Massive and massless supersymmetry: Multiplet structure and unitary irreducible representations
International Nuclear Information System (INIS)
Jarvis, P.D.
1976-01-01
UIR's of the supersymmetry algebra for the massive and massless cases are analyzed covariantly (without the use of induced representations) in terms of their component spins. For the massive case normalized basis vectors vertical-barp 2 >0, j 0 ; sigma; pjlambda> are constructed, where j 0 is the ''superspin'' and sigma is an additional quantum number serving to distinguish the different vertical-barpjlambda>, the constituent p 2 >0, spin-j UIR's of the Poincare group. For the massless case, normalized basis vectors vertical-barp 2 =0, lambda 0 ; plambda> are similarly constructed, where lambda 0 is the ''superhelicity.'' Matrix elements of the supersymmetry generators, in these bases, are explicitly given. The ''sigma basis'' is used to define weight diagrams for the massive UIR's of supersymmetry, and their properties are briefly described. Eigenfunctions ω/sub sigma/(theta) are also defined, and their connection with the reduction of higher spin massive superfields PHI/subJ/(x,theta) is discussed. Finally, it is shown how gauge dependence necessarily arises with certain massless superfields. The massless scalar superfield, both gauge-dependent and gauge-independent, is discussed as an example
Irreducible projective representations and their physical applications
Yang, Jian; Liu, Zheng-Xin
2018-01-01
An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur’s lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo simulations.
The finite - dimensional star and grade star irreducible representation of SU(n/1)
International Nuclear Information System (INIS)
Han Qi-zhi.
1981-01-01
We derive the conditions of star and grade star representations of SU(n/1) and give some examples of them. We also give a brief review of the finite - dimensional irreducible representations of SU(n/1). (author)
SU(N) Irreducible Schwinger Bosons
Mathur, Manu; Raychowdhury, Indrakshi; Anishetty, Ramesh
2010-01-01
We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).
Analytic vectors and irreducible representations of nilpotent Lie groups and algebras
International Nuclear Information System (INIS)
Arnal, D.
1978-01-01
Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, V the universal enveloping algebra of G, M a simple module on V with kernel ker dU, then there exists an automorphism of V keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U. (Auth.)
Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter
Ghose, Somdeb; Adhikari, R.
2014-03-01
Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.
On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
International Nuclear Information System (INIS)
Burdik, C.; Pashnev, A.; Tsulaya, M.
2001-01-01
The Lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is used adopted to the systems of the second class constraints by the construction of auxiliary representations of the algebras of constraints in terms of Verma modules
Baryonic sources using irreducible representations of the double-covered octahedral group
International Nuclear Information System (INIS)
Basak, S.; Edwards, R.; Fiebig, R.; Fleming, G.T.; Heller, U.M.; Morningstar, C.; Richards, D.; Sato, I.; Wallace, S.
2005-01-01
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation
Baryonic sources using irreducible representations of the double-covered octahedral group
International Nuclear Information System (INIS)
Basak, S.; Edwards, R.; Fiebig, R.; Fleming, G. T.; Heller, U. M.; Morningstar, C.; Richards, D.; Sato, I.; Wallace, S.
2004-01-01
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation
A bound for the Schur index of irreducible representations of finite groups
Energy Technology Data Exchange (ETDEWEB)
Kiselev, D D [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2013-08-31
We construct an optimal bound for the Schur index of irreducible complex representations of finite groups over the field of rational numbers, when only the prime divisors of the order of the group are known. We study relationships with compatible and universally compatible extensions of number fields. We give a simpler proof of the well-known Berman-Yamada bound for the Schur index over the field Q{sub p}. Bibliography: 7 titles.
On irreducible representations of the ultrahyperbolic BMS group
International Nuclear Information System (INIS)
McCarthy, Patrick J.; Melas, Evangelos
2003-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. Here, the generalisation B(2,2) appropriate to the ultrahyperbolic signature (+,+,-,-) is described in detail, and the irreducible unitary representations (IRs) of B(2,2) are analysed. It is proved that all induced IRs of B(2,2) arise from IRs of compact 'little groups'. These little groups, which are closed subgroups of K=SO(2)xSO(2), are classified here in detail, with particular attention paid to those of infinite order
Effect of pressure on magnetism of UIrGe
International Nuclear Information System (INIS)
Pospíšil, Jiří; Haga, Yoshinori; Tateiwa, Naoyuki; Kambe, Shinsaku; Yamamoto, Etsuji; Gouchi, Jun; Uwatoko, Yoshiya; Nagasaki, Shoko; Honda, Fuminori; Homma, Yoshiya
2017-01-01
We report the effect of hydrostatic pressure on the electronic state of the antiferromagnet UIrGe, which is isostructural and isoelectronic with the ferromagnetic superconductors UCoGe and URhGe. A series of electrical resistivity measurements in a piston–cylinder-type cell and a cubic-anvil cell were performed at hydrostatic pressures up to 15 GPa. The Néel temperature decreases with increasing pressure. We constructed a p–T phase diagram and estimated the critical pressure p_c, where the antiferromagnetism vanishes, as ∼12 GPa. The antiferromagnetic/paramagnetic transition appears to be first order. We suggest a scenario of competing antiferromagnetic inter-J- and ferromagnetic intra-J*-chain interactions in UIrGe. A moderate increase in the effective electron mass was detected in the vicinity of p_c. A discussion of the electronic specific heat γ and electron–electron correlation term A using the Kadowaki–Woods relation is given. (author)
International Nuclear Information System (INIS)
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F
2009-01-01
A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations
Representations of the q-deformed algebras Uq (so2,1) and Uq (so3,1)
International Nuclear Information System (INIS)
Gavrilik, O.M.; Klimyk, A.U.
1993-01-01
Representations of algebra U q (so 2 ,1) are studied. This algebra is a q-deformation of the universal enveloping algebra U(so 2 ,1) of the Lie algebra of the group SO 0 (2,1) and differs from the quantum algebra U q (SU 1 ,1). Classifications of irreducible representations and of infinitesimally irreducible representations of U q (SU 1 ,1). The sets of irreducible representations and of infinitesimally unitary irreducible representations of the algebra U q (so 3 ,1) are given. We also consider representations of U q (so n ,1) which are of class 1 with respect to subalgebra U q (so n ). (author). 22 refs
Orthogonality relations and supercharacter formulas of U(m|n) representations
International Nuclear Information System (INIS)
Alfaro, J.; Medina, R.; Urrutia, L.F.
1997-01-01
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish - Chandra - Itzykson endash Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m+n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. copyright 1997 American Institute of Physics
Magnetic, magnetoelastic and other electronic properties of a UIrAl single crystal
Czech Academy of Sciences Publication Activity Database
Andreev, Alexander V.; Mushnikov, N. V.; Honda, F.; Sechovyský, V.; Javorský, P.; Goto, T.
272-276, - (2004), e337-e339 ISSN 0304-8853 R&D Projects: GA ČR GA106/02/0943 Institutional research plan: CEZ:AV0Z1010914 Keywords : uranium intermetallics * UIrAl * UPtAl * ferromagnetism * pressure effects Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.031, year: 2004
Covariant fields on anti-de Sitter spacetimes
Cotăescu, Ion I.
2018-02-01
The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.
International Nuclear Information System (INIS)
Dumitrescu, T.S.
1977-01-01
A new method is applied in order to obtain the irreducible single row representations of the groups under study. For the case U(3) contained in SO(3) also an explicit realization is constructed. The method has the advantage of being simpler than the previously used ones. (author)
All unitary ray representations of the conformal group SU(2,2) with positive energy
International Nuclear Information System (INIS)
Mack, G.
1975-12-01
We find all those unitary irreducible representations of the infinitely - sheeted covering group G tilde of the conformal group SU(2,2)/Z 4 which have positive energy P 0 >= O. They are all finite component field representations and are labelled by dimension d and a finite dimensional irreducible representation (j 1 , j 2 ) of the Lorentz group SL(2C). They all decompose into a finite number of unitary irreducible representations of the Poincare subgroup with dilations. (orig.) [de
Wigner functions for a class of semi-direct product groups
International Nuclear Information System (INIS)
Krasowska, Anna E; Ali, S Twareque
2003-01-01
Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations from the discrete series and each unitary irreducible representation is associated with a coadjoint orbit. The set of all coadjoint orbits (hence UIRs) is finite and their union is dense in the dual of the Lie algebra. The simple structure of the groups and the orbits enables us to compute the various quantities appearing in the definition of the Wigner function explicitly. A large number of examples, with potential use in image analysis, is worked out
Description of the higher massless irreducible integer spins in the BRST approach
International Nuclear Information System (INIS)
Pashnev, A.; Tsulaya, M.
1998-01-01
The BRST approach is applied to the description of irreducible massless higher spins representations of the Poincare group in arbitrary dimensions. The total system of constraints in such theory includes both the first and the second class constraints. The corresponding nilpotent BRST charge contains terms up to the seventh degree in ghosts
Irreducibility conditions for extended superfields
International Nuclear Information System (INIS)
Sokatchev, E.
1981-05-01
The irreducible supermultiplets contained in an extended superfield are presented as sets of covariant derivatives of the superfield. Differential irreducibility constraints are easily obtained from this decomposition. (author)
The Weyl approach to the representation theory of reflection equation algebra
International Nuclear Information System (INIS)
Saponov, P A
2004-01-01
The present paper deals with the representation theory of reflection equation algebra, connected to a Hecke type R-matrix. Up to some reasonable additional conditions, the R-matrix is arbitrary (not necessary originating from quantum groups). We suggest a universal method for constructing finite dimensional irreducible representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed. The modules are parametrized by Young diagrams. The spectrum of central elements s k Tr q L k is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into a direct sum of irreducible components is also suggested
Covariant representations of nuclear *-algebras
International Nuclear Information System (INIS)
Moore, S.M.
1978-01-01
Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations
Degenerate representation from tensorial identities and quantum realisations of YBZF algebras
International Nuclear Information System (INIS)
Iosifescu, M.; Scutaru, H.
1987-06-01
The second- degree irreducible tensors in the enveloping algebra of the classical semisimple Lie algebras are determined and the irreducible representations on which these tensors vanish are derived.(authors)
International Nuclear Information System (INIS)
Deenen, J.; Quesne, C.
1985-01-01
Both non-Hermitian Dyson and Hermitian Holstein--Primakoff representations of the Sp(2d,R) algebra are obtained when the latter is restricted to a positive discrete series irreducible representation 1 +n/2>. For such purposes, some results for boson representations, recently deduced from a study of the Sp(2d,R) partially coherent states, are combined with some standard techniques of boson expansion theories. The introduction of Usui operators enables the establishment of useful relations between the various boson representations. Two Dyson representations of the Sp(2d,R) algebra are obtained in compact form in terms of ν = d(d+1)/2 pairs of boson creation and annihilation operators, and of an extra U(d) spin, characterized by the irreducible representation [lambda 1 xxxlambda/sub d/]. In contrast to what happens when lambda 1 = xxx = lambda/sub d/ = lambda, it is shown that the Holstein--Primakoff representation of the Sp(2d,R) algebra cannot be written in such a compact form for a generic irreducible representation. Explicit expansions are, however, obtained by extending the Marumori, Yamamura, and Tokunaga method of boson expansion theories. The Holstein--Primakoff representation is then used to prove that, when restricted to the Sp(2d,R) irreducible representation 1 +n/2>, the dn-dimensional harmonic oscillator Hamiltonian has a U(ν) x SU(d) symmetry group
Directory of Open Access Journals (Sweden)
J. Buitrago
Full Text Available A new classical 2-spinor approach to U(1 gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a U(1 local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representation condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials. Finally, the U(1 invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials. Keywords: Weyl 2-spinor lenguage, Dirac equation, Gauge theories, Charge quantization
International Nuclear Information System (INIS)
Nguyen Anh Ky; Stoilova, N.I.
1994-11-01
The construction approach proposed in the previous paper Ref.1 allows us there and in the present paper to construct at generic deformation parameter q all finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)]. The finite-dimensional U q [gl(2/2)]-modules W q constructed in Ref.1 are either irreducible or indecomposable. If a module W q is indecomposable, i.e. when the condition (4.41) in Ref.1 does not hold, there exists an invariant maximal submodule of W q , to say I q k , such that the factor-representation in the factor-module W q /I q k is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)] are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly. (author). 23 refs
International Nuclear Information System (INIS)
Nguyen Anh Ky.
1993-05-01
In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)] at generic deformation parameter q. As in the non-deformed case the finite-dimensional U q [gl(2/2)]-module W q obtained is irreducible and can be decomposed into finite-dimensional irreducible U q [l(2)+gl(2)]submodules V i q . (authohor). 32 refs
Irreducible Specht modules are signed Young modules
Hemmer, David J.
2005-01-01
Recently Donkin defined signed Young modules as a simultaneous generalization of Young and twisted Young modules for the symmetric group. We show that in odd characteristic, if a Specht module $S^\\lambda$ is irreducible, then $S^\\lambda$ is a signed Young module. Thus the set of irreducible Specht modules coincides with the set of irreducible signed Young modules. This provides evidence for our conjecture that the signed Young modules are precisely the class of indecomposable self-dual module...
