1: Photon collider at ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. Groups and Symmetry: A Guide to Discovering Mathematics. Geetha Venkataraman. Book Review Volume 4 Issue 10 October 1999 pp 91-92. Fulltext. Click here to view fulltext PDF. Permanent link:
R.W. Hamilton (Rebecca); S. Puntoni (Stefano); N.T. Tavassoli (Nader)
2006-01-01
textabstractCategorization is a core psychological process central to consumer and managerial decision-making. While a substantial amount of research has been conducted to examine individual categorization behaviors, relatively little is known about the group categorization process. In two
Unclonable Group Identification
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Dupont, Kasper; Pedersen, Michael Østergaard
2006-01-01
We introduce and motivate the concept of unclonable group identification, that provides maximal protection against sharing of identities while still protecting the anonymity of users. We prove that the notion can be realized from any one-way function and suggest a more efficient implementation...
CERN PhotoLab
1980-01-01
The Radiobiology Group carries out experiments to study the effect of radiation on living cells. The photo shows the apparatus for growing broad beans which have been irradiated by 250 GeV protons. The roots are immersed in a tank of running water (CERN Weekly Bulletin 26 January 1981 and Annual Report 1980 p. 160). Karen Panman, Marilena Streit-Bianchi, Roger Paris.
International Nuclear Information System (INIS)
Caldas, L.V.E.
1990-01-01
The main activities of the radiation dosimetry group is described, including the calibration of instruments, sources and radioactive solutions and the determination of neutron flux; development, production and market dosimetric materials; development radiation sensor make the control of radiation dose received by IPEN workers; development new techniques for monitoring, etc. (C.G.C.)
Working Group Report: Neutrinos
Energy Technology Data Exchange (ETDEWEB)
de Gouvea, A.; Pitts, K.; Scholberg, K.; Zeller, G. P. [et al.
2013-10-16
This document represents the response of the Intensity Frontier Neutrino Working Group to the Snowmass charge. We summarize the current status of neutrino physics and identify many exciting future opportunities for studying the properties of neutrinos and for addressing important physics and astrophysics questions with neutrinos.
Introduction to quantum groups
International Nuclear Information System (INIS)
Monteiro, Marco A.R.
1994-01-01
An elementary introduction to quantum groups is presented. The example of Universal Enveloping Algebra of deformed SU(2) is analysed in detail. It is also discussed systems made up of bosonic q-oscillators at finite temperature within the formalism of Thermo-Field Dynamics. (author). 39 refs
INDEPENDENT AND GROUP LEARNING.
DICKINSON, MARIE B.
IN CONTRAST TO THE TRADITIONAL EMPHASES ON ROTE LEARNING AND FACT ACCUMULATION, RECENT TRENDS EMERGING FROM EDUCATIONAL RESEARCH STRESS THE DEVELOPMENT OF THINKING PROCESSES SUCH AS THE ABILITY TO REASON ABSTRACTLY AND TO SYNTHESIZE. CHILDREN WORKING INDEPENDENTLY OR IN GROUPS MOVE THROUGH A DISCOVERY LEARNING CURRICULUM IN WHICH THE TEACHER…
Convolution Operators on Groups
Derighetti, Antoine
2011-01-01
This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson.
Toleration, Groups, and Multiculturalism
DEFF Research Database (Denmark)
Lægaard, Sune
2014-01-01
is routinely defined as involving an objection component, a power requirement and an acceptance component. The objection and acceptance components refer to reasons or dispositions of the subjects of toleration, e.g. public authorities deciding how to act in relation to groups. The power condition refers...
African Journals Online (AJOL)
Ehab
Professor of Pediatric Allergy and Immunology, Ain Shams University, Cairo, Egypt. Age groups vulnerable to serious attacks of anaphylaxis include infants, teenagers, pregnant women, and the elderly. Concomitant diseases, such as severe or uncontrolled asthma, cardiovascular disease, mastocytosis or clonal mast cell ...
The leukosis/sarcoma (L/S) group of diseases designates a variety of transmissible benign and malignant neoplasms of chickens caused by members that belong to the family Retroviridae. Because the expansion of the literature on this disease, it is no longer feasible to cite all relevant publications ...
Ramsey, E. Michele
2004-01-01
Objective: To integrate speaking practice with rhetorical theory. Type of speech: Persuasive. Point value: 100 points (i.e., 30 points based on peer evaluations, 30 points based on individual performance, 40 points based on the group presentation), which is 25% of course grade. Requirements: (a) References: 7-10; (b) Length: 20-30 minutes; (c)…
Hsiang, Wu-Yi
2017-01-01
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartans' theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books.We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius-Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1-4). It is a wonderful reality of the Lie t...
Cornwell, J F
1989-01-01
Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.
Indian Academy of Sciences (India)
IAS Admin
[17] M Sato, Chasing and escaping by three groups of species, Physical Review E, Vol.85, p.066102, 2012. [18] K Dutta, How birds fly together: The dynamics of flocking, Resonance, Vol.15, pp.1097–1110, 2010. [19] T Vicsek et al, Novel type of phase transition in a system of self-driven particles, Physical Review Letter, ...
Gartner Group. Stamford, CT
Gartner Group is the one of the leading independent providers of research and analysis material for IT professionals. Their reports provide in-depth analysis of dominant trends, companies and products. CERN has obtained a licence making these reports available online to anyone within CERN. The database contains not only current reports, updated monthly, but also some going back over a year.
International Nuclear Information System (INIS)
Lisboa, P.; Michael, C.
1982-01-01
We address the question of designing optimum discrete sets of points to represent numerically a continuous group manifold. We consider subsets which are extensions of the regular discrete subgroups. Applications to Monte Carlo simulation of SU(2) and SU(3) gauge theory are discussed. (orig.)
Public interest group involvement
International Nuclear Information System (INIS)
Shelley, P.
1986-01-01
Including public interest groups in the siting process for nuclear waste disposal facilities is of great importance. Controversial sitings often result in litigation, but involving public interest groups early in the process will lessen the change of this. They act as surrogates for the general public and should be considered as members of the team. It is important to remember though, that all public interest groups are different. In choosing public panels such as public advisory committees, members should not be chosen on the basis of some quota. Opposition groups should not be excluded. Also, it is important to put the right person in charge of the committee. The goal of public involvement is to identify the conflicts. This must be done during the decision process, because conflicts must be known before they can be eliminated. Regarding litigation, it is important to ease through and around legal battles. If the siting process has integrity and a good faith effort has been shown, the court should uphold the effort. In addition, it is important to be negotiable and to eliminate shortcuts
Energy Technology Data Exchange (ETDEWEB)
Mansard, E.; Sand, S.E.; Klinting, P.
1989-02-01
There are recent indications that distinct wave groupings can be found even in deep water. The main objective has been to give a statistical description suitable for the design of coastal and offshore structures and it is undertaken to make further investigations in this field by analyzing some prototype records using the concepts of run length of high waves and spectrum of squared elevation, the limitations and performances of which in nonlinear waves will be highlighted in this study. An attempt has been made to relate this wave grouping to the surge motion of a floating structure with a simple mooring arrangement and thereby to propose a motion-based grouping measure. It appears that the observed run length statistics can be suitably described by Kimura's predictions if the records are sufficiently long. Records whose duration are equal to, or less than, 0.6 h reflect a large statistical variability in the various wave grouping measures. The filter cut-off proposed in the concept of SIWEH for the estimation of Groupiness Factor appears to be too high to give meaningful contrasts with respect to prototype values of the peakedness factors. It is therefore proposed to use the Hilbert Transform of the time series and a cut-off which is relevant to the natural period of the test structure. In the absence of information about this natural period a cut-off fc less than or equal to f/sub p//15 may work better. The motion equivalent groupiness factor concept could be used effectively to determine the critical sea state conditions to be used for testing of floating structures. The directional resolution of the sea state and theoretical formulations defining statistical variabilities caused by finite record lengths could be useful in evaluating whether the wave grouping is a linear process. (AB) 49 refs.
Attraction to Group, Group Cohesiveness, and Individual Outcome: A Study of Training Groups.
Wright, Thomas L.; Duncan, Douglas
1986-01-01
Examined relationships between attraction to group and individual outcome in groups and between group cohesiveness and individual outcome in groups in four groups of 27 graduate students participating in a group psychotherapy experiential training program. Results revealed that attraction to group and group cohesiveness were both related to…
International Nuclear Information System (INIS)
2004-08-01
This document provides information on the Areva Group, a world nuclear industry leader, offering solutions for nuclear power generation, electricity transmission and distribution and interconnect systems to the telecommunications, computer and automotive markets. It presents successively the front end division including the group business lines involved in producing nuclear fuel for electric power generation (uranium mining, concentration, conversion and enrichment and nuclear fuel fabrication); the reactors and services division which designs and builds PWR, BWR and research reactors; the back end division which encompasses the management of the fuel that has been used in nuclear power plants; the transmission and distribution division which provides products, systems and services to the medium and high voltage energy markets; the connectors division which designs and manufactures electrical, electronic and optical connectors, flexible micro circuitry and interconnection systems. Areva is implemented in Europe, north and south america, africa and asia-pacific. (A.L.B.)
The Ombudperson Initiative Group
Laura Stewart
Following many discussions that took place at some of the ATLAS Women's Network lunch gatherings, a few ATLAS women joined forces with similarly concerned CERN staff women to form a small group last Fall to discuss the need for a CERN-wide Ombudsperson. This has since evolved into the Ombudsperson Initiative Group (OIG) currently composed of the following members: Barbro Asman, Stockholm University; Pierre Charrue, CERN AB; Anna Cook, CERN IT; Catherine Delamare, CERN and IT Ombudsperson; Paula Eerola, Lund University; Pauline Gagnon, Indiana University; Eugenia Hatziangeli, CERN AB; Doreen Klem, CERN IT; Bertrand Nicquevert, CERN TS and Laura Stewart, CERN AT. On June 12, members of the OIG met with representatives of Human Resources (HR) and the Equal Opportunity Advisory Panel (EOAP) to discuss the proposal drafted by the OIG. The meeting was very positive. Everybody agreed that the current procedures at CERN applicable in the event of conflict required a thorough review, and that a professionnally trai...
DEFF Research Database (Denmark)
Terslev, Lene; Iagnocco, Annamaria; Bruyn, George A W
2017-01-01
at least 1 joint abnormality versus 30% in the EA group. In HC, the findings of SH and PD were predominantly grade 1 whereas all grades were seen in the EA cohort, but SE was rare. In JIA, synovitis can be diagnosed based on B-mode findings alone because of the presence of physiological vascularization......OBJECTIVE: To provide an update from the Outcome Measures in Rheumatology (OMERACT) Ultrasound Working Group on the progress for defining ultrasound (US) minimal disease activity threshold at joint level in rheumatoid arthritis (RA) and for standardization of US application in juvenile idiopathic...... arthritis (JIA). METHODS: For minimal disease activity, healthy controls (HC) and patients with early arthritis (EA) who were naive to disease-modifying antirheumatic drugs were recruited from 2 centers. US was performed of the hands and feet, and scored semiquantitatively (0-3) for synovial hypertrophy (SH...
International Nuclear Information System (INIS)
Anon.