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.
1993-01-01
The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs
Products of Irreducible Characters Having Complex-Valued Constituents
Directory of Open Access Journals (Sweden)
Lisa R. Hendrixson
2017-06-01
Full Text Available First, we prove that when a finite solvable group $G$ has a faithful irreducible character $\\chi$ such that $\\chi\\overline{\\chi}$ has two irreducible constituents, both must be real-valued. Then, we study the situation where $\\chi\\overline{\\chi}$ has exactly three distinct nonprincipal irreducible constituents, two of which are complex conjugates. In this case, we prove that $G$ has derived length bounded above by $6$.
Irreducible Inguinal Hernias in the Paediatric Age Group | Ezomike ...
African Journals Online (AJOL)
BACKGROUND: An inguinal hernia is said to be irreducible when the content fails to return into the peritoneal cavity without surgical intervention. Irreducibility is an ever present risk in untreated inguinal hernias and its management remains an important part of pediatric surgery practice. When a hernia is irreducible ...
Using Video to Improve Pronunciation of The Second Years Students of FKI UIR Pekanbaru
Putra, Al Malikul Ikhwanda
2018-01-01
The purpose of the research is to find out the use of video to improve students’ pronunciation. The study employed a classroom action research. The participants of this study were 37 students. They were the second year students of FKIP (faculty of teacher training and education) in Islamic University Riau (UIR) Pekanbaru, Indonesia. This study was conducted in two cycles. Each cycle comprised four meetings. The data of this research were obtained through (1) observation sheets, (2) field note...
Representations of the algebra Uq'(son) related to quantum gravity
International Nuclear Information System (INIS)
Klimyk, A.U.
2002-01-01
The aim of this paper is to review our results on finite dimensional irreducible representations of the nonstandard q-deformation U q ' (so n ) of the universal enveloping algebra U(so(n)) of the Lie algebra so(n) which does not coincide with the Drinfeld-Jimbo quantum algebra U q (so n ).This algebra is related to algebras of observables in quantum gravity and to algebraic geometry.Irreducible finite dimensional representations of the algebra U q ' (so n ) for q not a root of unity and for q a root of unity are given
Symmetric group representations and Z
Adve, Anshul; Yong, Alexander
2017-01-01
We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as a Littlewood-Richardson coefficient and as a Kronecker coefficient.
An irreducible ankle fracture dislocation: the Bosworth injury
Schepers, Tim; Hagenaars, Tjebbe; den Hartog, Dennis
2012-01-01
Irreducible fracture dislocations of the ankle are rare and represent true orthopedic emergencies. We present a case of a fracture dislocation that was irreducible owing to a fixed dislocation of the proximal fibular fragment posterior to the lateral ridge of the tibia. This particular type of
Representation theory of lattice current algebras
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Eidgenoessische Technische Hochschule, Zurich; Faddeev, L.D.; Froehlich, L.D.; Schomerus, V.; Kyoto Univ.
1996-04-01
Lattice current algebras were introduced as a regularization of the left-and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U q (G). Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts. (orig.)
The Slice Algorithm For Irreducible Decomposition of Monomial Ideals
DEFF Research Database (Denmark)
Roune, Bjarke Hammersholt
2009-01-01
Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial ideals. The paper includes experiments showing good performance...
Irreducible multiqutrit correlations in Greenberger-Horne-Zeilinger-type states
Energy Technology Data Exchange (ETDEWEB)
Zhang, Fu-Lin [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China); Chen, Jing-Ling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin, 300071 (China); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)
2011-12-15
Following the idea of the continuity approach by D. L. Zhou [Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multiparty correlations in two families of n-qutrit Greenberger-Horne-Zeilinger-type states. For the pure states in one of the families, the irreducible 2-party, n-party, and (n-m)-party (0
Irreducible multiqutrit correlations in Greenberger-Horne-Zeilinger-type states
International Nuclear Information System (INIS)
Zhang, Fu-Lin; Chen, Jing-Ling
2011-01-01
Following the idea of the continuity approach by D. L. Zhou [Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multiparty correlations in two families of n-qutrit Greenberger-Horne-Zeilinger-type states. For the pure states in one of the families, the irreducible 2-party, n-party, and (n-m)-party (0< m< n-2) correlations are nonzero, which is different from the n-qubit case. We also derive the correlation distributions in the n-qutrit maximal slice state, which can be uniquely determined by its (n-1)-qutrit-reduced density matrices among pure states. It is proved that there is no irreducible n-qutrit correlation in the maximal slice state. This enlightens us to give a discussion about how to characterize the pure states with irreducible n-party correlation in arbitrarily high-dimensional systems by the way of the continuity approach.
International Nuclear Information System (INIS)
Schek, I.; Wyatt, R.E.
1986-01-01
Molecular multiphoton processes are treated in the Recursive Residue Generation Method (A. Nauts and R.E. Wyatt, Phys. Rev. Lett 51, 2238 (1983)) by converting the molecular-field Hamiltonian matrix into tridiagonal form, using the Lanczos equations. In this study, the self-energies (diagonal) and linking (off-diagaonal) terms in the tridiagonal matrix are obtained by comparing linked moment diagrams in both representations. The dynamics of the source state is introduced and computed in terms of the linked and the irreducible moments
Construction of the irreducibles of B(2, 2)
International Nuclear Information System (INIS)
Melas, Evangelos
2006-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian spacetimes. As such, B is the best candidate for the universal symmetry group of general relativity. However, in studying quantum gravity, spacetimes with signatures other than the usual Lorentzian one and complex spacetimes are frequently considered. Generalizations of B appropriate to these other signatures have been defined earlier. In particular, the generalization B(2, 2) appropriate to the ultrahyperbolic signature (+, +, -, -) has been described in detail, and the study of its irreducible unitary representations (IRs) of B(2, 2) has been initiated. The infinite little groups have been given explicitly, but the finite little groups have only been partially described. This study is completed by describing in detail the finite little groups and by giving all the necessary information in order to construct the IRs of B(2, 2) in all cases
Local normality properties of some infrared representations
International Nuclear Information System (INIS)
Doplicher, S.; Spera, M.
1983-01-01
We consider the positive energy representations of the algebra of quasilocal observables for the free massless Majorana field described in preceding papers. We show that by an appropriate choice of the (partially) occupied one particle modes we can find irreducible, type IIsub(infinite) or IIIsub(lambda) representations in this class which are unitarily equivalent to the vacuum representation when restricted to any forward light cone and disjoint from it when restricted to any backward light cone, or conversely. We give an elementary explicit proof of local normality of each representation in the above class. (orig.)
Reducibility of quantum representations of mapping class groups
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fjelstad, Jens
2010-01-01
that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture...... this decomposition is a complete decomposition into irreducible representations for high enough levels....
Irreducible almost simple subgroups of classical algebraic groups
Burness, Timothy C; Marion, Claude; Testerman, Donna M
2015-01-01
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p\\geq 0 with natural module W. Let H be a closed subgroup of G and let V be a nontrivial p-restricted irreducible tensor indecomposable rational KG-module such that the restriction of V to H is irreducible. In this paper the authors classify the triples (G,H,V) of this form, where V \
Irreducible geometric subgroups of classical algebraic groups
Burness, Timothy C; Testerman, Donna M
2016-01-01
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p \\ge 0 with natural module W. Let H be a closed subgroup of G and let V be a non-trivial irreducible tensor-indecomposable p-restricted rational KG-module such that the restriction of V to H is irreducible. In this paper the authors classify the triples (G,H,V) of this form, where H is a disconnected maximal positive-dimensional closed subgroup of G preserving a natural geometric structure on W.
Alexander-equivalent Zariski pairs of irreducible sextics
DEFF Research Database (Denmark)
Eyral, Christophe; Oka, Mutsuo
2009-01-01
The existence of Alexander-equivalent Zariski pairs dealing with irreducible curves of degree 6 was proved by Degtyarev. However, no explicit example of such a pair is available (only the existence is known) in the literature. In this paper, we construct the first concrete example.......The existence of Alexander-equivalent Zariski pairs dealing with irreducible curves of degree 6 was proved by Degtyarev. However, no explicit example of such a pair is available (only the existence is known) in the literature. In this paper, we construct the first concrete example....
Irreducible descriptive sets of attributes for information systems
Moshkov, Mikhail
2010-01-01
The maximal consistent extension Ext(S) of a given information system S consists of all objects corresponding to attribute values from S which are consistent with all true and realizable rules extracted from the original information system S. An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B. We show that there exists only one irreducible descriptive set of attributes. We present a polynomial algorithm for this set construction. We also study relationships between the cardinality of irreducible descriptive set of attributes and the number of attributes in S. The obtained results will be useful for the design of concurrent data models from experimental data. © 2010 Springer-Verlag.
Representation properties, Racah sum rule, and Biedenharn - Elliott identity for Uq(osp(1|2))
International Nuclear Information System (INIS)
Minnaert, P.; Mozrzymas, M.
1998-01-01
It is shown that the universal R matrix in the tensor product of two irreducible representation spaces of the quantum superalgebra U q (osp(1|2)) can be expressed by Clebsch - Gordan coefficients. The Racah sum rule satisfied by U q (osp(1|2)) Racah coefficients and 6-j symbols is derived from the properties of the universal R matrix in the tensor product of three representation spaces. Considering the tensor product of four irreducible representations, it is shown that Biedenharn - Elliott identity holds for U q (osp(1|2)) Racah coefficients and 6-j symbols. A recursion relation for U q (osp(1|2)) 6-j symbols is derived from the Biedenharn endash Elliott identity. copyright 1998 American Institute of Physics
A practical criterion of irreducibility of multi-loop Feynman integrals
International Nuclear Information System (INIS)
Baikov, P.A.
2006-01-01
A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial
Two-rowed Hecke algebra representations at roots of unity
International Nuclear Information System (INIS)
Welsh, T.A.
1996-01-01
The explicit construction of irreducible representations of the Hecke algebra H n (q) of type A n-1 was studied for the non-generic case where q is a root of unity. The approach is via the Specht modules of H n (q) which are irreducible in the generic case and possess a natural basis indexed by Young tableaux. The general framework in which the non-generic H n (q)-modules are to be constructed is set up and, in particular, the full set of modules corresponding to two-part partitions is described. Many examples are given. 12 refs
Kronecker product of Sp(2n) representations using generalized Young tableaux
International Nuclear Information System (INIS)
Girardi, G.; Sciarrino, A.; Sorba, P.
1981-09-01
Using generalized Young tableaux, we obtain an explicit formula for the reduction of the Kronecker product of irreducible representation of the symplectic groups. This extends a previous work devoted to the case of orthogonal groups
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...
Knot invariants and higher representation theory
Webster, Ben
2018-01-01
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \\mathfrak{sl}_2 and \\mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \\mathfrak{sl}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \\mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \\mathcal{O} for \\mathfrak{gl}_k.
Special functions and the theory of group representations
Vilenkin, N Ja
1968-01-01
A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group SU(2), and the hypergeometric function and representations of the group SL(2,R), as well as many other classes of special functions.
On the representation of generalized Dirac (Clifford) algebras
International Nuclear Information System (INIS)
Srivastava, T.
1981-10-01
Some results of Brauer and Weyl and of Jordan and Wigner on irreducible representations of generalized Dirac (Clifford) algebras have been proved, adopting a new and simple approach which (i) makes the whole subject straightforward for physicists and (ii) simplifies the demonstration of the fundamental theorem of Pauli. (author)
Dubbers, Dirk
2013-01-01
This concise tutorial provides the bachelor student and the practitioner with a short text on quantum physics that allows them to understand a wealth of quantum phenomena based on a compact, well readable, yet still concise and accurate description of nonrelativistic quantum theory. This “quadrature of the circle” is achieved by concentrating first on the simplest quantum system that still displays all basic features of quantum theory, namely, a system with only two quantized energy levels. For most readers it is very helpful to understand such simple systems before slowly proceeding to more demanding topics like particle entanglement, quantum chaos, or the use of irreducible tensors. This tutorial does not intend to replace the standard textbooks on quantum mechanics, but will help the average student to understand them, often for the first time.
Highest weight representations of the quantum algebra Uh(gl∞)
International Nuclear Information System (INIS)
Palev, T.D.; Stoilova, N.I.
1997-04-01
A class of highest weight irreducible representations of the quantum algebra U h (gl-∞) is constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators are explicitly written. (author). 16 refs
Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups
Beltita, Ingrid; Beltita, Daniel
2009-01-01
We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.
International Nuclear Information System (INIS)
Kent, R.D.; Schlesinger, M.
1987-01-01
For the purpose of computing matrix elements of quantum mechanical operators in complex N-particle systems it is necessary that as much of each irreducible representation be stored in high-speed memory as possible in order to achieve the highest possible rate of computations. A graph theoretic approach to the representation of N-particle systems involving arbitrary single-particle spin is presented. The method involves a generalization of a technique employed by Shavitt in developing the graphical group approach (GUGA) to electronic spin-orbitals. The methods implemented in GENDRT and DRTDIM overcome many deficiencies inherent in other approaches, particularly with respect to utilization of memory resources, computational efficiency in the recognition and evaluation of non-zero matrix elements of certain group theoretic operators and complete labelling of all the basis states of the permutation symmetry (S N ) adapted irreducible representations of SU(n) groups. (orig.)
Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation
International Nuclear Information System (INIS)
Kalmykov, Mikhail Yu.; Kniehl, Bernd A.
2017-06-01
A number of irreducible master integrals for L-loop sunrise and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via the Mellin-Barnes representation.
Orbit Representations from Linear mod 1 Transformations
Directory of Open Access Journals (Sweden)
Carlos Correia Ramos
2012-05-01
Full Text Available We show that every point $x_0in [0,1]$ carries a representationof a $C^*$-algebra that encodes the orbit structure of thelinear mod 1 interval map $f_{eta,alpha}(x=eta x +alpha$. Such $C^*$-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map $f_{eta,alpha}$. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every $alphain [0,1[$ and $etageq 1$.
Representations of some quantum tori Lie subalgebras
International Nuclear Information System (INIS)
Jiang, Jingjing; Wang, Song
2013-01-01
In this paper, we define the q-analog Virasoro-like Lie subalgebras in x ∞ =a ∞ (b ∞ , c ∞ , d ∞ ). The embedding formulas into x ∞ are introduced. Irreducible highest weight representations of A(tilde sign) q , B(tilde sign) q , and C(tilde sign) q -series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the A(tilde sign) q , B(tilde sign) q , C(tilde sign) q , and D(tilde sign) q -series of the q-analog Virasoro-like Lie algebras.
International Nuclear Information System (INIS)
Marion, J.
1984-01-01
The introduction of the concepts of energy machinery and energy structure of a manifold allows to construct a large class of energy representations of gauge groups including, as a very particular case, the ones known up to now. A synthesis of earlier works allows to give a sufficient condition for the irreducibility of these representations. (orig./HSI)
Some extensions and applications of Eisenstein Irreducibility ...
Indian Academy of Sciences (India)
Page 1. Some extensions and applications of Eisenstein Irreducibility. Criterion. Sudesh Kaur Khanduja ..... Beginning from the individual theorems, I grew ac- customed to delve more deeply into their relationships and to grasp whole theories as a single entity. That is how I conceived the idea of mathematical beauty .
On the Directly and Subdirectly Irreducible Many-Sorted Algebras
Directory of Open Access Journals (Sweden)
Climent Vidal J.
2015-03-01
Full Text Available A theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.
Closed-form irreducible differential formulations of the Wilson renormalization group
International Nuclear Information System (INIS)
Vvedensky, D.D.; Chang, T.S.; Nicoll, J.F.
1983-01-01
We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon 2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon 2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator
Irreducible lateral dislocation of the elbow.
Directory of Open Access Journals (Sweden)
Chhaparwal M
1997-01-01
Full Text Available A rare case of an irreducible post-traumatic lateral dislocation of elbow is presented. The mechanism of injury was fall on a flexed elbow with trauma on its medial aspect resulting in pronation of the forearm. At open reduction, the brachialis muscle was in the form of a tight band which prevented reduction. The ulnar nerve was entrapped in the joint.
Siudzińska, Katarzyna; Chruściński, Dariusz
2018-03-01
In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.
Irreducible multivariate polynomials obtained from polynomials in ...
Indian Academy of Sciences (India)
Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: Nicolae. ... Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ..... This shows us that deg ai = (n − i) deg f2 for each i = 0,..., n, so min k>0.
International Nuclear Information System (INIS)
Joos, H.; Schaefer, M.
1987-01-01
The symmetry group of staggered lattice fermions is discussed as a discrete subgroup of the symmetry group of the Dirac-Kaehler equation. For the representation theory of this group, G. Mackey's generalization of E.P. Wigner's procedure for the construction of unitary representations of groups with normal subgroups is used. A complete classification of these irreducible representations by ''momentum stars'', ''flavour orbits'' and ''reduced spins'' is given. (orig.)
Irreducible descriptive sets of attributes for information systems
Moshkov, Mikhail; Skowron, Andrzej; Suraj, Zbigniew
2010-01-01
. An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B
Parallel Construction of Irreducible Polynomials
DEFF Research Database (Denmark)
Frandsen, Gudmund Skovbjerg
Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....
On the ESQ Property of Certain Representations of Metacyclic Groups
Directory of Open Access Journals (Sweden)
János Wolosz
2017-06-01
Full Text Available A group representation is said to have the ESQ property if it is isomorphic to a quotient of its own exterior square. Let us denote the semidirect product of cyclic groups $Z_p\\rtimes Z_q$ by $F_{p,q}$, where p is a prime and $q | p − 1$. We investigate whether $F_{p,q}$ has an irreducible representation with the ESQ property. Fixing one of the parameters $q$ or $p−1$, we will be able to give an asymptotic answer to this question.
An Integral Representation of Standard Automorphic L Functions for Unitary Groups
Directory of Open Access Journals (Sweden)
Yujun Qin
2007-01-01
Full Text Available Let F be a number field, G a quasi-split unitary group of rank n. We show that given an irreducible cuspidal automorphic representation π of G(A, its (partial L function LS(s,π,σ can be represented by a Rankin-Selberg-type integral involving cusp forms of π, Eisenstein series, and theta series.
Irreducible diagrams in Landau-Ginzburg field theory
Energy Technology Data Exchange (ETDEWEB)
Witten, Jr, T A [Michigan Univ., Ann Arbor (USA). Dept. of Psychology
1981-10-19
It is shown that the free energy W of a Landau-Ginzburg-Wilson field theory with O(n) symmetry may be written in terms of the generating function V of diagrams irreducible in both propagator and interaction lines. This generalizes and simplifies a recent result of Des Cloizeaux. The functions W and V are related by a type of Legendre transformation on the bare mass variable.
Directory of Open Access Journals (Sweden)
Morteza Nakhaei Amroodi
2015-11-01
Full Text Available Background: Although anterior shoulder dislocation is the most prevalent type of body dislocation, irreducible anterior shoulder dislocation is seldom reported in the literature, which is usually due to physical obstacles. Objectives: This study presents our findings regarding the causes of irreducibility of anterior shoulder dislocation associated with displaced fracture of the greater tuberosity. Patients and Methods: CT scans, open reduction of the joint, and internal fixation of the tuberosity was performed in seven patients with irreducible anterior shoulder dislocation associated with displaced fracture of the greater tuberosity. Results: As confirmed by intraoperative findings, the CT scans showed the cause of irreducible shoulder dislocation in six cases was the interposition of the long head of biceps (LHB in the anterior of the head that was displaced from the fracture line between the greater and lesser tuberosities. In another case, the greater and lesser tuberosities were attached to each other and were separated from the head. This fractured part was trapped. Conclusions: We suggest that performing CT scans in all cases of anterior shoulder dislocations with displaced fracture of the greater tuberosity can help surgeons to diagnose the accompanying fractures and possible complications, such as irreducibility. If the fracture line passes through the bicipital groove or in the case of a shield fracture, possible irreducibility should be borne in mind.
Superalgebras, their quantum deformations and the induced representation method
International Nuclear Information System (INIS)
Nguyen Anh Ky.
1996-08-01
In this paper some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Up to now, based on the Kac representation theory we have succeeded in constructing representations of several higher rank superalgebras. When representations of quantum superalgebras are concerned, we develop a method which can be applied not only to the one-parametric quantum deformations but also to the multi-parametric ones. Here, being illustrations of the above-mentioned methods, the superalgebra gl(2/1) and its (one-parametric) quantum deformation U q [gl(2/1)] are considered as their finite-dimensional representations are investigated in detail and constructed explicitly. Also, it is shown that the finite-dimensional representations obtained constitute classes of all irreducible (typical and non-typical) finite-dimensional representations of gl(2/1) and U q [gl(2/1)]. Some of the detailed results may be simple but they are given for the first time. (author). 64 refs
International Nuclear Information System (INIS)
Dubbers, Dirk; Stoeckmann, Hans-Juergen
2013-01-01
Helps in a compact form to reach good understanding of quantum physics. Shows important analogies between problems across different disciplines. Concise and accurate, written in a readable and lively style. Concentrates on the simplest quantum system which still displays the basic features of quantum theory. Chapters end with a general outlook on multi-level systems. Results are applied to a multitude of topics in modern science, from particle physics and quantum optics to time standards and magnetic resonance imaging. This concise tutorial provides the bachelor student and the practitioner with a short text on quantum physics that allows them to understand a wealth of quantum phenomena based on a compact, well readable, yet still concise and accurate description of nonrelativistic quantum theory. This ''quadrature of the circle'' is achieved by concentrating first on the simplest quantum system that still displays all basic features of quantum theory, namely, a system with only two quantized energy levels. For most readers it is very helpful to understand such simple systems before slowly proceeding to more demanding topics like particle entanglement, quantum chaos, or the use of irreducible tensors. This tutorial does not intend to replace the standard textbooks on quantum mechanics, but will help the average student to understand them, often for the first time.
Exact results for Wilson loops in arbitrary representations
Energy Technology Data Exchange (ETDEWEB)
Fiol, Bartomeu; Torrents, Genís [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain)
2014-01-08
We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of N=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.
Irreducible Fifth Metatarsophalangeal Joint after Car Crush Injury
Turkmensoy, Fatih; Erinc, Samet; Ergin, Omer Naci; Ozkan, Korhan; Kemah, Bahattin
2015-01-01
Metatarsophalangeal joint dislocations are uncommon injuries. Herein, an irreducible dislocation of fifth metatarsophalangeal joint with fractures on the second, third, and fourth metatarsal head was reported. Joint reduction could not be achieved which necessitated open reduction. Six months after surgery the patient was walking and doing his daily activities without any complaints. He had returned to his pretrauma functional level. PMID:25861501
Irreducible Fifth Metatarsophalangeal Joint after Car Crush Injury
Directory of Open Access Journals (Sweden)
Fatih Turkmensoy
2015-01-01
Full Text Available Metatarsophalangeal joint dislocations are uncommon injuries. Herein, an irreducible dislocation of fifth metatarsophalangeal joint with fractures on the second, third, and fourth metatarsal head was reported. Joint reduction could not be achieved which necessitated open reduction. Six months after surgery the patient was walking and doing his daily activities without any complaints. He had returned to his pretrauma functional level.
General quantum polynomials: irreducible modules and Morita equivalence
International Nuclear Information System (INIS)
Artamonov, V A
1999-01-01
In this paper we continue the investigation of the structure of finitely generated modules over rings of general quantum (Laurent) polynomials. We obtain a description of the lattice of submodules of periodic finitely generated modules and describe the irreducible modules. We investigate the problem of Morita equivalence of rings of general quantum polynomials, consider properties of division rings of fractions, and solve Zariski's problem for quantum polynomials
Clifford algebras and the minimal representations of the 1D N-extended supersymmetry algebra
International Nuclear Information System (INIS)
Toppan, Francesco
2008-01-01
The Atiyah-Bott-Shapiro classification of the irreducible Clifford algebra is used to derive general properties of the minimal representations of the 1D N-Extended Supersymmetry algebra (the Z 2 -graded symmetry algebra of the Supersymmetric Quantum Mechanics) linearly realized on a finite number of fields depending on a real parameter t, the time. (author)
Representations of the infinite symmetric group
Borodin, Alexei
2016-01-01
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.
Irreducibility and co-primeness as an integrability criterion for discrete equations
International Nuclear Information System (INIS)
Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji
2014-01-01
We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor. 47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. (paper)
On the labeling and symmetry adaptation of the solvable finite groups representations
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.; Nogueira, S.R.A.
1987-01-01
We propose a method to simultaneously perform a symmetry adaptation and a labeling of the bases of the irreducible representations of the solvable finite groups. It is performed by difining a self-adjoint operator with ligenvalues which evidence the descent in symmetry of the group-subgroups sequences. We also prove two theorems on the canonicity of the cpomposition series of the solvable groups. (author) [pt
The irreducible needs of children for development: a frame of reference to health care
Directory of Open Access Journals (Sweden)
Maria De La Ó Ramallo Veríssimo
2018-03-01
Full Text Available ABSTRACT A comprehensive health care to children implies in caring for their development, by perceiving the needs based on a suitable reference to children’s specificities. This theoretical study aimed to analyze the “irreducible needs of children” frame of reference, based on a child development theory. We performed a comparative analysis between the contents of children’s irreducible needs and the components of the Bioecological Theory of Human Development. An extensive correspondence was verified among the components of the Bioecological Theory and the following essential needs: ongoing nurturing relationships; experiences tailored to individual differences; developmentally appropriate experiences; limit setting, structure and expectations; stable, supportive communities and cultural continuity. The need for physical protection, safety, and regulation is not explicit in the elements of the theory, although it is also verified in their definitions. We concluded that the irreducible needs’ reference can support nurses in health care and in child development promotion.
Quotients of irreducible N=2 superconformal coset theories by discrete symmetries
International Nuclear Information System (INIS)
Bailin, D.; Love, A.
1990-01-01
The spectrum of massless states is studied for the irreducible N=2 superconformal coset theories when these theories are quotiented by discrete symmetries, including the effect of embedding the discrete symmetries in the gauge group. (orig.)
On squares of representations of compact Lie algebras
International Nuclear Information System (INIS)
Zeier, Robert; Zimborás, Zoltán
2015-01-01
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems
On squares of representations of compact Lie algebras
Energy Technology Data Exchange (ETDEWEB)
Zeier, Robert, E-mail: robert.zeier@ch.tum.de [Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching (Germany); Zimborás, Zoltán, E-mail: zimboras@gmail.com [Department of Computer Science, University College London, Gower St., London WC1E 6BT (United Kingdom)
2015-08-15
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.
Irreducible mass for the Tomimatsu-Sato space-time
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Salmistraro, F; Catenacci, R
1979-01-01
A global definition of irreducible mass for the odd delta T-S metrics is investigated. It is found that its expression in terms of the source parameters is the same for all the members of the family and reduces to the formula that holds in the Kerr case (delta = 1). As a consequence, it is shown that processes with msub(ir) = const no longer imply zero variations of the horizon's area for delta > 1.
International Nuclear Information System (INIS)
Kutzelnigg, Werner; Mukherjee, Debashis
2004-01-01
The k-particle irreducible Brillouin conditions IBC k and the k-particle irreducible contracted Schroedinger equations ICSE k for a closed-shell state are analyzed in terms of a Moeller-Plesset-type perturbation expansion. The zeroth order is Hartree-Fock. From the IBC 2 (1) , i.e., from the two-particle IBC to first order in the perturbation parameter μ, one gets the leading correction λ 2 (1) to the two-particle cumulant λ 2 correctly. However, in order to construct the second-order energy E 2 , one also needs the second-order diagonal correction γ D (2) to the one-particle density matrix γ. This can be obtained: (i) from the idempotency of the n-particle density matrix, i.e., essentially from the requirement of n-representability; (ii) from the ICSE 1 (2) ; or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the ICSE 3 (2) to get λ 3 (2) , which is needed in the ICSE 2 (2) to get λ 2 (2) , which, in turn, is needed in the ICSE 1 (2) to get γ (2) . Generally the (k+1)-particle approximation is needed to obtain E k correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ICSE k , ignoring λ k+1 and λ k+2 , by a renormalized hierarchy, in which only λ k+2 is ignored, and λ k+1 is expressed in terms of the λ p of lower particle rank via the partial trace relation for λ k+2 . Then the k-particle approximation is needed to obtain E k correctly. This is still poorer than coupled-cluster theory, where the k-particle approximation yields E k+1 . We also study the possibility to use some simple necessary n-representability conditions, based on the non-negativity of γ (2) and two related matrices, in order to get estimates for γ D (2) in terms of λ 2 (1) . In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of λ 2
The quantum Rabi model and Lie algebra representations of sl2
International Nuclear Information System (INIS)
Wakayama, Masato; Yamasaki, Taishi
2014-01-01
The aim of the present paper is to understand the spectral problem of the quantum Rabi model in terms of Lie algebra representations of sl 2 (R). We define a second order element of the universal enveloping algebra U(sl 2 ) of sl 2 (R), which, through the image of a principal series representation of sl 2 (R), provides a picture equivalent to the quantum Rabi model drawn by confluent Heun differential equations. By this description, in particular, we give a representation theoretic interpretation of the degenerate part of the spectrum (i.e., Judd's eigenstates) of the Rabi Hamiltonian due to Kuś in 1985, which is a part of the exceptional spectrum parameterized by integers. We also discuss the non-degenerate part of the exceptional spectrum of the model, in addition to the Judd eigenstates, from a viewpoint of infinite dimensional irreducible submodules (or subquotients) of the non-unitary principal series such as holomorphic discrete series representations of sl 2 (R). (paper)
International Nuclear Information System (INIS)
Roche, Ph.
2016-01-01
We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, _q) and PGL(2, _q). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.
On relativistic irreducible quantum fields fulfilling CCR
International Nuclear Information System (INIS)
Baumann, K.
1987-01-01
Let phi be a relativistic scalar field fulfilling canonical commutation relations (CCR). Furthermore it is assumed that the time zero fields and momenta form an irreducible set. Based on estimates given by Herbst [I. W. Herbst, J. Math. Phys. 17, 1210 (1976)], and by methods developed by Powers [R. T. Powers, Commun. Math. Phys. 4, 145 (1967)], it is shown that phi has to be a free field in n>3 space dimensions. For n = 3 (resp. n = 2) restrictions that look similar to the restriction in a formal :phi 4 : 3 /sub +/ 1 (resp. :phi 6 : 2 /sub +/ 1 ) theory are obtained
On the representations of Poincare group associated with unstable particles
International Nuclear Information System (INIS)
Exner, RP.
1983-01-01
The problem of relativistically-covariant description of unstable particles is reexamined. We follow the approach which associates a unitary reducible representation of Poincare group with a larger isolated system, and compare it with the one ascribing a non-unitary irreducible representation to the unstable particle alone. It is shown that the problem roots in choice of the subspace Hsub(u) of the state Hilbert space which could be related to the unstable particle. Translational invariance of Hsub(u) is proved to be incompatible with unitarity of the boosts. Further we propose a concrete choice of Hsub(u) and argue that in most cases of the actual experimental arrangements, this subspace is effectively one-dimensional. A correct slow-down for decay of a moving particle is obtained
On the intersection of irreducible components of the space of finite-dimensional Lie algebras
International Nuclear Information System (INIS)
Gorbatsevich, Vladimir V
2012-01-01
The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.
Andrews, David L.
2009-08-01
In recent years it has become evident that the primary concept of the photon has multiple interpretations, with widely differing secondary connotations. Despite the all-pervasive nature of this concept in science, some of the ancillary properties with which the photon is attributed in certain areas of application sit uneasily alongside those invoked in other areas. Certainly the range of applications extends far beyond what was envisaged in the original conception, now entering subjects extending from elementary particle physics and cosmology through to spectroscopy, statistical mechanics and photochemistry. Addressing this diverse context invites the question: What is there, that it is possible to assert as incontrovertibly true about the photon? Which properties are non-controversial, if others are the subject of debate? This paper describes an attempt to answer these questions, establishing as far as possible an irreducible core of what can rightly be asserted about the photon, and setting aside some of what often is, but should never be so asserted. Some of the more bewildering difficulties and differences of interpretation owe their origin to careless descriptions, highlighting a need to guard semantic precision; although simplifications are frequently and naturally expedient for didactic purposes, they carry the risk of becoming indelible. Focusing on such issues, the aim is to identify how much or how little about the photon can be regarded as truly non-controversial.
Irreducible integrable theories form tensor products of conformal models
International Nuclear Information System (INIS)
Mathur, S.D.; Warner, N.P.
1991-01-01
By using Toda field theories we show that there are perturbations of direct products of conformal theories that lead to irreducible integrable field theories. The same affine Toda theory can be truncated to different quantum integrable models for different choices of the charge at infinity and the coupling. The classification of integrable models that can be obtained in this fashion follows the classification of symmetric spaces of type G/H with rank H = rank G. (orig.)
On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup
Directory of Open Access Journals (Sweden)
S.A. Grigoryan
2016-06-01
Full Text Available The class of С*-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These algebras have been proved to be Z-graded С*-algebras. For a certain class of algebras in the family under consideration the compact quantum semigroup structure has been constructed.
Invariant differential operators and characters of the AdS4 algebra
International Nuclear Information System (INIS)
Dobrev, V K
2006-01-01
The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalized to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors of the reducible AdS 4 Verma modules. These are used to obtain the AdS 4 invariant differential operators. Using this we display a new structure-a diagram involving four partially equivalent reducible representations one of which contains all finite-dimensional irreps of the AdS 4 algebra. We study in more detail the cases involving UIRs, in particular, the Di and the Rac singletons, and the massless UIRs. In the massless case, we discover the structure of sets of 2s 0 - 1 conserved currents for each spin s 0 UIR, s 0 = 1, 3/2,.... All massless cases are contained in a one-parameter subfamily of the quartet diagrams mentioned above, the parameter being the spin s 0 . Further we give the classification of the so(5,C) irreps presented in a diagrammatic way which makes easy the derivation of all character formulae. The paper concludes with a speculation on the possible applications of the character formulae to integrable models
Magnetic translation groups in an n-dimensional torus and their representations
International Nuclear Information System (INIS)
Tanimura, Shogo
2002-01-01
A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG in an n-dimensional torus is isomorphic to a central extension of a cyclic group Z ν 1 x···xZ ν 2l xT m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG in a three-torus and apply the representation theory to three examples. We briefly describe a representation theory for a general n-torus. The MTG in an n-torus can be regarded as a generalization of the so-called noncommutative torus
Wigner functions for noncommutative quantum mechanics: A group representation based construction
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com [Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)
2015-12-15
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.
Degenerate representations from quantum kinematical constraints
International Nuclear Information System (INIS)
Iosifescu, M.; Scutaru, H.
1987-11-01
We present a systematization of previous results concerning the finite-dimensional irreducible L-modules, for semisimple Lie algebras, on which the second-degree irreducible tensors from the enveloping algebra U(L) vanish.(authors)
Representations of algebras of extended supersymmetry and linearised supergravity theories
International Nuclear Information System (INIS)
Tejlor, Dzh.
1985-01-01
In the lecture an attempt is made to acquaint the reader with the theory of extended supersymmetry, to characterize the corresponding particle spectrum and to explain how it can be used in supersymmetry with the least difficulties. Superalgebras are classified, their irreducible representations are given. Superfields and superspace are introduced, their role in the superalgebra realization is analyzed. Examples of linearized Lagrangians and auxiliary fields for the theories of supergravity with N=1 and N=2 are presented. Methods of spin reduction with the central charges are considered. The possibility to construct supergravity model with N>=3 off mass shell is considered
An algorithm to compute the canonical basis of an irreducible Uq(g)-module
de Graaf, W. A.
2002-01-01
An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a tensor product of modules with known canonical bases.
International Nuclear Information System (INIS)
Carrington, M. E.; Kovalchuk, E.
2010-01-01
Transport coefficients can be obtained from two-point correlators using the Kubo formulas. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the resummed two-point function that is obtained from the three-loop three-particle irreducible resummed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the four-loop four-particle irreducible effective action for a scalar theory with cubic and quartic interactions, with a nonvanishing field expectation value. We obtain a set of integral equations that determine the resummed two-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.
Identities for the electron forms 2 and their 3D representation
International Nuclear Information System (INIS)
Minogin, Vladimir G.
2012-01-01
New type of identities for products of the electron forms 2 (Fs2) and the bilinear forms (BFs) are derived. The identities are found for both temporal Fs2 describing the electron energy and quasi energy densities and spatial Fs2 describing the linear momentum and quasi linear momentum densities. The identities allow one to transform the quasi energy densities into the energy densities as well as the quasi linear momentum densities into the linear momentum densities. It is shown that by choosing any one of the 16 electron temporal or spatial Fs2 one can represent the remaining 15 temporal or spatial Fs2 as combinations of a chosen form 2 (F2) and the derivatives of a number of BFs. Any one of such 16 sets of identities can be considered as a specific form of an irreducible representation for the temporal or spatial Fs2. Similar to the bilinear identities for BFs the derived identities can be used for reduction different physical quantities describing the electron to the forms defined by the basic physical observables. As an example we consider transformation of the electron energy density to a new fundamental form that presents the energy density through the linear momentum density. - Highlights: ► New type of identities connecting electron forms 2 and bilinear forms is derived.► Identities are found for temporal and spatial forms 2. ► Irreducible representation of the identities is derived. ► New forms of the electron energy density are presented.
Representations of affine Hecke algebras
Xi, Nanhua
1994-01-01
Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest
Energy Technology Data Exchange (ETDEWEB)
Larouche, M [Departement de Mathematiques et Statistique, Universite de Montreal, 2920 chemin de la Tour, Montreal, Quebec H3T 1J4 (Canada); Lemire, F W [Department of Mathematics, University of Windsor, Windsor, Ontario (Canada); Patera, J, E-mail: larouche@dms.umontreal.ca, E-mail: lemire@uwindsor.ca, E-mail: patera@crm.umontreal.ca [Centre de Recherches Mathematiques, Universite de Montreal, CP 6128-Centre ville, Montreal, Quebec H3C 3J7 (Canada)
2011-10-14
In this paper, we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given. (paper)
Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere
International Nuclear Information System (INIS)
Sabbah, C
2004-01-01
It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc
2017-04-01
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.