1993-01-01
A working group at a Canada/USA symposium on climate change and the Arctic identified major concerns and issues related to terrestrial resources. The group examined the need for, and the means of, involving resource managers and users at local and territorial levels in the process of identifying and examining the impacts and consequences of climatic change. Climatic change will be important to the Arctic because of the magnitude of the change projected for northern latitudes; the apparent sensitivity of its terrestrial ecosystems, natural resources, and human support systems; and the dependence of the social, cultural, and economic welfare of Arctic communities, businesses, and industries on the health and quality of their environment. Impacts of climatic change on the physical, biological, and associated socio-economic environment are outlined. Gaps in knowledge needed to quantify these impacts are listed along with their relationships with resource management. Finally, potential actions for response and adaptation are presented
Mindfulness for group facilitation
DEFF Research Database (Denmark)
Adriansen, Hanne Kirstine; Krohn, Simon
2014-01-01
thinking and ‘Eastern’ mindfulness which refers to an open, accepting state of mind, as intended with Buddhist-inspired techniques such as meditation. In this paper, we are interested in the latter type of mindfulness and demonstrate how Eastern mindfulness techniques can be used as a tool for facilitation......In this paper, we argue that mindfulness techniques can be used for enhancing the outcome of group performance. The word mindfulness has different connotations in the academic literature. Broadly speaking there is ‘mindfulness without meditation’ or ‘Western’ mindfulness which involves active....... A brief introduction to the physiology and philosophy of Eastern mindfulness constitutes the basis for the arguments of the effect of mindfulness techniques. The use of mindfulness techniques for group facilitation is novel as it changes the focus from individuals’ mindfulness practice...
TS Department
2008-01-01
Please note that owing the preparations for the Open Days, the FM Group will not able to handle specific requests for waste collection from 2nd to 6th of April, nor removal or PC transport requests between the 31 March and 11 April. We kindly ask you to plan the collection of all types of waste and any urgent transport of office furniture or PCs before 31 March. Waste collection requests must be made by contacting FM Support on 77777 or at the e-mail address mailto:Fm.Support@cern.ch; removal of office furniture or PC transport requests must be made using the EDH ‘Transport request’ form (select "Removals" or "PC transport" from the drop-down menu). For any question concerning the sorting of waste, please consult the following web site: http://dechets-waste.web.cern.ch/dechets-waste/ Thank you for your understanding and collaboration. TS/FM Group
Group leaders optimization algorithm
Daskin, Anmer; Kais, Sabre
2011-03-01
We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.
Metrically universal abelian groups
Czech Academy of Sciences Publication Activity Database
Doucha, Michal
2017-01-01
Roč. 369, č. 8 (2017), s. 5981-5998 ISSN 0002-9947 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : Abelian group Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.426, year: 2016 http://www.ams.org/journals/tran/2017-369-08/S0002-9947-2017-07059-8/
Energy Technology Data Exchange (ETDEWEB)
NONE
2001-07-01
The goal of this working group was to foment discussions about the use and limitations of multi-bunch, representatives from most operating or in-project synchrotron radiation sources (ALS, SPEAR, BESSY-2, SPRING-8, ANKA, DELTA, PEP-2, DIAMOND, ESRF...) have presented their experience. The discussions have been led around 3 topics: 1) resistive wall instabilities and ion instabilities, 2) higher harmonic cavities, and 3) multibunch feedback systems.
Formal groups and applications
Hazewinkel, Michiel
2012-01-01
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
International Nuclear Information System (INIS)
King, N.M.
1980-01-01
The Storage Ring Group set out to identify and pursue salient problems in accelerator physics for heavy ion fusion, divorced from any particular reference design concept. However, it became apparent that some basic parameter framework was required to correlate the different study topics. As the Workshop progressed, ring parameters were modified and updated. Consequently, the accompanying papers on individual topics will be found to refer to slightly varied parameters, according to the stage at which the different problems were tackled
Lyndon, Roger C
2001-01-01
From the reviews: "This book (...) defines the boundaries of the subject now called combinatorial group theory. (...)it is a considerable achievement to have concentrated a survey of the subject into 339 pages. This includes a substantial and useful bibliography; (over 1100 ÄitemsÜ). ...the book is a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews, AMS, 1979.
PCORnet's Collaborative Research Groups.
Pletcher, Mark J; Forrest, Christopher B; Carton, Thomas W
2018-01-01
The Patient-Centered Outcomes Research Institute (PCORI) launched a multi-institutional "network of networks" in 2013 - Patient-Centered Clinical Research Network (PCORnet) - that is designed to conduct clinical research that is faster, less expensive, and more responsive to the information needs of patients and clinicians. To enhance cross-network and cross-institutional collaboration and catalyze the use of PCORnet, PCORI has supported formation of 11 Collaborative Research Groups focusing on specific disease types (e.g., cardiovascular health and cancer) or particular patient populations (e.g., pediatrics and health disparities). PCORnet's Collaborative Research Groups are establishing research priorities within these focus areas, establishing relationships with potential funders, and supporting development of specific research projects that will use PCORnet resources. PCORnet remains a complex, multilevel, and heterogeneous network that is still maturing and building a diverse portfolio of observational and interventional people-centered research; engaging with PCORnet can be daunting, particularly for outside investigators. We believe the Collaborative Research Groups are stimulating interest and helping investigators navigate the complexity, but only time will tell if these efforts will bear fruit in terms of funded multicenter PCORnet projects.
Social group utility maximization
Gong, Xiaowen; Yang, Lei; Zhang, Junshan
2014-01-01
This SpringerBrief explains how to leverage mobile users' social relationships to improve the interactions of mobile devices in mobile networks. It develops a social group utility maximization (SGUM) framework that captures diverse social ties of mobile users and diverse physical coupling of mobile devices. Key topics include random access control, power control, spectrum access, and location privacy.This brief also investigates SGUM-based power control game and random access control game, for which it establishes the socially-aware Nash equilibrium (SNE). It then examines the critical SGUM-b
DEFF Research Database (Denmark)
Dove, Graham; Abildgaard, Sille Julie Jøhnk; Biskjær, Michael Mose
The Post-ItTM note is a frequently used, and yet seldom studied, design material. We investigate the functions Post-ItTM notes serve when providing cognitive support for creative design team practice. Our investigation considers the ways in which Post-ItTM notes function as design externalisations......, both individually and when grouped, and their role in categorisation in semantic long-term memory. To do this, we adopt a multimodal analytical approach focusing on interaction between humans, and between humans and artefacts, alongside language. We discuss in detail examples of four different...
Farmer, David W
1995-01-01
In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequ
Liao, Tim Futing
2011-01-01
An incomparably useful examination of statistical methods for comparisonThe nature of doing science, be it natural or social, inevitably calls for comparison. Statistical methods are at the heart of such comparison, for they not only help us gain understanding of the world around us but often define how our research is to be carried out. The need to compare between groups is best exemplified by experiments, which have clearly defined statistical methods. However, true experiments are not always possible. What complicates the matter more is a great deal of diversity in factors that are not inde
Public Participation Guide: Focus Groups
A focus group is a small group discussion with professional leadership. Focus groups are used to find out what issues are of most concern for a community or group when little or no information is available.
TS Department
2008-01-01
In order to prepare the organization of the Open Days, please note that FM Group will not able to take into account either specific requests for waste collection from 2nd to 6th of April, either removal or PC transport requests between the 31st and the 11th of March. We kindly ask you to plan the collection of any type of waste and the urgent transport of office furniture or PC before the 31st of March. Waste collection requests shall be formulated contacting FM Support at 77777 or at the email address mailto:Fm.Support@cern.ch; removal of office furniture or PC transport requests must be made using the EDH ‘Transport request’ form selecting the "Removals" or the "PC transport" category from the drop-down menu. For any question concerning the waste sorting, please consult the following web address: http://dechets-waste.web.cern.ch/dechets-waste/. Thank you for your understanding and collaboration. TS/FM Group
Meningococcal group B vaccines.
Findlow, Jamie
2013-06-01
Meningococcal disease remains a devastating and feared infection with a significant morbidity and mortality profile. The successful impact of meningococcal capsular group C glyconconjugate vaccines introduced into the UK infant immunization schedule in 1999, has resulted in >80% of disease now being attributable to meningococcal capsular group B (MenB). MenB glyconconjugate vaccines are not immunogenic and hence, vaccine design has focused on sub-capsular antigens. Recently, a four component vaccine to combat MenB disease (4CMenB) has progressed through clinical development and was approved by the European Medicines Agency at the end of 2012. This vaccine has proven safe and immunogenic and has been predicted to provide protection against ~73% of the MenB disease from England and Wales. Recommendation/implementation of the vaccine into the UK infant schedule is currently being evaluated. 4CMenB has the potential to provide protection against a significant proportion of MenB disease in the UK which is currently unpreventable.
Directory of Open Access Journals (Sweden)
Baltezarević Vesna
2009-01-01
Full Text Available Our reality, having been subject to the numerous social crises during the last decades of the 20th century, is characterized by frequent incidences of powerlessness and alienation. The man is more frequently a subject to loneliness and overcomes the feeling of worthlessness, no matter whether he considers himself an individual or a part of a whole larger social. Such an environment leads to development of aggression in all fields of ones life. This paper has as an objective the pointing out of the mental harassment that is manifested in the working environment. There is a prevalence of mobbing cases, as a mode of pathological communication. The result of this is that a person, subjected to this kind of abuse, is soon faced with social isolation. This research also aspires to initiate the need for social groups self-organization of which victims are part of. The reaction modality of a social group directly conditions the outcome of the deliberate social drama, one is subjected to it as a result of mobbing.
2013-01-01
The CERN Administration would like to remind you that staff members and fellows have the possibility to take out a life insurance contract on favourable terms through a Group Life Insurance. This insurance is provided by the company Helvetia and is available to you on a voluntary basis. The premium, which varies depending on the age and gender of the person insured, is calculated on the basis of the amount of the death benefit chosen by the staff member/fellow and can be purchased in slices of 10,000 CHF. The contract normally ends at the retirement age (65/67 years) or when the staff member/fellow leaves the Organization. The premium is deducted monthly from the payroll. Upon retirement, the staff member can opt to maintain his membership under certain conditions. More information about Group Life Insurance can be found at: Regulations (in French) Table of premiums The Pension Fund Benefit Service &...
ATLAS Detector Interface Group
Mapelli, L
Originally organised as a sub-system in the DAQ/EF-1 Prototype Project, the Detector Interface Group (DIG) was an information exchange channel between the Detector systems and the Data Acquisition to provide critical detector information for prototype design and detector integration. After the reorganisation of the Trigger/DAQ Project and of Technical Coordination, the necessity to provide an adequate context for integration of detectors with the Trigger and DAQ lead to organisation of the DIG as one of the activities of Technical Coordination. Such an organisation emphasises the ATLAS wide coordination of the Trigger and DAQ exploitation aspects, which go beyond the domain of the Trigger/DAQ project itself. As part of Technical Coordination, the DIG provides the natural environment for the common work of Trigger/DAQ and detector experts. A DIG forum for a wide discussion of all the detector and Trigger/DAQ integration issues. A more restricted DIG group for the practical organisation and implementation o...
International Nuclear Information System (INIS)
Doroshuk, B.W.
2000-01-01
The workshop of 26-27 june 2000, on nuclear power Plant LIfe Management (PLIM), also included working groups in which major issues facing PLIM activities for nuclear power plants were identified and discussed. The third group was on Business. The discussion concerned the following points: There are concerns about retaining experienced/trained personnel, and maintaining a good working relationship among them, as well as about the closure of research facilities, the reduction in staff numbers under increasing economic pressure and the lack of new nuclear power plant constructions. The marginal cost of producing electricity is lower for most existing nuclear power plants than for almost all other energy sources. Refurbishment costs are usually relatively small compared with new investments. The ongoing regulatory reform of the electricity market will bring increasing competition. Although PLIM has been carried out in many countries with favourable results, there are still uncertainties which affect business decisions regarding financial and market risks in PLIM activities. Recommendations were made. (author)
Energy Technology Data Exchange (ETDEWEB)
Artuso, M.; et al.,
2013-10-18
Sensors play a key role in detecting both charged particles and photons for all three frontiers in Particle Physics. The signals from an individual sensor that can be used include ionization deposited, phonons created, or light emitted from excitations of the material. The individual sensors are then typically arrayed for detection of individual particles or groups of particles. Mounting of new, ever higher performance experiments, often depend on advances in sensors in a range of performance characteristics. These performance metrics can include position resolution for passing particles, time resolution on particles impacting the sensor, and overall rate capabilities. In addition the feasible detector area and cost frequently provides a limit to what can be built and therefore is often another area where improvements are important. Finally, radiation tolerance is becoming a requirement in a broad array of devices. We present a status report on a broad category of sensors, including challenges for the future and work in progress to solve those challenges.