Dlouhy, Brian J; Policeni, Bruno A; Menezes, Arnold H
2017-07-01
OBJECTIVE Os odontoideum (OO) is a craniovertebral junction (CVJ) abnormality in which an ossicle (small bone) is cranial to a hypoplastic dens by a variable gap. This abnormality can result in instability, which may be reducible or irreducible. What leads to irreducibility in OO is unclear. Therefore, the authors sought to better understand the causes of irreducibility in OO. METHODS A retrospective review was conducted, which identified more than 200 patients who had undergone surgical treatment for OO between 1978 and 2015 at the University of Iowa Hospitals and Clinics. Only the 41 patients who had irreducible OO were included in this study. All inpatient and outpatient records were retrospectively reviewed, and patient demographics, clinical presentation, radiographic findings, surgical treatment, and operative findings were recorded and analyzed. RESULTS The cohort of 41 patients who were found to have irreducible OO included both children and adults. A majority of patients were adults (61% were 18 years or older). Clinical presentation included neck pain and headache in the majority of patients (93%). Weakness, sensory disturbances, and myelopathy were invariably present in all 41 patients (100%). Down syndrome was much more common in the pediatric cohort than in the adult cohort; of the 16 pediatric patients, 6 had Down syndrome (38%), and none of the adults did. Of the 16 pediatric patients, 5 had segmentation failure (31%) in the subaxial spine, and none of the adults did. A form of atlantoaxial dislocation was seen in all cases. On CT imaging, atlantoaxial facets were dislocated in all 41 cases but did not have osseous changes that would have prevented reduction. On MRI, the transverse ligament was identified anterior and inferior to the ossicle and superior to the hypoplastic odontoid process in all cases in which these studies were available (i.e., post-MRI era; 36 of 36 cases). The ligament was hypointense on T2-weighted images but also had an
Ryttov, Thomas A
2007-01-01
We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vector-like matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories developing an infrared stable fixed point. We find that exactly 50 % of the asymptotically free theories can develop an infrared fixed point while for the nonsupersymmetric theories it is circa 25 %. When considering multiple representations, only for the nonsupersymmetric case, the conformal regions quickly dominate over the nonconformal ones. For four representations, 70 % of the asymptotically free space is filled by the ...
Representations of the Virasoro algebra from lattice models
International Nuclear Information System (INIS)
Koo, W.M.; Saleur, H.
1994-01-01
We investigate in detail how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic relations are obeyed in the scaling limit. The latter is under reasonable control thanks to the Bethe-ansatz solution. The results, which are mostly numerical for technical reasons, are remarkably precise. They are also corroborated by exact pieces of information from various sources, in particular Temperley-Lieb algebra representation theory. Most features of the Virasoro algebra (like central term, null vectors, metric properties, etc.) can thus be observed using the lattice models. This seems of general interest for lattice field theory, and also more specifically for finding relations between conformal invariance and lattice integrability, since a basis for the irreducible representations of the Virasoro algebra should now follow (at least in principle) from Bethe-ansatz computations. ((orig.))
BMS symmetry, soft particles and memory
Chatterjee, Atreya; Lowe, David A.
2018-05-01
In this work, we revisit unitary irreducible representations of the Bondi–Metzner–Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of supermomenta in addition to 4-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing 4-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.
Graded Fock-like representations for a system of algebraically interacting paraparticles
International Nuclear Information System (INIS)
Kanakoglou, Konstantinos; Herrera-Aguilar, Alfredo
2011-01-01
We will present and study an algebra describing a mixed paraparticle model, known in the bibliography as 'The Relative Parabose Set (RPBS)'. Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom P (1,1) BF , we will construct a class of Fock-like representations of this algebra, dependent on a positive parameter p a kind of generalized parastatistics order. Mathematical properties of the Fock-like modules will be investigated for all values of p and constructions such as ladder operators, irreducibility (for the carrier spaces) and (Z 2 x Z 2 )-gradings (for both the carrier spaces and the algebra itself) will be established.
Modular representations of GL(n) distinguished by GL(n-1) over a p-adic field
Sécherre , Vincent; Venketasubramanian , C. G.
2015-01-01
Let $\\F$ be a non-Archimedean locally compact field, $q$ be the cardinality of its residue field, and $\\R$ be an algebraically closed field of characteristic $\\ell$ not dividing $q$.We classify all irredu\\-cible smooth $\\R$-representations of $\\GL\\_n(\\F)$ having a nonzero $\\GL\\_{n-1}(\\F)$-inva\\-riant linear form, when $q$ is not congruent to $1$ mod $\\ell$.Partial results in the case when $q$ is $1$ mod $\\ell$ show that, unlike the complex case, the space of $\\GL\\_{n-1}(\\F)$-invariant linear ...
On the geometry of certain irreducible non-torus plane sextics
DEFF Research Database (Denmark)
Eyral, Christophe; Oka, Mutsuo
2009-01-01
An irreducible non-torus plane sextic with simple singularities is said to be special if its fundamental group factors to a dihedral group. There exist (exactly) ten configurations of simple singularities that are realizable by such curves. Among them, six are realizable by non-special sextics...... as well. We conjecture that for each of these six configurations there always exists a non-special curve whose fundamental group is abelian, and we prove this conjecture for three configurations (another one has already been treated in one of our previous papers). As a corollary, we obtain new explicit...
Three remarks on Powers' theorem about irreducible fields fulfilling CAR
International Nuclear Information System (INIS)
Baumann, K.
1986-01-01
First it is shown that within a relativistic Fermi field theory, a bound parallelPsi/sub k/( f,t)parallel 2 already implies canonical anticommutation relations (CAR). Then under Powers' assumptions a linear, first-order differential equation for the fields psi/sub k/(x,t) is derived. This shows that in the set of generalized free fields fulfilling CAR only the free fields are irreducible at time zero. Finally Fermi fields in two space-time dimensions are considered. It is shown that only four-fermion interaction might be compatible with CAR and a bound on the coupling strength is derived
Coupling coefficients for tensor product representations of quantum SU(2)
International Nuclear Information System (INIS)
Groenevelt, Wolter
2014-01-01
We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions
Coupling coefficients for tensor product representations of quantum SU(2)
Groenevelt, Wolter
2014-10-01
We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.
SU(2) X SU(2) X U(1) basis for symmetric SO(6) representations: matrix elements of the generators
International Nuclear Information System (INIS)
Piepenbring, R.; Silvestre-Brac, B.; Szymanski, Z.
1987-01-01
Matrix elements of the group generators for the symmetric irreducible representations of SO(6) are explicitly calculated in a closed form employing thedecomposition chain SO(6) is contained in SU(2) X SU(2) X U(1) (which is different from the well known Wigner supermultiplet scheme). The relation to the Gel'fand Tsetlin method using SO(6) contained in SO(5) up to ... SO(2) is indicated. An example of a physical application is given
Energy Technology Data Exchange (ETDEWEB)
Roche, Ph., E-mail: philippe.roche@univ-montp2.fr [Université Montpellier 2, CNRS, L2C, IMAG, Montpellier (France)
2016-03-15
We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.
DU and UD-invariants of unitary groups
International Nuclear Information System (INIS)
Aguilera-Navarro, M.C.K.
1977-01-01
Four distint ways of obtaining the eigenvalues of unitary groups, in any irreducible representation, are presented. The invariants are defined according to two different contraction conventions. Their eigenvalue can be given in terms of two classes of special partial hooks associated with the young diagram characterizing the irreducible representation considered
International Nuclear Information System (INIS)
Burdík, C; Reshetnyak, A
2012-01-01
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.
Mozrzymas, Marek; Studziński, Michał; Horodecki, Michał
2018-03-01
Herein we continue the study of the representation theory of the algebra of permutation operators acting on the n -fold tensor product space, partially transposed on the last subsystem. We develop the concept of partially reduced irreducible representations, which allows us to significantly simplify previously proved theorems and, most importantly, derive new results for irreducible representations of the mentioned algebra. In our analysis we are able to reduce the complexity of the central expressions by getting rid of sums over all permutations from the symmetric group, obtaining equations which are much more handy in practical applications. We also find relatively simple matrix representations for the generators of the underlying algebra. The obtained simplifications and developments are applied to derive the characteristics of a deterministic port-based teleportation scheme written purely in terms of irreducible representations of the studied algebra. We solve an eigenproblem for the generators of the algebra, which is the first step towards a hybrid port-based teleportation scheme and gives us new proofs of the asymptotic behaviour of teleportation fidelity. We also show a connection between the density operator characterising port-based teleportation and a particular matrix composed of an irreducible representation of the symmetric group, which encodes properties of the investigated algebra.
Directory of Open Access Journals (Sweden)
Álvaro Duque S.J.
2002-06-01
Full Text Available Las matrices de las representaciones irreducibles de un grupo G se usan para el cómputo de la Transformada Generalizada de Fourier de una función definida en G. Existen muchas otras aplicaciones para las representaciones irreducibles de un grupo. Nosotros elaborarnos un software que calcula las matrices de las representacionesirreducibles del grupo simétrico en la forma serninormal de Young. Este programa corre en el Sistema Algebraico Computacional CoCoA.
Revisiting the Zassenhaus conjecture on torsion units for the integral ...
Indian Academy of Sciences (India)
k-th root of unity. Our assumptions that χ(ud) = χ(vd) for d > 1 dividing k and that u and v have the same partial augmentations mean that the right-hand side of the collection of LP-equations for the .... have been produced using the irreducible representations produced by the GAP command. IrreducibleRepresentations(G).
Quasiaverages, symmetry breaking and irreducible Green functions method
Directory of Open Access Journals (Sweden)
A.L.Kuzemsky
2010-01-01
Full Text Available The development and applications of the method of quasiaverages to quantum statistical physics and to quantum solid state theory and, in particular, to quantum theory of magnetism, were considered. It was shown that the role of symmetry (and the breaking of symmetries in combination with the degeneracy of the system was reanalyzed and essentially clarified within the framework of the method of quasiaverages. The problem of finding the ferromagnetic, antiferromagnetic and superconducting "symmetry broken" solutions of the correlated lattice fermion models was discussed within the irreducible Green functions method. A unified scheme for the construction of generalized mean fields (elastic scattering corrections and self-energy (inelastic scattering in terms of the equations of motion and Dyson equation was generalized in order to include the "source fields". This approach complements previous studies of microscopic theory of antiferromagnetism and clarifies the concepts of Neel sublattices for localized and itinerant antiferromagnetism and "spin-aligning fields" of correlated lattice fermions.
International Nuclear Information System (INIS)
Ryttov, Thomas A.; Sannino, Francesco
2007-01-01
We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vectorlike matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories developing an infrared stable fixed point. We find that exactly 50% of the asymptotically free theories can develop an infrared fixed point while for the nonsupersymmetric theories it is circa 25%. When considering multiple representations, only for the nonsupersymmetric case, the conformal regions quickly dominate over the nonconformal ones. For four representations, 70% of the asymptotically free space is filled by the conformal region. According to our theoretical landscape survey the unparticle physics world occupies a sizable amount of the particle world, at least in theory space, and before mixing it (at the operator level) with the nonconformal one
International Nuclear Information System (INIS)
Ketov, S.V.
1996-01-01
The simplest free-field realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G 2 affine currents, respectively, are investigated. Both the N=8 and N=7 algebras are found to admit unitary and highest-weight irreducible representations in terms of a single free boson and free fermions in 8 of Spin(7) or 7 of G 2 , respectively, at level k=1 and the corresponding central charges c 8 =26/5 and c 7 =5. (orig.)
Campoamor-Stursberg, R.
2018-03-01
A procedure for the construction of nonlinear realizations of Lie algebras in the context of Vessiot-Guldberg-Lie algebras of first-order systems of ordinary differential equations (ODEs) is proposed. The method is based on the reduction of invariants and projection of lowest-dimensional (irreducible) representations of Lie algebras. Applications to the description of parameterized first-order systems of ODEs related by contraction of Lie algebras are given. In particular, the kinematical Lie algebras in (2 + 1)- and (3 + 1)-dimensions are realized simultaneously as Vessiot-Guldberg-Lie algebras of parameterized nonlinear systems in R3 and R4, respectively.
Experimental test of the irreducible four-qubit Greenberger-Horne-Zeilinger paradox
Su, Zu-En; Tang, Wei-Dong; Wu, Dian; Cai, Xin-Dong; Yang, Tao; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Żukowski, Marek; Pan, Jian-Wei
2017-03-01
The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly 20 years ago, followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to a three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The bound of a three-setting-per-party Bell-GHZ inequality is violated by 7 σ . The fidelity of the GHZ state was around 81 % , and an entanglement witness reveals a violation of the separability threshold by 19 σ .
Connections between quantized affine algebras and superalgebras
International Nuclear Information System (INIS)
Zhang, R.B.
1992-08-01
Every affine superalgebra with a symmetrizable Cartan matrix is closely related to an ordinary affine algebra with the same Cartan matrix. It is shown that the quantum supergroup associated with the former is essentially isomorphic to the quantum group associated with the latter in an appropriate class of representations. At the classical level, each integrable irreducible highest weight representation of the affine superalgebra has a corresponding irreducible representation of the affine algebra, which has the same weight space decomposition. (author). 5 refs, 3 tabs
Quartic trace identity for exceptional Lie algebras
International Nuclear Information System (INIS)
Okubo, S.
1979-01-01
Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation ]lambda] of the Lie algebra. Then, for all exceptional Lie algebras as well as A 1 and A 2 , we can prove the validity of a quartic trace identity Tr(X 4 ) =K (lambda)[Tr(X 2 )] 2 , where the constant K (lambda) depends only upon the irreducible representation ]lambda], and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed
International Nuclear Information System (INIS)
Bros, J.