International Nuclear Information System (INIS)
Cornwell, J.F.
1984-01-01
The aim of these two volumes (Vol. 1 includes chapters 1-9, Vol. 2 chapters 10-19) has been to provide a comprehensive and self-contained account of those parts of group theory that have been found to be most useful and of their main applications to physical problems. Starting with basic concepts they also include some of the more recent developments (to 1984). The areas of physics that are covered include atomic physics (chapters 1-6, 10-12), electronic energy bands in solids (chapters 1-6, 8 and 9), molecular vibrations (chapters 1, 2, 4-7), lattice vibrations in solids (chapters 1, 2, 4-9) and elementary particles (chapters 10-19). (U.K.)
Optimised Renormalisation Group Flows
Litim, Daniel F
2001-01-01
Exact renormalisation group (ERG) flows interpolate between a microscopic or classical theory and the corresponding macroscopic or quantum effective theory. For most problems of physical interest, the efficiency of the ERG is constrained due to unavoidable approximations. Approximate solutions of ERG flows depend spuriously on the regularisation scheme which is determined by a regulator function. This is similar to the spurious dependence on the ultraviolet regularisation known from perturbative QCD. Providing a good control over approximated ERG flows is at the root for reliable physical predictions. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regulator. We study specific optimised regulators for bosonic and fermionic fields and compare the optimised ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and non-vanishing temperature. An optimised flow for a ``proper-time ren...
2013-01-01
The CERN Administration wishes to inform staff members and fellows having taken out optional life insurance under the group contract signed by CERN that the following changes to the rules and regulations entered into force on 1 January 2013: The maximum age for an active member has been extended from 65 to 67 years. The beneficiary clause now allows insured persons to designate one or more persons of their choice to be their beneficiary(-ies), either at the time of taking out the insurance or at a later date, in which case the membership/modification form must be updated accordingly. Beneficiaries must be clearly identified (name, first name, date of birth, address). The membership/modification form is available on the FP website: http://fp.web.cern.ch/helvetia-life-insurance For further information, please contact: Valentina Clavel (Tel. 73904) Peggy Pithioud (Tel. 72736)
Quantum Secure Group Communication.
Li, Zheng-Hong; Zubairy, M Suhail; Al-Amri, M
2018-03-01
We propose a quantum secure group communication protocol for the purpose of sharing the same message among multiple authorized users. Our protocol can remove the need for key management that is needed for the quantum network built on quantum key distribution. Comparing with the secure quantum network based on BB84, we show our protocol is more efficient and securer. Particularly, in the security analysis, we introduce a new way of attack, i.e., the counterfactual quantum attack, which can steal information by "invisible" photons. This invisible photon can reveal a single-photon detector in the photon path without triggering the detector. Moreover, the photon can identify phase operations applied to itself, thereby stealing information. To defeat this counterfactual quantum attack, we propose a quantum multi-user authorization system. It allows us to precisely control the communication time so that the attack can not be completed in time.
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Group Milieu in systemic and psychodynamic group therapy
DEFF Research Database (Denmark)
Lau, Marianne Engelbrecht
subscales: Cohesion (pgroup milieu were seen. The systemic group turned out to be evaluated as the most structured therapy and also...... in a randomized study of systemic versus psychodynamic group therapy, that the short-term outcome for patients who received systemic group psychotherapy was significantly better than the outcome for patients who received psychodynamic group psychotherapy. The current study assessed the group milieu in both groups....... Methods: This randomized prospective study included 106 women: 52 assigned to psychodynamic group psychotherapy and 54 assigned to systemic group psychotherapy. The Group Environment Scale (GES) was filled in the mid phase of therapy and analysed in three dimensions and 10 subscales. Results: The systemic...
Group Milieu in systemic and psychodynamic group therapy
DEFF Research Database (Denmark)
Lau, Marianne Engelbrecht
subscales: Cohesion (psystemic group turned out to be evaluated as the most structured therapy and also...... in a randomized study of systemic versus psychodynamic group therapy, that the short-term outcome for patients who received systemic group psychotherapy was significantly better than the outcome for patients who received psychodynamic group psychotherapy. The current study assessed the group milieu in both groups....... Methods: This randomized prospective study included 106 women: 52 assigned to psychodynamic group psychotherapy and 54 assigned to systemic group psychotherapy. The Group Environment Scale (GES) was filled in the mid phase of therapy and analysed in three dimensions and 10 subscales. Results: The systemic...
Emotional collectives : How groups shape emotions and emotions shape groups
van Kleef, G.A.; Fischer, A.H.
2016-01-01
Group settings are epicentres of emotional activity. Yet, the role of emotions in groups is poorly understood. How do group-level phenomena shape group members’ emotional experience and expression? How are emotional expressions recognised, interpreted and shared in group settings? And how do such
Huang, Junzhou; Zhang, Tong
2010-01-01
This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
Becoming a group: value convergence and emergent work group identities.
Meeussen, Loes; Delvaux, Ellen; Phalet, Karen
2014-06-01
This study examines the process of group identity formation through social interaction in real-life work groups, with a focus on achievement values as content of work group identities. Extending research on social identity formation, we examined the process of value convergence as group members negotiate common group goals. Specifically, we predicted that work group members would influence each other's achievement values and that value convergence over time would underlie emergent work group identities and work group performance. Using a fully cross-lagged multilevel design with four repeated measures in 68 work groups, we find that group members' achievement values converge through mutual social influence. Moreover, multilevel polynomial regression analysis reveals that value convergence - rather than group members' initial value fit - longitudinally predicts work group identification and performance. © 2013 The British Psychological Society.
The Liabilities Management Group
International Nuclear Information System (INIS)
Whitehead, A.W.
1998-01-01
The Liabilities Management Group (LMG) was initiated by DTI. It is a cooperative forum which was set up in 1995. The current participants are DTI, UKAEA, NLM (for BNFL), MOD and Magnox Electric. The LMG was initiated to produce closer cooperation between public sector liability management organizations, achieve more cost-effective management of UK nuclear liabilities and enhance development of the UK nuclear decommissioning and waste management strategy. The objectives are to compare practices between liabilities management organizations discuss the scope for collaboration identify priority areas for possible collaboration agree action plans for exploring and undertaking such collaboration.Four task forces have been formed to look at specific areas (R and D, safety, contracts, and project management) and each reports separately to the LMG. The LMG has achieved its original aim of bringing together those with public sector liability management responsibilities. All participants feel that the LMG has been useful and that it should continue. Looking to the future, there is a continuing need for the LMG to facilitate removal of barriers to the achievement of best value for money. The LMG might also consider addressing the 'business process' elements that a liability management organization must be good at in order to define best practice in these. (author)
International Nuclear Information System (INIS)
Von Maravic, H.
1993-01-01
Natural analogue studies have been carried out for several years in the framework of the European Community's R and D programme on radioactive waste; and within its recent fourth five-year programme on 'Management and storage of radioactive waste (1990-94)' the Community is participating in the Oklo study, natural analogue for transfer processes in a geological repository. The Oklo project is coordinated by CEA-IPSN (F) and involves laboratories from several CEA directorates (IPSN, DTA and DCC) which collaborate with other institutions from France: CREGU, Nancy; CNRS, Strasbourg and ENSMD, Fontainebleau. Moreover, institutes from non-EC member States are also taking part in the Oklo study. The second joint CEC-CEA progress meeting of the Oklo Working Group was held in April 1992 in Brussels and gave the possibility of reviewing and discussing progress made since its first meeting in February 1991 at CEA in Fontenay-aux-Roses. About 40 participants from 15 laboratories and organizations coming from France, Canada, Gabon, Japan, Sweden and the USA underline the great interest in the ongoing research activities. The meeting focused on the different tasks within the CEC-CEA Oklo project concerning (i) field survey and sampling, (ii) characterization of the source term, (iii) studies of the petrographical and geochemical system, and (iv) studies of the hydrogeological system and hydrodynamic modelling. (author) 17 papers are presented
Saving Face and Group Identity
DEFF Research Database (Denmark)
Eriksson, Tor; Mao, Lei; Villeval, Marie-Claire
2015-01-01
their self- but also other group members' image. This behavior is frequent even in the absence of group identity. When group identity is more salient, individuals help regardless of whether the least performer is an in-group or an out-group. This suggests that saving others' face is a strong social norm....
Making Cooperative Learning Groups Work.
Hawley, James; De Jong, Cherie
1995-01-01
Discusses the use of cooperative-learning groups with middle school students. Describes cooperative-learning techniques, including group roles, peer evaluation, and observation and monitoring. Considers grouping options, including group size and configuration, dyads, the think-pair-share lecture, student teams achievement divisions, jigsaw groups,…
Fermilab Steering Group Report
Energy Technology Data Exchange (ETDEWEB)
Beier, Eugene; /Pennsylvania U.; Butler, Joel; /Fermilab; Dawson, Sally; /Brookhaven; Edwards, Helen; /Fermilab; Himel, Thomas; /SLAC; Holmes, Stephen; /Fermilab; Kim, Young-Kee; /Fermilab /Chicago U.; Lankford, Andrew; /UC, Irvine; McGinnis, David; /Fermilab; Nagaitsev, Sergei; /Fermilab; Raubenheimer, Tor; /SLAC /Fermilab
2007-01-01
The Fermilab Steering Group has developed a plan to keep U.S. accelerator-based particle physics on the pathway to discovery, both at the Terascale with the LHC and the ILC and in the domain of neutrinos and precision physics with a high-intensity accelerator. The plan puts discovering Terascale physics with the LHC and the ILC as Fermilab's highest priority. While supporting ILC development, the plan creates opportunities for exciting science at the intensity frontier. If the ILC remains near the Global Design Effort's technically driven timeline, Fermilab would continue neutrino science with the NOVA experiment, using the NuMI (Neutrinos at the Main Injector) proton plan, scheduled to begin operating in 2011. If ILC construction must wait somewhat longer, Fermilab's plan proposes SNuMI, an upgrade of NuMI to create a more powerful neutrino beam. If the ILC start is postponed significantly, a central feature of the proposed Fermilab plan calls for building an intense proton facility, Project X, consisting of a linear accelerator with the currently planned characteristics of the ILC combined with Fermilab's existing Recycler Ring and the Main Injector accelerator. The major component of Project X is the linac. Cryomodules, radio-frequency distribution, cryogenics and instrumentation for the linac are the same as or similar to those used in the ILC at a scale of about one percent of a full ILC linac. Project X's intense proton beams would open a path to discovery in neutrino science and in precision physics with charged leptons and quarks. World-leading experiments would allow physicists to address key questions of the Quantum Universe: How did the universe come to be? Are there undiscovered principles of nature: new symmetries, new physical laws? Do all the particles and forces become one? What happened to the antimatter? Building Project X's ILC-like linac would offer substantial support for ILC development by accelerating the
Linear deformations of discrete groups and constructions of multivalued groups
International Nuclear Information System (INIS)
Yagodovskii, Petr V
2000-01-01
We construct deformations of discrete multivalued groups described as special deformations of their group algebras in the class of finite-dimensional associative algebras. We show that the deformations of ordinary groups producing multivalued groups are defined by cocycles with coefficients in the group algebra of the original group and obtain classification theorems on these deformations. We indicate a connection between the linear deformations of discrete groups introduced in this paper and the well-known constructions of multivalued groups. We describe the manifold of three-dimensional associative commutative algebras with identity element, fixed basis, and a constant number of values. The group algebras of n-valued groups of order three (three-dimensional n-group algebras) form a discrete set in this manifold
Topological K-Kolmogorov groups
International Nuclear Information System (INIS)
Abd El-Sattar, A. Dabbour.
1987-07-01
The idea of the K-groups was used to define K-Kolmogorov homology and cohomology (over pairs of coefficient groups) which are descriptions of certain modifications of the Kolmogorov groups. The present work is devoted to the study of the topological properties of the K-Kolmogorov groups which lie at the root of the group duality based essentially upon Pontrjagin's concept of group multiplication. 14 refs
Harmonic Analysis and Group Representation
Figa-Talamanca, Alessandro
2011-01-01
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.
Zientek, Michael L.; Loferski, Patricia J.; Parks, Heather L.; Schulte, Ruth F.; Seal, Robert R.; Schulz, Klaus J.; DeYoung,, John H.; Seal, Robert R.; Bradley, Dwight C.
2017-12-19
The platinum-group elements (PGEs)—platinum, palladium, rhodium, ruthenium, iridium, and osmium—are metals that have similar physical and chemical properties and tend to occur together in nature. PGEs are indispensable to many industrial applications but are mined in only a few places. The availability and accessibility of PGEs could be disrupted by economic, environmental, political, and social events. The United States net import reliance as a percentage of apparent consumption is about 90 percent.PGEs have many industrial applications. They are used in catalytic converters to reduce carbon monoxide, hydrocarbon, and nitrous oxide emissions in automobile exhaust. The chemical industry requires platinum or platinum-rhodium alloys to manufacture nitric oxide, which is the raw material used to manufacture explosives, fertilizers, and nitric acid. In the petrochemical industry, platinum-supported catalysts are needed to refine crude oil and to produce aromatic compounds and high-octane gasoline. Alloys of PGEs are exceptionally hard and durable, making them the best known coating for industrial crucibles used in the manufacture of chemicals and synthetic materials. PGEs are used by the glass manufacturing industry in the production of fiberglass and flat-panel and liquid crystal displays. In the electronics industry, PGEs are used in computer hard disks, hybridized integrated circuits, and multilayer ceramic capacitors.Aside from their industrial applications, PGEs are used in such other fields as health, consumer goods, and finance. Platinum, for example, is used in medical implants, such as pacemakers, and PGEs are used in cancer-fighting drugs. Platinum alloys are an ideal choice for jewelry because of their white color, strength, and resistance to tarnish. Platinum, palladium, and rhodium in the form of coins and bars are also used as investment commodities, and various financial instruments based on the value of these PGEs are traded on major exchanges
Group Leader Development: Effects of Personal Growth and Psychoeducational Groups
Ohrt, Jonathan H.; Robinson, E. H., III; Hagedorn, W. Bryce
2013-01-01
The purpose of this quasi-experimental study was to compare the effects of personal growth groups and psychoeducational groups on counselor education students' (n = 74) empathy and group leader self-efficacy. Additionally, we compared the degree to which participants in each group valued: (a) cohesion, (b) catharsis, and (c) insight. There were no…
The path group construction of Lie group extensions
Vizman, Cornelia
2007-01-01
We present an explicit realization of abelian extensions of infinite dimensional Lie groups using abelian extensions of path groups, by generalizing Mickelsson's approach to loop groups and the approach of Losev-Moore-Nekrasov-Shatashvili to current groups. We apply our method to coupled cocycles on current Lie algebras and to Lichnerowicz cocycles on the Lie algebra of divergence free vector fields.
Interagency Advanced Power Group -- Steering group meeting minutes
Energy Technology Data Exchange (ETDEWEB)
1993-11-18
This document contains the draft meeting minutes of the Steering Group of the Interagency Advanced Power Group. Included are the discussions resulting from the presentation of working group reports and the results of a discussion of IAPG policies and procedures. In the appendix are the reports of the following working groups: Electrical, Mechanical, Solar, and Systems.
In-group favouritism and out-group discimination in naturally occurring groups
Donna Harris; Klaus Abbink
2012-01-01
We study in-group favouritism and out-group discrimination in a multiplayer dictator game. An allocator divides a large sum of money among three groups of 20 recipients each and Self. Allocations to groups are divided equally among the group members. The three groups are supporters of the two rival political movements in Thailand (â€œyellow shirtsâ€ versus â€œred shirtsâ€ ) and political neutral subjects. A control treatment with artificial groups (â€œgroup Aâ€ , â€œgroup Bâ€ , and â€œnon-aff...
Emotional collectives: How groups shape emotions and emotions shape groups.
van Kleef, Gerben A; Fischer, Agneta H
2016-01-01
Group settings are epicentres of emotional activity. Yet, the role of emotions in groups is poorly understood. How do group-level phenomena shape group members' emotional experience and expression? How are emotional expressions recognised, interpreted and shared in group settings? And how do such expressions influence the emotions, cognitions and behaviours of fellow group members and outside observers? To answer these and other questions, we draw on relevant theoretical perspectives (e.g., intergroup emotions theory, social appraisal theory and emotions as social information theory) and recent empirical findings regarding the role of emotions in groups. We organise our review according to two overarching themes: how groups shape emotions and how emotions shape groups. We show how novel empirical approaches break important new ground in uncovering the role of emotions in groups. Research on emotional collectives is thriving and constitutes a key to understanding the social nature of emotions.
2010 Chemical Working Group Status
Reid, Concha M.
2010-01-01
The Steering Group for the Interagency Advanced Power Group (IAPG) held their business meeting on November 30-December 1st in McLean, Virginia. Status reports were presented from each of the IAPG's Working Groups. These charts contain a brief summary of the IAPG Chemical Working Group's activities during 2010 and its plans for 2011.
Indian Journal of Adult Education, 1975
1975-01-01
Sub-group proceedings at the 28th all-India Adult Education Conference held in October, 1975, are summarized. Sub-groups discussed the theme "non-formal education" as it applies to one of five population groups: school drop-outs, youth, women, farmers, and industrial workers. The sixth sub-group considered policy and financing for…
Combinatorial Group Theory -42-----------------------------~-----------R ...
Indian Academy of Sciences (India)
GENERAL I ARTICLE. Combinatorial Group Theory. Group Theory via Generators and Relations. B Sury is with the School of Mathematics, TIFR,. Mumbai. The concept of groups surfaced with the fundamental works of the great mathematicians. Evariste Galois and Niels Henrik. Abel. The advent of group theory.
Group B Streptococcus and Pregnancy
f AQ FREQUENTLY ASKED QUESTIONS FAQ105 PREGNANCY Group B Strep and Pregnancy • What is group B streptococcus (GBS)? • What does it mean to be ... a planned cesarean birth? •Glossary What is group B streptococcus (GBS)? Group B streptococcus is one of ...
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
Crisp, John; Wiest, Bert
2003-01-01
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) nev...
The contemporary czech art groups
Nývlt, Matěj
2011-01-01
Bachelor's thesis describes the current Czech art droups and their directly related topics. The introduction describes the general problems of creation iside the art group and puts in to historical context of development of Czech art for the last two hundred years. Next is the theme of artistic groups widened by the choice of some of the world's art groups. The current czech art groups are described in several medallions representing the youngest generation groups that are actively involved i...
Group covariance and metrical theory
International Nuclear Information System (INIS)
Halpern, L.
1983-01-01
The a priori introduction of a Lie group of transformations into a physical theory has often proved to be useful; it usually serves to describe special simplified conditions before a general theory can be worked out. Newton's assumptions of absolute space and time are examples where the Euclidian group and translation group have been introduced. These groups were extended to the Galilei group and modified in the special theory of relativity to the Poincare group to describe physics under the given conditions covariantly in the simplest way. The criticism of the a priori character leads to the formulation of the general theory of relativity. The general metric theory does not really give preference to a particular invariance group - even the principle of equivalence can be adapted to a whole family of groups. The physical laws covariantly inserted into the metric space are however adapted to the Poincare group. 8 references
Group analysis of differential equations
Ovsiannikov, L V
1982-01-01
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g
The influence of ethnic group composition on focus group discussions.
Greenwood, Nan; Ellmers, Theresa; Holley, Jess
2014-09-20
Focus groups are commonly used to explore participants' experiences in health and social care research. Although it is suggested that having demographically homogenous groups may help put participants at ease, the evidence is sparse.The aims of the paper are to: explore the impact of relative ethnic homogeneity and heterogeneity of focus group participants on the group discussions; improve understanding of homogeneity and heterogeneity in focus groups; suggest ways to operationalise concepts such as being 'more comfortable' with other focus group participants. Digitally recorded focus groups were undertaken with family carers of stroke survivors and were later transcribed and analysed using framework analysis. Groups were designated as more or less ethnically homogenous. More homogenous groups included, for example, only White British or Asian Indian participants whilst more heterogeneous groups comprised a mixture of, for example, Asian, White British and Black Caribbean participants. Forty-one carers participated in seven focus groups. Analysis revealed differences in discussions around ethnicity between the more or less ethnically homogenous groups. For example, participants in more ethnically homogenous focus groups were more likely to say ethnicity might influence perceptions of social care services. On the other hand, more heterogeneous groups emphasised similarity in carers' experiences, irrespective of ethnicity. Participants in the more homogenous groups were also more likely to make potentially controversial comments relating to ethnic differences. Additionally they appeared to be more at ease with each other discussing the topic. For example, they spontaneously mentioned ethnic differences earlier in these groups.In contrast, analysis of topics not specifically related to ethnicity, such as the difficult experiences of being a carer, produced no discernible patterns when comparing more and less homogenous focus groups. Considerations around focus group
African Journals Online (AJOL)
Jane T. B, Nlandu M, Matondo M, Evelyn G. L.. Factors Inﬂuencing the Use of Traditional versus. Modern Family Planning Methods in Bas Zaire. Studies in Family Planning, November/December. 1885;16(6):332-34l. Peter W. H. A natural method of child spacing. American Journal of Obstetrics and Gynecology,. December ...
African Journals Online (AJOL)
and promote family planning and child health services to ensure a healthier life for isolated communities during their integration ... traditional methods are still used as the main method of fertility regulation in African societies. The social, cultural and traditional beliefs and practices that are .... An elderly man said, "We space.
Coordinated Control of Vehicle Groups
National Research Council Canada - National Science Library
Kumar, Vijay
2004-01-01
.... There are three main objectives: (1) to develop a theoretical paradigm for formalizing the concepts of a group, a team, and control of groups, with specified tasks such as exploring, mapping, searching, and transporting objects; (2...
Criminal groups and criminal subculture
Romanova N.M.
2013-01-01
The paper provides a classification of criminal groups, structured by the following parameters: a) operation mode (secret/open), b) law-enforcement and administrative support (presence/absence). We describe four types of criminal groups: a) legitimized criminal organization, b) secret criminal organization engaged in illegal business, c) secret general crime group, and d) general crime group operating openly. The four types differ in the content of criminal subculture. Modern criminal subcult...
Relationship Groups in SNOMED CT
Cornet, Ronald; Schulz, Stefan
2009-01-01
Relationship groups are a construct which is particular for the representation of concepts in SNOMED CT. In this paper, the July 2008 version of SNOMED CT is analyzed to determine the usage of relationship groups. Relationship groups are used with 36 out of 65 relations, playing a role in 28% of all
Ability Grouping in Social Studies.