1984-01-01
An account is given of the present status of many-particle structure analysis in the general framework of massive quantum field theory. Two main questions are discussed, namely: i) the equivalence between the asymptotic completeness of a field and the r-particle irreducibility of associated Bether-Salpeter type kernels; ii) the derivation of extended analyticity properties of the Green functions and multiparticle collision amplitudes around the corresponding physical regions. Substantial results concerning the 3→3 particle processes are described. An analogous multiparticle version of these results yields a partial understanding of the general case
International Nuclear Information System (INIS)
Anderson, Gregory W.; Blazek, Tomas
2005-01-01
E 6 is an attractive group for unification model building. However, the complexity of a rank 6 group makes it nontrivial to write down the structure of higher dimensional operators in an E 6 theory in terms of the states labeled by quantum numbers of the standard model gauge group. In this paper, we show the results of our computation of the Clebsch-Gordan coefficients for the products of the 27 with irreducible representations of higher dimensionality: 78, 351, 351 ' , 351, and 351 ' . Application of these results to E 6 model building involving higher dimensional operators is straightforward
International Nuclear Information System (INIS)
Horiai, Koui; Uehara, Hiromichi
2011-01-01
Graphical abstract: Available rotational and vibrational-rotational spectral lines of DF and HF are analyzed simultaneously using a non-Born-Oppenheimer effective Hamiltonian. Research highlights: → Simultaneous analysis of DF and HF spectral data. → Application of a non-Born-Oppenheimer effective Hamiltonian. → Twenty irreducible molecular constants for HF have been determined. - Abstract: Analytic expressions of corrections for the breakdown of the Born-Oppenheimer approximation to Dunham's Y ij with optimal parameters, i.e., determinable clusters of expansion coefficients, are applied to a data analysis of the rotational and vibrational-rotational transitions of HF reported in the literature. All the available spectral lines of the two isotopologues, DF and HF, are simultaneously fitted to a single set of molecular parameters of HF within experimental errors. Fitting of a data set of 595 spectral transitions for DF and HF has generated only 20 minimal independent parameter values, i.e., 'irreducible' molecular constants of HF, that are sufficient to precisely generate 82 Y ij coefficients and 144 band constants in total: 41 Y ij and 72 band constants each for DF and HF.
String-localized quantum fields and modular localization
Energy Technology Data Exchange (ETDEWEB)
Mund, J. [Juiz de Fora Univ., MG (Brazil). Dept. de Fisica; Schroer, B. [FU-Berlin, Berlin (Germany). Inst. fuer Theoretische Physik; Yngvason, J. [Erwin Schroedinger Institute for Mathematical Physics, Vienna (Austria)
2005-12-15
We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincare group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting. (author)
String-localized quantum fields and modular localization
International Nuclear Information System (INIS)
Mund, J.
2005-12-01
We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincare group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting. (author)
First results on the representation theory of the Ultrahyperbolic BMS group UHB(2, 2)
International Nuclear Information System (INIS)
Melas, Evangelos
2016-01-01
The Bondi–Metzner–Sachs (BMS) group B is the common asymptotic group of all asymptotically flat (lorentzian) space–times, and is the best candidate for the universal symmetry group of General Relativity (G.R.). B admits generalizations to real space–times of any signature, to complex space–times, and supersymmetric generalizations for any space— time dimension. With this motivation McCarthy constructed the strongly continuous unitary irreducible representations (IRs) of B some time ago, and he identified B(2,2) as the generalization of B appropriate to the to the ultrahyperbolic signature (+,+,−,−) and asymptotic flatness in null directions. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). We report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner–Mackeys inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. (paper)
Pryadko, Leonid P.; Dumer, Ilya; Kovalev, Alexey A.
2015-03-01
We construct a lower (existence) bound for the threshold of scalable quantum computation which is applicable to all stabilizer codes, including degenerate quantum codes with sublinear distance scaling. The threshold is based on enumerating irreducible operators in the normalizer of the code, i.e., those that cannot be decomposed into a product of two such operators with non-overlapping support. For quantum LDPC codes with logarithmic or power-law distances, we get threshold values which are parametrically better than the existing analytical bound based on percolation. The new bound also gives a finite threshold when applied to other families of degenerate quantum codes, e.g., the concatenated codes. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.
Representations of the ultrahyperbolic BMS group UHB(2, 2). I. General Results
International Nuclear Information System (INIS)
Melas, Evangelos
2015-01-01
The ordinary Bondi—Metzner—Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian space—times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). However, in studying quantum gravity, space—times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. In particular, the generalisation B(2, 2) appropriate to the ultrahyperbolic signature (+,+, —,—) has been described in detail, and the study of its irreducible unitary representations (IRs) of B(2, 2) has been initiated. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). In this paper we report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner—Mackey's inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. (paper)
International Nuclear Information System (INIS)
Guenaydin, M.; Saclioglu, C.
1981-06-01
We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups Sp(2n,IR) and SO(2n) from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n >= 4 and stops at n = 8 leading to the Lie algebras of SU(4) x SU(1,1), SU(5,1), SO(12) and Esub(7(7)). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for Esub(7(7)) and SO(12) obtained from the extended construction). We illustrate our construction with the examples of SU(5,1) and SO(12). (orig.)
Nucleus with filled shells as an example of exactly solved genealogical problem
International Nuclear Information System (INIS)
Kurovskij, V.V.; Chuvil'skij, Yu.M.
1984-01-01
The explicit form of Clebsch-Jordan coefficients of scalar representation n expansion into the products of irreducible representations for a wide class of groups in the random reduction chain was obtained
International Nuclear Information System (INIS)
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2005-01-01
We reexpress the quantum Calogero-Sutherland model for the Lie algebra E 7 and the particular value of the coupling constant κ=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra
Coadjoint orbits and conformal field theory
International Nuclear Information System (INIS)
Taylor, W. IV.
1993-08-01
This thesis is primarily a study of certain aspects of the geometric and algebraic structure of coadjoint orbit representations of infinite-dimensional Lie groups. The goal of this work is to use coadjoint orbit representations to construct conformal field theories, in a fashion analogous to the free-field constructions of conformal field theories. The new results which are presented in this thesis are as follows: First, an explicit set of formulae are derived giving an algebraic realization of coadjoint orbit representations in terms of differential operators acting on a polynomial Fock space. These representations are equivalent to dual Verma module representations. Next, intertwiners are explicitly constructed which allow the construction of resolutions for irreducible representations using these Fock space realizations. Finally, vertex operators between these irreducible representations are explicitly constructed as chain maps between the resolutions; these vertex operators allow the construction of rational conformal field theories according to an algebraic prescription
Recent developments in the N-extended supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Toppan, Francesco
2007-01-01
In this paper we review some recent developments in the understanding of the supersymmetric quantum mechanics for large-N values of the extended supersymmetries. A list of the topics here covered includes the new available classification of the finite linear irreducible representations, the construction of manifestly off-shell invariant actions without introducing a superfield formalism, the notion of the 'fusion algebra' of the irreducible representations, the connection (for N = 8) with the octonionic structure constants, etc. The results presented are based on the work of the author and his collaborators. (author)
Proceedings of the 29. Annual ESNA/UIR Meeting: Soil-Plant Relationships
International Nuclear Information System (INIS)
Gerzabek, M.H.
1999-10-01
The annual meeting were presented in 42 papers by scientists originating from 15 countries. The first part of the sessions dealt with recent developments in terrestrial radioecology, addressing both agricultural and semi-natural environments (12 oral presentations, 2 posters). Mitchell (U.K.) reported on the present status of the flux database of UIR, which, due to its 17000 entries provides an excellent basis for applying or testing new model approaches. One paper was presented on the upward movement of mobile (Na, CI) and less mobile (Cs) radionuclides in soil columns (Wadey/UK). Skarlou/Greece and Goncharova/Byelorussia highlighted important impact factors on soil-plant transfer of Cs and Sr as soil pH and ageing of contaminants/hot particles. Two presentations (Kirchner/Germany, Konopleva/Russia) focused on successful soil scientific approaches to describe plant uptake of Cs and Sr taking into account ion competition in soil. Klemt/Germany presented an interesting model to estimate Cs-transfer to roe leer and highlighted the importance of mushroom in this respect. The important role of fungi for Cs-dynamics in forest soil was confirmed by the data of Nikolova/Bulgaria. Spiridonov/Russia presented a radioecological model describing Cs-dynamics in forest ecosystems. The forestland/fortree model is parameterized for both deciduous and coniferous forests. A set of three papers (Tkachenko/Ukraine, Goncharova/Byelorussia, Oncsik/Hungary) focused on countermeasures. lt became quite evident that the effect of applications of macro- and micronutrients, clay minerals and zeolithes on radionuclide soil-plant transfer is highly site specific and needs consideration of soil properties. Two papers described the long-term impact of radionuclide contamination on the collective dose of the population (Kravets/Ukraine, Goncharova/Byelorussia). The contribution in the field of soil and plant sciences covered a broad range of topics. Influencing soil physical properties by
Irreducible Tests for Space Mission Sequencing Software
Ferguson, Lisa
2012-01-01
As missions extend further into space, the modeling and simulation of their every action and instruction becomes critical. The greater the distance between Earth and the spacecraft, the smaller the window for communication becomes. Therefore, through modeling and simulating the planned operations, the most efficient sequence of commands can be sent to the spacecraft. The Space Mission Sequencing Software is being developed as the next generation of sequencing software to ensure the most efficient communication to interplanetary and deep space mission spacecraft. Aside from efficiency, the software also checks to make sure that communication during a specified time is even possible, meaning that there is not a planet or moon preventing reception of a signal from Earth or that two opposing commands are being given simultaneously. In this way, the software not only models the proposed instructions to the spacecraft, but also validates the commands as well.To ensure that all spacecraft communications are sequenced properly, a timeline is used to structure the data. The created timelines are immutable and once data is as-signed to a timeline, it shall never be deleted nor renamed. This is to prevent the need for storing and filing the timelines for use by other programs. Several types of timelines can be created to accommodate different types of communications (activities, measurements, commands, states, events). Each of these timeline types requires specific parameters and all have options for additional parameters if needed. With so many combinations of parameters available, the robustness and stability of the software is a necessity. Therefore a baseline must be established to ensure the full functionality of the software and it is here where the irreducible tests come into use.
To an effective local Langlands correspondence
Bushnell, Colin J
2014-01-01
Let F be a non-Archimedean local field. Let \\mathcal{W}_{F} be the Weil group of F and \\mathcal{P}_{F} the wild inertia subgroup of \\mathcal{W}_{F}. Let \\widehat {\\mathcal{W}}_{F} be the set of equivalence classes of irreducible smooth representations of \\mathcal{W}_{F}. Let \\mathcal{A}^{0}_{n}(F) denote the set of equivalence classes of irreducible cuspidal representations of \\mathrm{GL}_{n}(F) and set \\widehat {\\mathrm{GL}}_{F} = \\bigcup _{n\\ge 1} \\mathcal{A}^{0}_{n}(F). If \\sigma \\in \\widehat {\\mathcal{W}}_{F}, let ^{L}{\\sigma }\\in \\widehat {\\mathrm{GL}}_{F} be the cuspidal representation matched with \\sigma by the Langlands Correspondence. If \\sigma is totally wildly ramified, in that its restriction to \\mathcal{P}_{F} is irreducible, the authors treat ^{L}{\\sigma} as known. From that starting point, the authors construct an explicit bijection \\mathbb{N}:\\widehat {\\mathcal{W}}_{F} \\to \\widehat {\\mathrm{GL}}_{F}, sending \\sigma to ^{N}{\\sigma}. The authors compare this "naïve correspondence" with the L...
Kleshchev, Alexander
2017-01-01
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
Spin foam models of matter coupled to gravity
International Nuclear Information System (INIS)
Mikovic, A
2002-01-01
We construct a class of spin foam models describing matter coupled to gravity, such that the gravitational sector is described by the unitary irreducible representations of the appropriate symmetry group, while the matter sector is described by the finite-dimensional irreducible representations of that group. The corresponding spin foam amplitudes in the four-dimensional gravity case are expressed in terms of the spin network amplitudes for pentagrams with additional external and internal matter edges. We also give a quantum field theory formulation of the model, where the matter degrees of freedom are described by spin network fields carrying the indices from the appropriate group representation. In the non-topological Lorentzian gravity case, we argue that the matter representations should be appropriate SO(3) or SO(2) representations contained in a given Lorentz matter representation, depending on whether one wants to describe a massive or a massless matter field. The corresponding spin network amplitudes are given as multiple integrals of propagators which are matrix spherical functions
Radial head button holing: a cause of irreducible anterior radial head dislocation
Energy Technology Data Exchange (ETDEWEB)
Shin, Su-Mi; Chai, Jee Won; You, Ja Yeon; Park, Jina [Seoul National University Seoul Metropolitan Government Boramae Medical Center, Department of Radiology, Seoul (Korea, Republic of); Bae, Kee Jeong [Seoul National University Seoul Metropolitan Government Boramae Medical Center, Department of Orthopedic Surgery, Seoul (Korea, Republic of)
2016-10-15
''Buttonholing'' of the radial head through the anterior joint capsule is a known cause of irreducible anterior radial head dislocation associated with Monteggia injuries in pediatric patients. To the best of our knowledge, no report has described an injury consisting of buttonholing of the radial head through the annular ligament and a simultaneous radial head fracture in an adolescent. In the present case, the radiographic findings were a radial head fracture with anterior dislocation and lack of the anterior fat pad sign. Magnetic resonance imaging (MRI) clearly demonstrated anterior dislocation of the fractured radial head through the torn annular ligament. The anterior joint capsule and proximal portion of the annular ligament were interposed between the radial head and capitellum, preventing closed reduction of the radial head. Familiarity with this condition and imaging findings will aid clinicians to make a proper diagnosis and fast decision to perform an open reduction. (orig.)