Social Education, 1992
1992-01-01
Presents a position statement of the National Council for the Social Studies (NCSS). Reports that the NCSS objects to ability grouping in social studies. Argues that ability grouping disadvantages minority, handicapped, and low ability students. Suggests that ability grouping undermines the democratic ideals that should be the basis of the social…
Strategies for Successful Group Work
Nipp, Mary Beth; Palenque, Stephanie Maher
2017-01-01
The thought of group work, or CLC Groups often strikes fear and loathing in the hearts and minds of both students and instructors. According to Swan, Shen, and Hiltz (2006) collaborative work presents the possibilities of many difficulties including a largely unequal contribution of group participants, an inability of the students to manage the…
Group Cooperation in Outdoor Education
Matthews, Bruce E.
1978-01-01
Utilizing the Beatles' Yellow Submarine fantasy (e.g., the Blue Meanies), this outdoor education program is designed for sixth graders and special education students. Activities developed at the Cortland Resident Outdoor Education Camp include a series of group stress/challenge activities to be accomplished by everyone in the group, as a group.…
Diagram Techniques in Group Theory
Stedman, Geoffrey E.
2009-09-01
Preface; 1. Elementary examples; 2. Angular momentum coupling diagram techniques; 3. Extension to compact simple phase groups; 4. Symmetric and unitary groups; 5. Lie groups and Lie algebras; 6. Polarisation dependence of multiphoton processes; 7. Quantum field theoretic diagram techniques for atomic systems; 8. Applications; Appendix; References; Indexes.
K-Kolmogorov cohomology groups
International Nuclear Information System (INIS)
Abd El-Sattar, A. Dabbour.
1986-07-01
In the present work we use the idea of K-groups to give a description of certain modification of the Kolmogorov cohomology groups for the case of a pair (G,G') of discrete coefficient groups. Their induced homomorphisms and coboundary operators are also defined, and then we study the resulting construction from the point of view of Eilenberg-Steenrod axioms. (author)
Defense Mechanisms in Group Counseling.
Clark, Arthur J.
1992-01-01
Presents considerations and strategies for conceptualizing, recognizing, and modifying defense mechanisms through the group counseling process. Provides awareness of defense mechanisms in planning for and implementation of group counseling, describes interaction patterns for identifying defenses among group participants, and clarifies modification…
Conceptualizing Group Flow: A Framework
Duncan, Jana; West, Richard E.
2018-01-01
This literature review discusses the similarities in main themes between Csikszentmihályi theory of individual flow and Sawyer theory of group flow, and compares Sawyer's theory with existing concepts in the literature on group work both in education and business. Because much creativity and innovation occurs within groups, understanding group…
Designing for informed group formation
DEFF Research Database (Denmark)
Nicolajsen, Hanne Westh; Juel Jacobsen, Alice; Riis, Marianne
2012-01-01
A new design ―project preparation‖ preparing for the group formation in problem based project work is proposed and investigated. The main problem is to overcome group formation based on existing relations. The hypothesis is that theme development and group formation are somewhat counterproductive...
Group Music Therapy for Prisoners
DEFF Research Database (Denmark)
Chen, Xi Jing; Hannibal, Niels; Xu, Kevin
2014-01-01
study aims to investigate the effectiveness of group music therapy to reduce anxiety and depression, and raise self-esteem in prisoners. One hundred and ninety two inmates from a Chinese prison will be allocated to two groups through randomisation. The experimental group will participate in biweekly...... group music therapy for 10 weeks (20 sessions) while the control group will be placed on a waitlist. Anxiety, depression and self-esteem will be measured by self-report scales three times: before, at the middle, and at the end of the intervention. Logs by the participants and their daily routine...
Concave 1-norm group selection.
Jiang, Dingfeng; Huang, Jian
2015-04-01
Grouping structures arise naturally in many high-dimensional problems. Incorporation of such information can improve model fitting and variable selection. Existing group selection methods, such as the group Lasso, require correct membership. However, in practice it can be difficult to correctly specify group membership of all variables. Thus, it is important to develop group selection methods that are robust against group mis-specification. Also, it is desirable to select groups as well as individual variables in many applications. We propose a class of concave [Formula: see text]-norm group penalties that is robust to grouping structure and can perform bi-level selection. A coordinate descent algorithm is developed to calculate solutions of the proposed group selection method. Theoretical convergence of the algorithm is proved under certain regularity conditions. Comparison with other methods suggests the proposed method is the most robust approach under membership mis-specification. Simulation studies and real data application indicate that the [Formula: see text]-norm concave group selection approach achieves better control of false discovery rates. An R package grppenalty implementing the proposed method is available at CRAN. © Published by Oxford University Press 2014. This work is written by (a) US Government employee(s) and is in the public domain in the US.
Group percolation in interdependent networks
Wang, Zexun; Zhou, Dong; Hu, Yanqing
2018-03-01
In many real network systems, nodes usually cooperate with each other and form groups to enhance their robustness to risks. This motivates us to study an alternative type of percolation, group percolation, in interdependent networks under attack. In this model, nodes belonging to the same group survive or fail together. We develop a theoretical framework for this group percolation and find that the formation of groups can improve the resilience of interdependent networks significantly. However, the percolation transition is always of first order, regardless of the distribution of group sizes. As an application, we map the interdependent networks with intersimilarity structures, which have attracted much attention recently, onto the group percolation and confirm the nonexistence of continuous phase transitions.
Clifford algebras, spinors, spin groups and covering groups
International Nuclear Information System (INIS)
Magneville, C.; Pansart, J.P.
1991-03-01
The Dirac equation uses matrices named Υ matrices which are representations of general algebraic structures associated with a metric space. These algebras are the Clifford algebras. In the first past, these algebras are studied. Then the notion of spinor is developed. It is shown that Majorana and Weyl spinors only exist for some particular metric space. In the second part, Clifford and spinor groups are studied. They may be interpreted as the extension of the notion of orthogonal group for Clifford algebras and their spaces for representation. The rotation of a spinor is computed. In the last part, the connexion between the spinor groups and the Universal Covering Groups is presented [fr
[Group cohesion: a concept analysis].
Lin, Yen-Ru; Chen, Yu-Jung; Tzeng, Wen-Chii; Chou, Kuei-Ru
2007-10-01
Group cohesion is considered an essential condition for achieving a successful treatment team. High cohesion groups more readily reach their goals, with group members also feeling more secure about their functions and contributions. In clinical practice, nurses use group teaching and group therapy to help patient and family members gain knowledge and skills related to illness treatment and recuperation. Effective group leadership helps minimize non-productive time and manpower and enhance interpersonal interaction. A further advantage of group cohesion is that the more effective administration of nursing programs that results can raise the profession level of staffs and reduce turnover. Walker and Avant (1995) employ concept analysis to use defining attributes in order to apply the same definition and communication to the same profession. The purpose of this paper was to apply this methodology to an analysis of group cohesion. Steps used include a review of the literature on conceptual definitions of group cohesion, a determination of defining attributes, model construction, identification of borderline, contrary, and related cases, and identification of antecedents and consequences and empirical tools. It is hoped that this analysis can help nursing staff to gain a better understanding of the concept of group cohesion and to apply such to clinical practice and nursing administration.
Duality group actions on fermions
International Nuclear Information System (INIS)
Pantev, Tony; Sharpe, Eric
2016-01-01
In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2,ℤ) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by ℤ 2 , to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N=4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial ℤ 2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.
Strategic Groups: One Perspective on Integrating Strategic and Group Therapies.
Leahey, Maureen; Wallace, Evie
1988-01-01
Describes a short-term, strategic, solution-focused self-esteem group in an outpatient mental health setting. Discusses constructs that form foundations of both strategic and group therapies. Training, supervision, and outcome issues arising from integrating the two therapies are addressed. (Author/NB)
Good for the group? Explaining apparent group-level selection
Smallegange, I.M.; Egas, M.
2015-01-01
The idea that group selection can explain adaptive trait evolution is still controversial. Recent empirical work proposes evidence for group-level adaptation in a social spider, but the findings can also be explained from an individual-level perspective. The challenge remains to identify situations
Group Journaling: A Tool for Reflection, Fun and Group Development
Asfeldt, Morten
2012-01-01
Personal journaling is common practice in outdoor programs and is an important means of reflection and meaning-making. For over 20 years the author has used group journals to promote reflection and understanding, raise important questions, explore difficult issues, develop writing and speaking skills, and enhance group development. In this…
Group lending and the role of the group leader
Eijkel, van R.; Hermes, N.; Lensink, B.W.
2011-01-01
This paper investigates strategic monitoring behavior within group lending. We show that monitoring efforts of group members differ in equilibrium due to the asymmetry between members in terms of future profits. In particular, we show that the entrepreneur with the highest future profits also puts
Group lending and the role of the group leader
van Eijkel, R.; Hermes, C.L.M.; Lensink, B.W.
This paper investigates strategic monitoring behavior within group lending. We show that monitoring efforts of group members differ in equilibrium due to the asymmetry between members in terms of future profits. In particular, we show that the entrepreneur with the highest future profits also puts
Discrepancy in abo blood grouping
International Nuclear Information System (INIS)
Khan, M.N.; Ahmed, Z.; Khan, T.A.
2013-01-01
Discrepancies in blood typing is one of the major reasons in eliciting a transfusion reaction. These discrepancies can be avoided through detailed analysis for the blood typing. Here, we report a subgroup of blood group type-B in the ABO system. Donor's blood was analyzed by employing commercial antisera for blood grouping. The results of forward (known antisera) and reverse (known antigen) reaction were not complimentary. A detailed analysis using the standard protocols by American Association of Blood Banking revealed the blood type as a variant of blood group-B instead of blood group-O. This is suggestive of the fact that blood group typing should be performed with extreme care and any divergence, if identified, should be properly resolved to avoid transfusion reactions. Moreover, a major study to determine the blood group variants in Pakistani population is needed. (author)
Group Analytic Psychotherapy in Brazil.
Penna, Carla; Castanho, Pablo
2015-10-01
Group analytic practice in Brazil began quite early. Highly influenced by the Argentinean Pichon-Rivière, it enjoyed a major development from the 1950s to the early 1980s. Beginning in the 1970s, different factors undermined its development and eventually led to its steep decline. From the mid 1980s on, the number of people looking for either group analytic psychotherapy or group analytic training decreased considerably. Group analytic psychotherapy societies struggled to survive and most of them had to close their doors in the 1990s and the following decade. Psychiatric reform and the new public health system have stimulated a new demand for groups in Brazil. Developments in the public and not-for-profit sectors, combined with theoretical and practical research in universities, present promising new perspectives for group analytic psychotherapy in Brazil nowadays.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Group discussion improves lie detection.
Klein, Nadav; Epley, Nicholas
2015-06-16
Groups of individuals can sometimes make more accurate judgments than the average individual could make alone. We tested whether this group advantage extends to lie detection, an exceptionally challenging judgment with accuracy rates rarely exceeding chance. In four experiments, we find that groups are consistently more accurate than individuals in distinguishing truths from lies, an effect that comes primarily from an increased ability to correctly identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions (a "wisdom-of-crowds" effect) or of altering response biases (such as reducing the "truth bias"). Interventions to improve lie detection typically focus on improving individual judgment, a costly and generally ineffective endeavor. Our findings suggest a cheap and simple synergistic approach of enabling group discussion before rendering a judgment.
Group conflict and faculty engagement
DEFF Research Database (Denmark)
Selmer, Jan; Jonasson, Charlotte; Lauring, Jakob
2013-01-01
engagement has been argued to lead to more satisfied, more productive and healthier staff. In this study, based on a sample consisting of 489 members of multicultural university departments, we set out to investigate the relationship between trust, conflict and academic staff engagement. More specifically we...... assessed the effect of group trust, group relational conflict and group task conflict on indicators of behavioural, cognitive and emotional engagement. Our findings show a strong positive association between group trust and all academic staff engagement variables as well as a strong negative association...... between group relational conflict and all staff engagement variables. Task conflict was negatively associated with indicators of staff cognitive engagement. However, surprisingly, group trust did not have any moderating effect. Implications for educational organisation managers and policy makers...
Modelling group dynamic animal movement
DEFF Research Database (Denmark)
Langrock, Roland; Hopcraft, J. Grant C.; Blackwell, Paul G.
2014-01-01
in non-ideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer......Group dynamic movement is a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognised, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However......, to date, practical statistical methods which can include group dynamics in animal movement models have been lacking. We consider a flexible modelling framework that distinguishes a group-level model, describing the movement of the group's centre, and an individual-level model, such that each individual...
Group theory and its applications
Patra, Prasanta Kumar
2018-01-01
Every molecule possesses symmetry and hence has symmetry operations and symmetry elements. From symmetry properties of a system we can deduce its significant physical results. Consequently it is essential to operations of a system forms a group. Group theory is an abstract mathematical tool that underlies the study of symmetry and invariance. By using the concepts of symmetry and group theory, it is possible to obtain the members of complete set of known basis functions of the various irreducible representations of the group. I practice this is achieved by applying the projection operators to linear combinations of atomic orbital (LCAO) when the valence electrons are tightly bound to the ions, to orthogonalized plane waves (OPW) when valence electrons are nearly free and to the other given functions that are judged to the particular system under consideration. In solid state physics the group theory is indispensable in the context of finding the energy bands of electrons in solids. Group theory can be applied...
Statistics of sunspot group clusters
Directory of Open Access Journals (Sweden)
Getko Ryszarda
2013-03-01
Full Text Available The Zubrzycki method is utilized to find all sunspot groups which are close to each other during each Carrington rotation. The sunspot group areas and their positions for the years 1874–2008 are used. The descending, the ascending and the maximum phases of solar cycles for each solar hemisphere are considered separately. To establish the size of the region D where the clusters are searched, the correlation function dependent on the distance between two groups is applied. The method estimates the weighted area of each cluster. The weights dependent on the correlation function of distances between sunspot groups created each cluster. For each cluster the weighted position is also evaluated. The weights dependent on the areas of sunspot groups created a given cluster. The number distribution of the sunspot groups created each cluster and the cluster statistics within different phases of the 11-year cycle and within all considered solar cycles are also presented.
Geometric group theory an introduction
Löh, Clara
2017-01-01
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Contractions of group representations. - I
International Nuclear Information System (INIS)
Celeghini, E.; Tarlini, M.
1981-01-01
A new definition of contraction as a limit on the parameters defining the basis of the space of representations is given. From the representations of the original group, those of the contracted one are directly obtained. The contraction of inner automorphisms into outer automorphisms and the splitting of one representation into representations of the same or different group are discussed and illustrated by examples. The procedure is also a technique for the study of representations of non-semi-simple groups. (author)
Group decision-making: Factors that affect group effectiveness
Directory of Open Access Journals (Sweden)
Juliana Osmani
2016-03-01
Full Text Available Organizations are operating in a dynamic and turbulent environment. In these conditions, they have to make decisions for new problems or situations. Most of decisions are therefore non-programmed and unstructured, accompanied by risk and uncertainty. Moreover, the problems and situations are complex. All organizations are oriented towards group decisionmaking processes, as useful tools to cope with uncertainty and complexity. Apart from the necessity, companies are turning towards participatory processes also to benefit from the important advantages that these processes offer. Organizations have realized the importance of group decision-making processes to contribute to the creation of sustainable competitive advantages. Main objective of this paper is to show that group decision-making processes do not offer guarantee for good decisions, because the effectiveness of group is affected by many factors. So, the first thing done in this paper is discussing about the benefits and limitations that accompany the use of groups with decision-making purpose. Afterwards, we stop on the different factors that influence the group’s ability to make good decisions. The aim is to emphasize that regardless of the many advantages of groups, some factors as group size, type of communication within the group, leadership style, the norms, the differentiation of roles and statuses, cohesion and compliance degree should be the main elements to keep into consideration because they affect the effectiveness of group. In this regard, is discussed how such factors influence the quality of decision and then we try to draw some conclusions that can improve and make better and easier group decision-making processes.
EDF Group - Annual Report 2013
International Nuclear Information System (INIS)
2014-01-01
The EDF Group is emerging as a global leader in electricity and an industrial benchmark spanning the entire business from generation and networks to sales and marketing. The group is growing stronger and changing. A long-term vision and relentless determination to provide a modern public service underpin its robust business model. This document is EDF Group's annual report for the year 2013. It contains information about Group profile, governance, business, development strategy, sales and marketing, positions in Europe and international activities. The document comprises the Activity Report and the Sustainable Development Indicators
Measuring group climate in prison
van der Helm, P.; Stams, G.J.; van der Laan, P.
2011-01-01
The present study examines the construct validity and reliability of the Prison Group Climate Instrument (PGCI) in a sample of 77 adolescents placed in a Dutch youth prison and 49 adult prisoners living in a Dutch psychiatric prison with a therapeutic living group structure. Confirmatory factor analysis of a four-factor model—with “repression,” “support,” “growth,” and “group atmosphere” as first-order factors—and “overall group climate” as a second-order factor shows an adequate fit to the d...
DEFF Research Database (Denmark)
Christensen, Gerd
2017-01-01
will take its point of departure in pedagogical textbook introductions where group work is often presented as a means to learning social skills and co-workability. However, as most students and teachers know, this is not always the case. Observations of long-term group work show that this can be a tough...... experience for the students (Christensen 2013). Contrary to expectations, the group work seemed to foster anti-social behavior and development of selfish skills. The paper will therefore conclude by suggesting how the (often) laissez-faire group pedagogy, which is dominant in Denmark, could be improved...
Hanford Waste Tank Grouping Study
International Nuclear Information System (INIS)
Remund, K.M.; Simpson, B.C.
1996-01-01
This letter report discusses the progress and accomplishments of the Tank Grouping Study in FY96. Forty-one single-shell tanks (SSTs) were included in the FY95. In FY96, technical enhancements were also made to data transformations and tank grouping methods. The first focus of the FY96 effort was a general tank grouping study in which the 41 SSTs were grouped into classes with similar waste properties. The second FY96 focus was a demonstration of how multivariate statistical methods can be used to help resolve tank safety issues
Group supervision for general practitioners
DEFF Research Database (Denmark)
Galina Nielsen, Helena; Sofie Davidsen, Annette; Dalsted, Rikke
2013-01-01
considered important prerequisites for disclosing and discussing professional problems. CONCLUSION: The results of this study indicate that participation in a supervision group can be beneficial for maintaining and developing GPs' skills in dealing with patients with mental health problems. Group supervision......AIM: Group supervision is a sparsely researched method for professional development in general practice. The aim of this study was to explore general practitioners' (GPs') experiences of the benefits of group supervision for improving the treatment of mental disorders. METHODS: One long...
Defining and Classifying Interest Groups
DEFF Research Database (Denmark)
Baroni, Laura; Carroll, Brendan; Chalmers, Adam
2014-01-01
of lobbying actors coded according to different coding schemes. We systematically assess the performance of different schemes by comparing how actor types in the different schemes differ with respect to a number of background characteristics. This is done in a two-stage approach where we first cluster actors...... in the organizational attributes of specific interest group types. As expected, our comparison of coding schemes reveals a closer link between group attributes and group type in narrower classification schemes based on group organizational characteristics than those based on a behavioral definition of lobbying....
Evolutionary dynamics of group formation.
Javarone, Marco Alberto; Marinazzo, Daniele
2017-01-01
Group formation is a quite ubiquitous phenomenon across different animal species, whose individuals cluster together forming communities of diverse size. Previous investigations suggest that, in general, this phenomenon might have similar underlying reasons across the interested species, despite genetic and behavioral differences. For instance improving the individual safety (e.g. from predators), and increasing the probability to get food resources. Remarkably, the group size might strongly vary from species to species, e.g. shoals of fishes and herds of lions, and sometimes even within the same species, e.g. tribes and families in human societies. Here we build on previous theories stating that the dynamics of group formation may have evolutionary roots, and we explore this fascinating hypothesis from a purely theoretical perspective, with a model using the framework of Evolutionary Game Theory. In our model we hypothesize that homogeneity constitutes a fundamental ingredient in these dynamics. Accordingly, we study a population that tries to form homogeneous groups, i.e. composed of similar agents. The formation of a group can be interpreted as a strategy. Notably, agents can form a group (receiving a 'group payoff'), or can act individually (receiving an 'individual payoff'). The phase diagram of the modeled population shows a sharp transition between the 'group phase' and the 'individual phase', characterized by a critical 'individual payoff'. Our results then support the hypothesis that the phenomenon of group formation has evolutionary roots.
Leadership in moving human groups.
Directory of Open Access Journals (Sweden)
Margarete Boos
2014-04-01
Full Text Available How is movement of individuals coordinated as a group? This is a fundamental question of social behaviour, encompassing phenomena such as bird flocking, fish schooling, and the innumerable activities in human groups that require people to synchronise their actions. We have developed an experimental paradigm, the HoneyComb computer-based multi-client game, to empirically investigate human movement coordination and leadership. Using economic games as a model, we set monetary incentives to motivate players on a virtual playfield to reach goals via players' movements. We asked whether (I humans coordinate their movements when information is limited to an individual group member's observation of adjacent group member motion, (II whether an informed group minority can lead an uninformed group majority to the minority's goal, and if so, (III how this minority exerts its influence. We showed that in a human group--on the basis of movement alone--a minority can successfully lead a majority. Minorities lead successfully when (a their members choose similar initial steps towards their goal field and (b they are among the first in the whole group to make a move. Using our approach, we empirically demonstrate that the rules of swarming behaviour apply to humans. Even complex human behaviour, such as leadership and directed group movement, follow simple rules that are based on visual perception of local movement.
Strategic Groups and Banks’ Performance
Directory of Open Access Journals (Sweden)
Gregorz Halaj
2009-06-01
Full Text Available The theory of strategic groups predicts the existence of stable groups of companies that adopt similar business strategies. The theory also predicts that groups will differ in performance and in their reaction to external shocks. We use cluster analysis to identify strategic groups in the Polish banking sector. We find stable groups in the Polish banking sector constituted after the year 2000 following the major privatisation and ownership changes connected with transition to the mostly-privately-owned banking sector in the late 90s. Using panel regression methods we show that the allocation of banks to groups is statistically significant in explaining the profitability of banks. Thus, breaking down the banks into strategic groups and allowing for the different reaction of the groups to external shocks helps in a more accurate explanation of profits of the banking sector as a whole.Therefore, a more precise ex ante assessment of the loss absorption capabilities of banks is possible, which is crucial for an analysis of banking sector stability. However, we did not find evidence of the usefulness of strategic groups in explaining the quality of bank portfolios as measured by irregular loans over total loans, which is a more direct way to assess risks to financial stability.
Stick with your group: young children's attitudes about group loyalty.
Misch, Antonia; Over, Harriet; Carpenter, Malinda
2014-10-01
For adults, loyalty to the group is highly valued, yet little is known about how children evaluate loyalty. We investigated children's attitudes about loyalty in a third-party context. In the first experiment, 4- and 5-year-olds watched a video of two groups competing. Two members of the losing group then spoke. The disloyal individual said she wanted to win and therefore would join the other group. The loyal individual said she also wanted to win but would stay with her group. Children were then asked five forced-choice questions about these two individuals' niceness, trustworthiness, morality, and deservingness of a reward. The 5-year-olds preferred the loyal person across all questions; results for the 4-year-olds were considerably weaker but in the same direction. The second experiment investigated the direction of the effect in 5-year-olds. In this experiment, children answered questions about either a loyal individual, a disloyal individual, or a neutral individual. Children rated both the loyal and neutral individuals more positively than the disloyal individual across a number of measures. Thus, whereas disloyal behavior is evaluated unfavorably by children, loyal behavior is the expected norm. These results suggest that, at least from 5 years of age, children understand that belonging to a group entails certain commitments. This marks an important step in their own ability to negotiate belonging and become trustworthy and reliable members of their social groups. Copyright © 2014 Elsevier Inc. All rights reserved.