On the Representation Theory of the Ultrahyperbolic BMS group UHB(2, 2). I. General Results
International Nuclear Information System (INIS)
Melas, Evangelos
2015-01-01
The Bondi-Metzner-Sachs (BMS) group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of General Relativity (G.R.). B admits generalizations to real space-times of any signature, to complex space-times, and supersymmetric generalizations for any space- time dimension. With this motivation McCarthy constructed the strongly continuous unitary irreducible representations (IRs) of B some time ago, and he identified B(2,2) as the generalization of B appropriate to the to the 'ultrahyperbolic signature' (+,+,−,−) and asymptotic flatness in null directions. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). In this short paper we report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner-Mackey's inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. At the end of the paper we comment on the significance of these results
Undecidability and Irreducibility Conditions for Open-Ended Evolution and Emergence.
Hernández-Orozco, Santiago; Hernández-Quiroz, Francisco; Zenil, Hector
2018-01-01
Is undecidability a requirement for open-ended evolution (OEE)? Using methods derived from algorithmic complexity theory, we propose robust computational definitions of open-ended evolution and the adaptability of computable dynamical systems. Within this framework, we show that decidability imposes absolute limits on the stable growth of complexity in computable dynamical systems. Conversely, systems that exhibit (strong) open-ended evolution must be undecidable, establishing undecidability as a requirement for such systems. Complexity is assessed in terms of three measures: sophistication, coarse sophistication, and busy beaver logical depth. These three complexity measures assign low complexity values to random (incompressible) objects. As time grows, the stated complexity measures allow for the existence of complex states during the evolution of a computable dynamical system. We show, however, that finding these states involves undecidable computations. We conjecture that for similar complexity measures that assign low complexity values, decidability imposes comparable limits on the stable growth of complexity, and that such behavior is necessary for nontrivial evolutionary systems. We show that the undecidability of adapted states imposes novel and unpredictable behavior on the individuals or populations being modeled. Such behavior is irreducible. Finally, we offer an example of a system, first proposed by Chaitin, that exhibits strong OEE.
Wu, Bofeng; Huang, Chao-Guang
2018-04-01
The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.
Irreducible Traumatic Posterior Shoulder Dislocation
Directory of Open Access Journals (Sweden)
Blake Collier
2017-01-01
coracoid, marked limitation of abduction, and complete absence of external rotation with a fixed internal rotation deformity.2 Lesions commonly associated with traumatic posterior subluxation/dislocation are the reverse Hill-Sachs,3 a posterior labral detachment, glenohumeral ligament lesions,4 rotator cuff tears or posterior bony fractures.1 In order to make an accurate diagnosis it is important to obtain adequate x-ray imaging, including a “Y” view.2 Anteroposterior x-rays may show widening of the glenohumeral joint resembling a “light bulb” shape of the humeral head. However, definitive diagnosis is made by the “Y” view which shows the humeral head displaced posteriorly and no longer covering the glenoid fossa6. Irreducible acute posterior dislocation of the shoulder is extremely rare5 and only one other case has been reported in the literature.7
Irreducible Greens' Functions method in the theory of highly correlated systems
International Nuclear Information System (INIS)
Kuzemsky, A.L.
1994-09-01
The self-consistent theory of the correlation effects in Highly Correlated Systems (HCS) is presented. The novel Irreducible Green's Function (IGF) method is discussed in detail for the Hubbard model and random Hubbard model. The interpolation solution for the quasiparticle spectrum, which is valid for both the atomic and band limit is obtained. The (IGF) method permits to calculate the quasiparticle spectra of many-particle systems with the complicated spectra and strong interaction in a very natural and compact way. The essence of the method deeply related to the notion of the Generalized Mean Fields (GMF), which determine the elastic scattering corrections. The inelastic scattering corrections leads to the damping of the quasiparticles and are the main topic of the present consideration. The calculation of the damping has been done in a self-consistent way for both limits. For the random Hubbard model the weak coupling case has been considered and the self-energy operator has been calculated using the combination of the IGF method and Coherent Potential Approximation (CPA). The other applications of the method to the s-f model, Anderson model, Heisenberg antiferromagnet, electron-phonon interaction models and quasiparticle tunneling are discussed briefly. (author). 79 refs
Algebraic special functions and SO(3,2)
International Nuclear Information System (INIS)
Celeghini, E.; Olmo, M.A. del
2013-01-01
A ladder structure of operators is presented for the associated Legendre polynomials and the sphericas harmonics. In both cases these operators belong to the irreducible representation of the Lie algebra so(3,2) with quadratic Casimir equals to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be homomorphic to the space of linear operators acting on the L 2 functions defined on (−1,1)×Z and on the sphere S 2 , respectively. The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining in this way the “algebraic special functions” that are proposed to be the connection between Lie algebras and square-integrable functions so that the space of linear operators on the L 2 functions is homomorphic to the universal enveloping algebra. The passage to the group, by means of the exponential map, shows that the associated Legendre polynomials and the spherical harmonics support the corresponding unitary irreducible representation of the group SO(3,2). -- Highlights: •The algebraic ladder structure is constructed for the associated Legendre polynomials (ALP). •ALP and spherical harmonics support a unitary irreducible SO(3,2)-representation. •A ladder structure is the condition to get a Lie group representation defining “algebraic special functions”. •The “algebraic special functions” connect Lie algebras and L 2 functions
International Nuclear Information System (INIS)
Quesne, C.
1986-01-01
In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 1 +n/2> encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary-operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of lambda 1 ,...,lambda/sub d/, subject to the conditions lambda 1 > or =lambda 2 > or = x x x > or =lambda/sub d/> or =0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisfied by the coherent states in the representation space of the irreducible representation is obtained. The Hilbert space of analytic functions arising from the coherent state representation is studied in detail. Finally, some applications of the formalism developed in the present paper are outlined
Irreducibility and Computational Equivalence 10 Years After Wolfram's A New Kind of Science
2013-01-01
It is clear that computation is playing an increasingly prominent role in the development of mathematics, as well as in the natural and social sciences. The work of Stephen Wolfram over the last several decades has been a salient part in this phenomenon helping founding the field of Complex Systems, with many of his constructs and ideas incorporated in his book A New Kind of Science (ANKS) becoming part of the scientific discourse and general academic knowledge--from the now established Elementary Cellular Automata to the unconventional concept of mining the Computational Universe, from today's widespread Wolfram's Behavioural Classification to his principles of Irreducibility and Computational Equivalence. This volume, with a Foreword by Gregory Chaitin and an Afterword by Cris Calude, covers these and other topics related to or motivated by Wolfram's seminal ideas, reporting on research undertaken in the decade following the publication of Wolfram's NKS book. Featuring 39 authors, its 23 contributions are o...
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
International Nuclear Information System (INIS)
Weis, Stephan
2015-01-01
We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero
Hayman, Jonathan; Phillips, Ryan; Chen, Di; Perin, Jamie; Narang, Amol K; Trieu, Janson; Radwan, Noura; Greco, Stephen; Deville, Curtiland; McNutt, Todd; Song, Daniel Y; DeWeese, Theodore L; Tran, Phuoc T
2018-06-01
Undetectable End of Radiation PSA (EOR-PSA) has been shown to predict improved survival in prostate cancer (PCa). While validating the unfavorable intermediate-risk (UIR) and favorable intermediate-risk (FIR) stratifications among Johns Hopkins PCa patients treated with radiotherapy, we examined whether EOR-PSA could further risk stratify UIR men for survival. A total of 302 IR patients were identified in the Johns Hopkins PCa database (178 UIR, 124 FIR). Kaplan-Meier curves and multivariable analysis was performed via Cox regression for biochemical recurrence free survival (bRFS), distant metastasis free survival (DMFS), and overall survival (OS), while a competing risks model was used for PCa specific survival (PCSS). Among the 235 patients with known EOR-PSA values, we then stratified by EOR-PSA and performed the aforementioned analysis. The median follow-up time was 11.5 years (138 months). UIR was predictive of worse DMFS and PCSS (P = 0.008 and P = 0.023) on multivariable analysis (MVA). Increased radiation dose was significant for improved DMFS (P = 0.016) on MVA. EOR-PSA was excluded from the models because it did not trend towards significance as a continuous or binary variable due to interaction with UIR, and we were unable to converge a multivariable model with a variable to control for this interaction. However, when stratifying by detectable versus undetectable EOR-PSA, UIR had worse DMFS and PCSS among detectable EOR-PSA patients, but not undetectable patients. UIR was significant on MVA among detectable EOR-PSA patients for DMFS (P = 0.021) and PCSS (P = 0.033), while RT dose also predicted PCSS (P = 0.013). EOR-PSA can assist in predicting DMFS and PCSS among UIR patients, suggesting a clinically meaningful time point for considering intensification of treatment in clinical trials of intermediate-risk men. © 2018 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Wang Fan; Chen Zhida
2006-01-01
A new strategy to search for the good quantum numbers for the corner-sharing spin systems, as archetypal plaquettes of the lattices, was suggested for the first time in order to study on geometric spin frustration. The calculations on energy spectra by using the irreducible tensor operator method with the new strategy can be much reduced. As representative examples the energy spectra for the spin pentamer of the tetrahedron with a centered spin site and the spin heptamer of three corner-sharing equilateral-triangle were examined in order to confirm efficiency of the new strategy. Through our code, with automatically searching for the good quantum numbers, the projection operators S iz , S ix and S iy matrices in the ground state space for the spin heptamer were reliably constructed
Coherent states for quantum compact groups
Jurco, B
1996-01-01
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the q--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}
AdS/CFT correspondence and supersymmetry
International Nuclear Information System (INIS)
Dobrev, V.K.
2002-05-01
We use the group-theoretic interpretation of the AdS/CFT correspondence which we proposed earlier in order to lift intertwining operators acting between boundary conformal representations to intertwining operators acting between bulk conformal representations. Further, we present the classification of the positive energy (lowest weight) unitary irreducible representations of the D=6 superconformal algebras osp(8*/2N). (author)
International Nuclear Information System (INIS)
Partensky, A.; Maguin, C.
1976-11-01
The main results of a work concerning the calculation of the matrices of the generators of SU(4) in a given (p,p',p'') irreducible representation, in which the states are labelled by the spin quantum numbers, S, MS, are given. Then the SU(4) algebra is defined, the labelling problem of the states is discussed and the Racah formula transformed, which facilitates the calculation. The semi-reduced matrix elements of the Q, Vsup(Q) and Wsup(Q) vectors are defined. Finally an explicit formulation of the matrix elements of Q is given, in the particular case T=p for any S, or S=p for any T; the example of the (3 2 0) irreducible representation is treated
Poincare group and relativistic wave equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)
1997-09-07
Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)
Kraiem, Hazar; Manon, Yannick; Anne-Archard, Dominique; Fillaudeau, Luc
2012-01-01
During cell cultures in bioreactor, micro-organism physiology closely interacts with physico-chemical parameters (gas and feed flow rates, mixing, temperature, pH, pressure). The specificity of microbial bioreactions in relation with irreducible couplings between heat and mass transfers and fluid mechanics, led into complex (three phases medium) and dynamic (auto-biocatalytic reaction) systems. Our scientific approach aims to investigate, understand and control dynamic interactions between ph...
Mascia, Corrado
2016-01-01
This paper examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds vi with transition rates μij. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the differences vi -vj generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters vi and μij, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities vi. The diffusion matrix has a more complicate representation, based on the graph with vertices the velocities vi and arcs weighted by the transition rates μij. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree Theorem from graph theory.
Peng, L.; Pan, H.; Ma, H.; Zhao, P.; Qin, R.; Deng, C.
2017-12-01
The irreducible water saturation (Swir) is a vital parameter for permeability prediction and original oil and gas estimation. However, the complex pore structure of the rocks makes the parameter difficult to be calculated from both laboratory and conventional well logging methods. In this study, an effective statistical method to predict Swir is derived directly from nuclear magnetic resonance (NMR) data based on fractal theory. The spectrum of transversal relaxation time (T2) is normally considered as an indicator of pore size distribution, and the micro- and meso-pore's fractal dimension in two specific range of T2 spectrum distribution are calculated. Based on the analysis of the fractal characteristics of 22 core samples, which were drilled from four boreholes of tight lithologic oil reservoirs of Ordos Basin in China, the positive correlation between Swir and porosity is derived. Afterwards a predicting model for Swir based on linear regressions of fractal dimensions is proposed. It reveals that the Swir is controlled by the pore size and the roughness of the pore. The reliability of this model is tested and an ideal consistency between predicted results and experimental data is found. This model is a reliable supplementary to predict the irreducible water saturation in the case that T2 cutoff value cannot be accurately determined.