Faculty of the Academic Groups
1995-01-01
The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government. This report contains information of research projects in the four interdisciplinary groups, Command, Control & Communications Academic Group, Electronic Warfare Academic Group, Space Systems Academic Group and Undersea Warfare Academic Group, which were carried out under funding of the Naval Postgraduate School Research...
Energy Innovation. IVO group`s research and development report
Energy Technology Data Exchange (ETDEWEB)
Salminen, P.; Laiho, Y.; Kaikkonen, H.; Leisio, C.; Hinkkanen, S.; Fletcher, R. [eds.
1997-11-01
This annual booklet of the IVO Group`s research and development activities presents a number of articles, written by experts from IVO. The products described are examples of the environmentally-oriented selection made available by the IVO Group. In fact, the entire energy technology developed in Finland is environmentally oriented, if seen from the international perspective. The new business potential of environmental technology is great, and it is believed that in the year 2000, exportation of Finnish know-how in the field of energy-saving and efficiency will exceed the value of out energy imports
Punctured torus groups and 2-bridge knot groups
Akiyoshi, Hirotaka; Wada, Masaaki; Yamashita, Yasushi
2007-01-01
This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
2002 annual report EDF group; 2002 rapport annuel groupe EDF
Energy Technology Data Exchange (ETDEWEB)
NONE
2002-07-01
This document is the 2002 annual report of Electricite de France (EdF) group, the French electric utility. Content: Introductory section (EDF at a glance, Chairman's message, 2002 Highlights); Corporate governance and Group strategy (Corporate governance, sustainable growth strategy, EDF branches); Financial performance (Reaching critical mass, Margins holding up well, Balance sheet); Human resources (Launching Group-wide synergies, Optimising human resources); Customers (Major customers, SMEs and professional customers, Local authorities, Residential customers, Ensuring quality access to electricity); Generation (A balanced energy mix, Nuclear generation, Fossil-fuelled generation, Renewable energies); Corporate social responsibility (Global and local partnerships, Promoting community development)
Energy Innovation. IVO Group`s Research and Development Report
Energy Technology Data Exchange (ETDEWEB)
Salminen, P.; Laiho, Y.; Kaikkonen, H.; Leisio, C.; Hinkkanen, S. [eds.
1996-11-01
This annual booklet of the IVO Group`s research and development activities presents a number of articles, written by experts from IVO. The products described are examples of the environmentally-oriented selection made available by the IVO Group. In fact, the entire energy technology developed in Finland is environmentally oriented, if seen from the international perspective. The new business potential of environmental technology is great, and it is believed that in the year 2000, exportation of Finnish know-how in the field of energy-saving and efficiency will exceed the value of out energy imports
Group Counseling for Navy Children.
Mitchum, Nancy Taylor
1991-01-01
Conducted six-session group counseling program for Navy children (n=22) enrolled in public schools whose fathers were on deployment. Pretest and posttest scores on the Coopersmith Self-Esteem Inventory suggest that participation in the group counseling unit positively affected self-esteem of Navy children whose fathers were on deployment. Found…
... Grains All about the Grains Group Print Share What foods are in the Grains Group? Any food made ... Whole Grains Food Gallery Take the Grains Quiz What Is MyPlate? Food Guide History MyPlate, MyWins Fruits All About the ...
Group Work with Transgender Clients
Dickey, Lore M.; Loewy, Michael I.
2010-01-01
Drawing on the existing literature, the authors' research and clinical experiences, and the first author's personal journey as a member and leader of the transgender community, this article offers a brief history of group work with transgender clients followed by suggestions for group work with transgender clients from a social justice…
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
Group Activities for Math Enthusiasts
Holdener, J.; Milnikel, R.
2016-01-01
In this article we present three group activities designed for math students: a balloon-twisting workshop, a group proof of the irrationality of p, and a game of Math Bingo. These activities have been particularly successful in building enthusiasm for mathematics and camaraderie among math faculty and students at Kenyon College.
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
This is the report of the subgroup QCD of Working Group-4 at WHEPP-9. We present the activities that had taken place in the subgroup and report some of the partial results arrived at following the discussion at the working group meetings. Keywords. Quantum chromodynamics; resummation; extra dimensions; multi-leg.
Group theoretical methods in Physics
International Nuclear Information System (INIS)
Olmo, M.A. del; Santander, M.; Mateos Guilarte, J.M.
1993-01-01
The meeting had 102 papers. These was distributed in following areas: -Quantum groups,-Integrable systems,-Physical Applications of Group Theory,-Mathematical Results,-Geometry, Topology and Quantum Field Theory,-Super physics,-Super mathematics,-Atomic, Molecular and Condensed Matter Physics. Nuclear and Particle Physics,-Symmetry and Foundations of classical and Quantum mechanics
Factorizable sheaves and quantum groups
Bezrukavnikov, Roman; Schechtman, Vadim
1998-01-01
The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.
A Course on Topological Groups
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 8. A Course on Topological Groups - A Pellucid Little Book on Topological Groups. K Parthasarathy. Book Review Volume 2 Issue 8 August 1997 pp 82-83. Fulltext. Click here to view fulltext PDF. Permanent link:
Measuring group climate in prison
Peer van der Helm PhD; P.H. van der Laan; G.J.J.M. Stams
2011-01-01
The present study examines the construct validity and reliability of the Prison Group Climate Instrument (PGCI) in a sample of 77 adolescents placed in a Dutch youth prison and 49 adult prisoners living in a Dutch psychiatric prison with a therapeutic living group structure. Confirmatory factor
Understanding Nomadic Collaborative Learning Groups
Ryberg, Thomas; Davidsen, Jacob; Hodgson, Vivien
2018-01-01
The paper builds on the work of Rossitto "et al." on collaborative nomadic work to develop three categories of practice of nomadic collaborative learning groups. Our study is based on interviews, workshops and observations of two undergraduate student's group practices engaged in self-organised, long-term collaborations within the frame…
Challenges Facing Group Work Online
Chang, Bo; Kang, Haijun
2016-01-01
Online group work can be complicated because of its asynchronous characteristics and lack of physical presence, and its requirements for skills in handling technology, human relationships, and content-related tasks. This study focuses on the administrative, logistical and relationship-related challenges in online group work. Challenges in areas…
The Globalization of Cooperative Groups.
Valdivieso, Manuel; Corn, Benjamin W; Dancey, Janet E; Wickerham, D Lawrence; Horvath, L Elise; Perez, Edith A; Urton, Alison; Cronin, Walter M; Field, Erica; Lackey, Evonne; Blanke, Charles D
2015-10-01
The National Cancer Institute (NCI)-supported adult cooperative oncology research groups (now officially Network groups) have a longstanding history of participating in international collaborations throughout the world. Most frequently, the US-based cooperative groups work reciprocally with the Canadian national adult cancer clinical trial group, NCIC CTG (previously the National Cancer Institute of Canada Clinical Trials Group). Thus, Canada is the largest contributor to cooperative groups based in the United States, and vice versa. Although international collaborations have many benefits, they are most frequently utilized to enhance patient accrual to large phase III trials originating in the United States or Canada. Within the cooperative group setting, adequate attention has not been given to the study of cancers that are unique to countries outside the United States and Canada, such as those frequently associated with infections in Latin America, Asia, and Africa. Global collaborations are limited by a number of barriers, some of which are unique to the countries involved, while others are related to financial support and to US policies that restrict drug distribution outside the United States. This article serves to detail the cooperative group experience in international research and describe how international collaboration in cancer clinical trials is a promising and important area that requires greater consideration in the future. Copyright © 2015 Elsevier Inc. All rights reserved.
Focus groups as anticipatory methodology
Macnaghten, Phil
2017-01-01
Focus group practitioners have tended to emphasize the capacity of the methodology for exploring how people think about topics that are familiar and that have some grounding in everyday experience. Less articulated in the literature is the role of focus groups as an anticipatory methodology, as a
My Career: Group Fitness Instructor
Green, Kathleen
2013-01-01
This article presents an interview with Tammy Kenney, who teaches a yoga-Pilates class in several different gyms. In this interview, Kenney talks about her career as a group fitness instructor and gives her best advice for someone who wants to teach group fitness.
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
Abstract. This is the report of the QCD working sub-group at WHEPP-8 which was part of the QCD and QGP working group. Discussion and work on some aspects of resummation and parton distribution are reported. Keywords. Quantum chromodynamics; resummation; polarised scattering; parton dis- tributions. PACS No.
Working group report: Quantum chromodynamics
Indian Academy of Sciences (India)
The participants of the QCD working sub-group are: Rahul Basu, D Indumathi,. E Laenen, Swapan Majhi, Prakash Mathews, Anuradha Misra, Asmita Mukherjee,. R Ratabole, V Ravindran and W Vogelsang. The main focus of this working group had been to concentrate on some issues in resummation which are essential to ...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Stereotypes of Norwegian social groups.
Bye, Hege H; Herrebrøden, Henrik; Hjetland, Gunnhild J; Røyset, Guro Ø; Westby, Linda L
2014-10-01
We present a pilot study and two main studies that address the nature of stereotypes of social groups in Norway within the framework of the Stereotype Content Model (SCM). The first study focused on stereotypes of a wide range of groups across categories such as gender, age, religious conviction, socioeconomic and health status. The second study focused on stereotypes of immigrant groups. Participants (n = 244 and n = 63, respectively) rated the groups on perceived warmth, competence, status, and competition. Results from both studies support the applicability of the SCM in Norway and provides a unique insight into stereotypes of Norwegian social groups. © 2014 The Authors. Scandinavian Journal of Psychology published by Scandinavian Psychological Associations and John Wiley & Sons Ltd.
Understanding nomadic collaborative learning groups
DEFF Research Database (Denmark)
Ryberg, Thomas; Davidsen, Jacob; Hodgson, Vivien
2018-01-01
-term collaborations within the frame of Problem and Project Based Learning. By analysing the patterns of nomadic collaborative learning we identify and discuss how the two groups of students incorporate mobile and digital technologies as well as physical and/or non-digital technologies into their group work......The paper builds on the work of Rossitto et al. on collaborative nomadic work to develop three categories of practice of nomadic collaborative learning groups. Our study is based on interviews, workshops and observations of two undergraduate student's group practices engaged in self-organised, long....... Specifically, we identify the following categories of nomadic collaborative learning practices: “orchestration of work phases, spaces and activities,” “the orchestration of multiple technologies” and “orchestration of togetherness.” We found that for both groups of students there was a fluidity, situatedness...
Goldberg, Simon B; Hoyt, William T
2015-06-01
The notion that individuals' interpersonal behaviors in the context of therapy reflects their interpersonal behaviors outside of therapy is a fundamental hypothesis underlying numerous systems of psychotherapy. The social microcosm hypothesis, in particular, claims the interpersonal therapy group becomes a reflection of group members' general tendencies, and can thus be used as information about members' interpersonal functioning as well as an opportunity for learning and behavior change. The current study tested this hypothesis using data drawn from 207 individuals participating in 22 interpersonal process groups. Ratings were made on 2 key interpersonal domains (Dominance and Affiliation) at baseline and at Weeks 2, 5, and 8 of the group. Two-level multilevel models (with participants nested within groups) were used to account for the hierarchical structure, and the social relations model (SRM; Kenny, 1994) was used to estimate peer ratings (target effects in SRM) unconfounded with rater bias. Participants showed consensus at all time points during the interpersonal process groups on one another's levels of dominance and affiliation. In addition, self- and peer ratings were stable across time and correlated with one another. Importantly, self-ratings made prior to group significantly predicted ratings (self- and peer) made within the group, with effect sizes within the medium range. Taken together, these results provide robust support for the social microcosm hypothesis and the conjecture that interpersonal style within-group therapy is reflective of broader interpersonal tendencies. (c) 2015 APA, all rights reserved).
EDF group - annual report 2003; Groupe EDF - rapport annuel 2003
Energy Technology Data Exchange (ETDEWEB)
NONE
2004-07-01
This document contains the magazine, the financial statements and the sustainable development report of Electricite de France (EdF) group for 2003: 1 - the magazine (chairman's statement, group profile, vision and strategy); 2 - the consolidated financial statements for the period ended 31 December 2003 (statutory auditors' report on the consolidated financial statements, EDF's summary annual financial statements); 3 - sustainable development report (transparency and dialogue, responsibility, commitment, partnerships for progress). (J.S.)
Bayesian Hierarchical Grouping: perceptual grouping as mixture estimation
Froyen, Vicky; Feldman, Jacob; Singh, Manish
2015-01-01
We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian Hierarchical Grouping (BHG). In BHG we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some generative assumptions. Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are “owned” by which objects. We present a tractable implementation of the framework, based on the hierarchical clustering approach of Heller and Ghahramani (2005). We illustrate it with examples drawn from a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Our approach yields an intuitive hierarchical representation of image elements, giving an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. We show that BHG accounts well for a diverse range of empirical data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing unifying account of the elusive Gestalt notion of Prägnanz. PMID:26322548
EDF group - Reference Document 2004
International Nuclear Information System (INIS)
2005-01-01
The EDF Group is an integrated energy supplier operating in a wide range of electricity-related businesses: generation, transmission, distribution, sale and trading of energy. It is the main operator in the French electricity market and one of the leading electricity groups in Europe. With an installed capacity of 125,4 GW, it contributes to the supply of energy and services to more than 42 million customers throughout the world (with approximately 36 million customers in Europe, more than 28 million of whom are in France). The EDF Group has built a business model balanced between deregulated and regulated operations in France and an international presence. In 2004, the Group recorded consolidated sales of euros 46,928 million, net income (Group share) of euros 1,341 million, and it achieved earnings before interests, taxes, depreciation and amortization of euros 12,127 million. This document is EDF Group's Reference Document for the year 2004. It contains information about: the Group activities, capital, relations with Gaz de France utility, strategy, industrial environment, history, activity in France, international activity, transverse activities and functions, disputes, arbitration and risk factors, Property, Plants and Equipment, Operating and Financial Review, Administrative, Management, and Supervisory Bodies and Senior Management, Remuneration and Benefits, recent trends and perspectives
Group theory approach to scattering
International Nuclear Information System (INIS)
Wu, J.
1985-01-01
For certain physical systems, there exists a dynamical group which contains the operators connecting states with the same energy but belonging to potentials with different strengths. This group is called the potential group of that system. The SO(2,1) potential groups structure is introduced to describe physical systems with mixed spectra, such as Morse and Poeschl-teller potentials. The discrete spectrum describes bound states and the continuous spectrum describes bound states and the continuous spectrum describes scattering states. A solvable class of one-dimensional potentials given by Natanzon belongs to this structure with an SO(2,2) potential group. The potential group structure provides us with an algebraic procedure generating the recursion relations for the scattering matrix, which can be formulated in a purely algebraic fashion, divorced from any differential realization. This procedure, when applied to the three-dimensional scattering problem with SO(3,1) symmetry, generates the scattering matrix of the Coulomb problem. Preliminary phenomenological models for elastic scattering in a heavy-ion collision are constructed on the basis. The results obtained here can be regarded as an important extension of the group theory techniques to scattering problems similar to that developed for bound state problems
EDF group - Reference Document 2005
International Nuclear Information System (INIS)
2006-01-01
The EDF Group is an integrated energy supplier operating in a wide range of electricity-related businesses: generation, transmission, distribution, sale and trading of energy. It is the main operator in the French electricity market and one of the leading electricity groups in Europe. With an installed capacity of 130.8 GW (123.9 GW in Europe), it contributes to the supply of energy and services to more than 40 million customers throughout the world (with approximately 36.7 million customers in Europe, more than 28 million of whom are in France). The EDF Group has built a business model balanced between deregulated and regulated operations in France and an international presence. In 2005, the Group recorded consolidated sales of euros 51,051 million, net income (Group share) of euros 3,242 million, and it achieved earnings before interests, taxes, depreciation and amortization of euros 13,010 million. This document is EDF Group's Reference Document for the year 2005. It contains information about: the Group activities, risk factors, Business Overview, Organizational Structure, Property, Plants and Equipment, Operating and Financial Review, Capital Resources, Research and Development, Patents and Licences, Trend Information, Financial Prospects, Administrative, Management, and Supervisory Bodies and Senior Management, Remuneration and Benefits, Board Practices, Employees/Human Resources, Major Shareholders, Related Party Transactions, Financial Information Concerning the Company's Assets and Liabilities, Financial Position and Profits and Losses, Material Contracts, Information on Holdings etc
EDF group - Reference Document 2006
International Nuclear Information System (INIS)
2007-01-01
The EDF Group is an integrated energy supplier operating in a wide range of electricity-related businesses: generation, transmission, distribution, sale and trading of energy. It is the main operator in the French electricity market and holds strong positions in the other three principal European markets (Germany, the United Kingdom, Italy) making it one of the leading electricity groups in Europe, and a recognized actor in the gas market. With an installed capacity of 123.7 GW in Europe (128.2 GW worldwide) it holds, among the major European energy specialists, the largest production fleet and the one emitting the least CO 2 , owing to the share of nuclear technology and hydropower in its generation mix. The EDF group supplies electricity, gas and associated services to more than 37.8 million customers throughout the world and in Europe (more than 28 million of whom are in France). The EDF Group has built a business model balanced between France and the international markets, and between deregulated and regulated operations. In 2006, the Group recorded consolidated sales of euros 58,932 million, net income (Group share) of euros 5,605 million, and it achieved earnings before interest, taxes, depreciation and amortization of euros 13,930 million. From July 1, 2007, the EDF group will carry out its trading activities in a European energy market fully open to competition. This document is EDF Group's Reference Document for the year 2006. It contains information about: the Group activities, risk factors, Business overview, Organizational structure, Property, plants and equipment, Operating and financial review, Capital resources and cash flows, Research and Development, Patents and Licenses, Trend information, Financial forecasts or estimates, Administrative, management and supervisory bodies and senior management, Remuneration and benefits, Board practices, Employees/Human resources, Major shareholders, Related party transactions, Financial information
International Nuclear Information System (INIS)
1998-12-01
The partnership between the Cogema group and Japan in the domain of fuel cycle started about 20 years ago and the 10 Japanese nuclear operators are all clients of the Cogema group. The 1997 turnover realized with Japan reached 3.6 billions of francs (11% of the total turnover of the group). This short paper presents briefly the nuclear program of Japan (nuclear park, spent fuels reprocessing-recycling strategy) and the contracts between Cogema and the Japanese nuclear operators (natural uranium, uranium conversion and enrichment, spent fuel reprocessing, plutonium recycle and MOX fuel production markets). (J.S.)
Derived equivalences for group rings
König, Steffen
1998-01-01
A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.
Wave propagation and group velocity
Brillouin, Léon
1960-01-01
Wave Propagation and Group Velocity contains papers on group velocity which were published during the First World War and are missing in many libraries. It introduces three different definitions of velocities: the group velocity of Lord Rayleigh, the signal velocity of Sommerfeld, and the velocity of energy transfer, which yields the rate of energy flow through a continuous wave and is strongly related to the characteristic impedance. These three velocities are identical for nonabsorbing media, but they differ considerably in an absorption band. Some examples are discussed in the last chapter
DEFF Research Database (Denmark)
Mejdell, C.M.; Jorgensen, G.M.; Keeling, L.
2014-01-01
to categorize 1124 injuries in 478 horses. Most of these horses were allocated to groups to study the effect of group composition (i.e. same age or mixed, same gender or mixed, socially stable or unstable groups) on behaviour and injuries. The material included mainly riding and leisure purpose horses...... of different breeds, age and gender. Most injuries occurred the day after mixing. Injuries of the more severe categories 4 and 5, which normally would necessitate veterinary care and/or loss of function for some time, were not observed at all. The minor injuries categorized as 1-2 counted for 99% of the total...
Geometry, rigidity, and group actions
Farb, Benson; Zimmer, Robert J
2011-01-01
The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others.The p
International Nuclear Information System (INIS)
2002-01-01
This document is the 2002 annual report of Electricite de France (EdF) group, the French electric utility. Content: Introductory section (EDF at a glance, Chairman's message, 2002 Highlights); Corporate governance and Group strategy (Corporate governance, sustainable growth strategy, EDF branches); Financial performance (Reaching critical mass, Margins holding up well, Balance sheet); Human resources (Launching Group-wide synergies, Optimising human resources); Customers (Major customers, SMEs and professional customers, Local authorities, Residential customers, Ensuring quality access to electricity); Generation (A balanced energy mix, Nuclear generation, Fossil-fuelled generation, Renewable energies); Corporate social responsibility (Global and local partnerships, Promoting community development)
Genodermatoses in paediatric age group
Directory of Open Access Journals (Sweden)
Kumar Sunil
1996-01-01
Full Text Available Pattern of genodermatoses in paediatric age group was studied. The relative incidence of genodermatoses in paediatric dermatology out patient department was 0.62%. The commonest genodermatoses observed was ichthyosis.
The Group Treatment of Bulimia.
Weinstein, Harvey M.; Richman, Ann
1984-01-01
Bulimia has become an increasing problem in the college population. This article describes a group psychotherapeutic treatment approach to the problem. A theoretical formulation of the psychodynamics that may underlie the development of bulimia is offered. (Author/DF)
The FACA MOVES Review Work Group was formed under the Mobile Sources Technical Review Subcommittee (MSTRS), and is charged to provide input to EPA via the MSTRS and the Clean Air Act Advisory Committee on specific issues regarding MOVES development.
NISE (Nursing Inservice Education Group)
Clubine, Marilyn; And Others
1973-01-01
The purpose of the Toronto Inservice Education Group became to meet regularly in order to provide an opportunity to assist and guide those responsible for formulating and carrying out inservice education. Article outlines their objectives. (Author/RK)
Asymptotic invariants of homotopy groups
Manin, Fedor
We study the homotopy groups of a finite CW complex X via constraints on the geometry of representatives of their elements. For example, one can measure the "size" of alpha ∈ pi n (X) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in pin(X), analogously to the way that such functions are studied in asymptotic geometric group theory. We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those X in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.
Inflation and nonequilibrium renormalization group
International Nuclear Information System (INIS)
Zanella, Juan; Calzetta, Esteban
2007-01-01
We study the spectrum of primordial fluctuations and the scale dependence of the inflaton spectral index due to self-interactions of the field. We compute the spectrum of fluctuations by applying nonequilibrium renormalization group techniques
Remainder Wheels and Group Theory
Brenton, Lawrence
2008-01-01
Why should prospective elementary and high school teachers study group theory in college? This paper examines applications of abstract algebra to the familiar algorithm for converting fractions to repeating decimals, revealing ideas of surprising substance beneath an innocent facade.
On characters of finite groups
Broué, Michel
2017-01-01
This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).