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Coherent states for quantum compact groups
International Nuclear Information System (INIS)
Jurco, B.; Stovicek, P.; CTU, Prague
1996-01-01
Coherent states are introduced and their properties are discussed for simple quantum compact groups A l , B l , C l and D l . The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)
Indian Academy of Sciences (India)
fashion several Interesting courses out of this book at the. M.Sc. level. products via the use of induced representations, and this is immediately deployed to achieve Wigner's classification of the irreducible unitary representations of the universal cover of the Poincare group. In the physically relevant cases, these tum out to be.
Ionization of Polycyclic Aromatic Hydrocarbon Molecules around the Herbig Ae/be ENVIRONMENT*
Sakon, Itsuki; Onaka, Takashi; Okamoto, Yoshiko K.; Kataza, Hirokazu; Kaneda, Hidehiro; Honda, Mitsuhiko
We present the results of mid-infrared N-band spectroscopy of the Herbig Ae/Be system MWC1080 using the Cooled Mid-Infrared Camera and Spectrometer (COMICS) on board the 8 m Subaru Telescope. The MWC1080 has a geometry such that the diffuse nebulous structures surround the central Herbig B0 type star. We focus on the properties of polycyclic aromatic hydrocarbons (PAHs) and PAH-like species, which are thought to be the carriers of the unidentified infrared (UIR) bands in such environments. A series of UIR bands at 8.6, 11.0, 11.2, and 12.7 μm is detected throughout the system and we find a clear increase in the UIR 11.0 μm/11.2 μm ratio in the vicinity of the central star. Since the UIR 11.0 μm feature is attributed to a solo-CH out-of-plane wagging mode of cationic PAHs while the UIR 11.2 μm feature to a solo-CH out-of-plane bending mode of neutral PAHs, the large 11.0 μm/11.2 μm ratio directly indicates a promotion of the ionization of PAHs near the central star.
Quantization and Superselection Sectors I:. Transformation Group C*-ALGEBRAS
Landsman, N. P.
Quantization is defined as the act of assigning an appropriate C*-algebra { A} to a given configuration space Q, along with a prescription mapping self-adjoint elements of { A} into physically interpretable observables. This procedure is adopted to solve the problem of quantizing a particle moving on a homogeneous locally compact configuration space Q=G/H. Here { A} is chosen to be the transformation group C*-algebra corresponding to the canonical action of G on Q. The structure of these algebras and their representations are examined in some detail. Inequivalent quantizations are identified with inequivalent irreducible representations of the C*-algebra corresponding to the system, hence with its superselection sectors. Introducing the concept of a pre-Hamiltonian, we construct a large class of G-invariant time-evolutions on these algebras, and find the Hamiltonians implementing these time-evolutions in each irreducible representation of { A}. “Topological” terms in the Hamiltonian (or the corresponding action) turn out to be representation-dependent, and are automatically induced by the quantization procedure. Known “topological” charge quantization or periodicity conditions are then identically satisfied as a consequence of the representation theory of { A}.
Directory of Open Access Journals (Sweden)
Michael Brown
2015-11-01
Full Text Available Approximations based on two-particle irreducible (2PI effective actions (also known as Φ-derivable, Cornwall–Jackiw–Tomboulis or Luttinger–Ward functionals depending on context have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Padé approximation and are competitive with Borel–Padé resummation. Finally, we introduce a hybrid 2PI–Padé method.
Neural Mechanisms of Updating under Reducible and Irreducible Uncertainty.
Kobayashi, Kenji; Hsu, Ming
2017-07-19
Adaptive decision making depends on an agent's ability to use environmental signals to reduce uncertainty. However, because of multiple types of uncertainty, agents must take into account not only the extent to which signals violate prior expectations but also whether uncertainty can be reduced in the first place. Here we studied how human brains of both sexes respond to signals under conditions of reducible and irreducible uncertainty. We show behaviorally that subjects' value updating was sensitive to the reducibility of uncertainty, and could be quantitatively characterized by a Bayesian model where agents ignore expectancy violations that do not update beliefs or values. Using fMRI, we found that neural processes underlying belief and value updating were separable from responses to expectancy violation, and that reducibility of uncertainty in value modulated connections from belief-updating regions to value-updating regions. Together, these results provide insights into how agents use knowledge about uncertainty to make better decisions while ignoring mere expectancy violation. SIGNIFICANCE STATEMENT To make good decisions, a person must observe the environment carefully, and use these observations to reduce uncertainty about consequences of actions. Importantly, uncertainty should not be reduced purely based on how surprising the observations are, particularly because in some cases uncertainty is not reducible. Here we show that the human brain indeed reduces uncertainty adaptively by taking into account the nature of uncertainty and ignoring mere surprise. Behaviorally, we show that human subjects reduce uncertainty in a quasioptimal Bayesian manner. Using fMRI, we characterize brain regions that may be involved in uncertainty reduction, as well as the network they constitute, and dissociate them from brain regions that respond to mere surprise. Copyright © 2017 the authors 0270-6474/17/376972-11$15.00/0.
International Nuclear Information System (INIS)
Raković, Milun J
2011-01-01
The standard quantum mechanical description of the motion of a charged particle in the field of a stationary magnetic monopole is notorious for the presence of unnatural singularities in the Hamiltonian operator originating in the vector potential A(r) used to describe the magnetic field of the monopole. In this paper, an elementary quantum mechanical formulation of the problem which involves only the physically observable field B(r) is presented. This is achieved by treating as a fundamental observable of the charged particle its kinetic momentum instead of the linear momentum p. An irreducible representation of the fundamental commutation relations involving the operators r-hat. It is shown that the existence of an irreducible representation requires that Dirac’s charge quantization condition is satisfied. Also, it is demonstrated that, from the quantum mechanical perspective, the singularities (appearing when the vector potential is introduced) are in fact properties of coordinate representations of the fundamental commutation relations. (paper)
Coherent states for quantum compact groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Stovicek, P. [Ceske Vysoke Uceni Technicke, Prague (Czech Republic). Dept. of Mathematics]|[CTU, Prague (Czech Republic). Doppler Inst.
1996-12-01
Coherent states are introduced and their properties are discussed for simple quantum compact groups A{sub l}, B{sub l}, C{sub l} and D{sub l}. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)
Brillouin-zone database on the Bilbao Crystallographic Server.
Aroyo, Mois I; Orobengoa, Danel; de la Flor, Gemma; Tasci, Emre S; Perez-Mato, J Manuel; Wondratschek, Hans
2014-03-01
The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.
Strong coupling and quasispinor representations of the SU(3) rotor model
International Nuclear Information System (INIS)
Rowe, D.J.; De Guise, H.
1992-01-01
We define a coupling scheme, in close parallel to the coupling scheme of Elliott and Wilsdon, in which nucleonic intrinsic spins are strongly coupled to SU(3) spatial wave functions. The scheme is proposed for shell-model calculations in strongly deformed nuclei and for semimicroscopic analyses of rotations in odd-mass nuclei and other nuclei for which the spin-orbit interaction is believed to play an important role. The coupling scheme extends the domain of utility of the SU(3) model, and the symplectic model, to heavy nuclei and odd-mass nuclei. It is based on the observation that the low angular-momentum states of an SU(3) irrep have properties that mimic those of a corresponding irrep of the rotor algebra. Thus, we show that strongly coupled spin-SU(3) bands behave like strongly coupled rotor bands with properties that approach those of irreducible representations of the rigid-rotor algebra in the limit of large SU(3) quantum numbers. Moreover, we determine that the low angular-momentum states of a strongly coupled band of states of half-odd integer angular momentum behave to a high degree of accuracy as if they belonged to an SU(3) irrep. These are the quasispinor SU(3) irreps referred to in the title. (orig.)
Spinor Structure and Internal Symmetries
Varlamov, V. V.
2015-10-01
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.
A conjecture for the effective condition of Jimbo's method
International Nuclear Information System (INIS)
Ma Zhongqi
1992-01-01
The method for constructing the spectrum-dependent solutions to the Yang-Baxter equation, according to Jimbo's theorem, is based on the existence of the representation matrix of e 0 , corresponding to the lowest negative root, in an irreducible representation of a quantum enveloping algebra. In this paper a conjecture for the existent condition of the representation matrix of e 0 is made. As an example, the adjoint representation of U q C 2 is discussed where the representation matrix e 0 does not exist because the existent condition is violated
Nazarov, Anton
2012-11-01
In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent
Clifford theory for group representations
Karpilovsky, G
1989-01-01
Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpos
International Nuclear Information System (INIS)
Berezin, F.A.
1977-01-01
The Laplace-Cazimir operators on the Lie supergroups are defined, and their radial parts are calculated under some general assumptions on supergroup. Under the same assumptions the characters of nondegenerate irreducible finite-dimensional representations are found
Comparing Amazon Mechanical Turk with unpaid internet resources in online clinical trials
Directory of Open Access Journals (Sweden)
Eduardo Bunge
2018-06-01
Full Text Available Internet interventions face significant challenges in recruitment and attrition rates are typically high and problematic. Finding innovative yet scientifically valid avenues for attaining and retaining participants is therefore of considerable importance. The main goal of this study was to compare recruitment process and participants characteristics between two similar randomized control trials of mood management interventions. One of the trials (Bunge et al., 2016 was conducted with participants recruited from Amazon's Mechanical Turk (AMT, and the other trial recruited via Unpaid Internet Resources (UIR. Methods: The AMT sample (Bunge et al., 2016 consisted of 765 adults, and the UIR sample (recruited specifically for this study consisted of 329 adult US residents. Participants' levels of depression, anxiety, confidence, motivation, and perceived usefulness of the intervention were assessed. The AMT sample was financially compensated whereas the UIR was not. Results: AMT yielded higher recruitment rates per month (p < .05. At baseline, the AMT sample reported significantly lower depression and anxiety scores (p < .001 and p < .005, respectively and significantly higher mood, motivation, and confidence (all p < .001 compared to the UIR sample. AMT participants spent significantly less time on the site (p < .05 and were more likely to complete follow-ups than the UIR sample (p < .05. Both samples reported a significant increase in their level of confidence and motivation from pre- to post-intervention. AMT participants showed a significant increase in perceived usefulness of the intervention (p < .0001, whereas the UIR sample did not (p = .1642. Conclusions: By using AMT, researchers can recruit very rapidly and obtain higher retention rates; however, these participants may not be representative of the general online population interested in clinical interventions. Considering that AMT and UIR participants
Ober, Ciprian-Andrei; Peștean, Cosmin Petru; Bel, Lucia Victoria; Taulescu, Marian; Cătoi, Cornel; Bogdan, Sidonia; Milgram, Joshua; Schwarz, Guenter; Oana, Liviu Ioan
2016-09-22
True vaginal prolapse is a rare condition in dogs and it is occasionally observed in animals with constipation, dystocia, or forced separation during breeding. If a true prolapse occurs, the bladder, the uterine body and/or distal part of the colon, may be present in the prolapse. A 2-year-old intact non pregnant Central Asian Shepherd dog in moderate condition, was presented for a true vaginal and rectal prolapse. The prolapses were confirmed by physical examination and ultrasonography. Herniation of the urinary bladder was identified within the vaginal prolapse. The necrotic vaginal wall was resected, the urinary bladder was reduced surgically and fixed to the right abdominal wall to prevent recurrence. Rectal resection and anastomosis was necessary to correct the rectal prolapse. Recurrence of the prolapses was not observed and the dog recovered completely after the surgical treatment. In our opinion, extreme tenesmus arising from constipation may have predisposed to the vaginal prolapse with bladder incarceration and secondarily to rectal prolapse. In the young female dog, true vaginal prolapse with secondary involvement of the urinary bladder and irreducible rectal prolapse is an exceptionally rare condition.
A Small Fullerene (C{sub 24}) may be the Carrier of the 11.2 μ m Unidentified Infrared Band
Energy Technology Data Exchange (ETDEWEB)
Bernstein, L. S.; Shroll, R. M. [Spectral Sciences, Inc., 4 Fourth Ave., Burlington, MA 01803 (United States); Lynch, D. K. [Thule Scientific, P.O. Box 953, Topanga, CA 90290 (United States); Clark, F. O., E-mail: larry@spectral.com, E-mail: rshroll@spectral.com, E-mail: dave@caltech.edu, E-mail: frank.clark@gmail.com [Wopeco Research, 125 South Great Road, Lincoln, MA 01773 (United States)
2017-02-20
We analyze the spectrum of the 11.2 μ m unidentified infrared band (UIR) from NGC 7027 and identify a small fullerene (C{sub 24}) as a plausible carrier. The blurring effects of lifetime and vibrational anharmonicity broadening obscure the narrower, intrinsic spectral profiles of the UIR band carriers. We use a spectral deconvolution algorithm to remove the blurring, in order to retrieve the intrinsic profile of the UIR band. The shape of the intrinsic profile—a sharp blue peak and an extended red tail—suggests that the UIR band originates from a molecular vibration–rotation band with a blue band head. The fractional area of the band-head feature indicates a spheroidal molecule, implying a nonpolar molecule and precluding rotational emission. Its rotational temperature should be well approximated by that measured for nonpolar molecular hydrogen, ∼825 K for NGC 7027. Using this temperature, and the inferred spherical symmetry, we perform a spectral fit to the intrinsic profile, which results in a rotational constant implying C{sub 24} as the carrier. We show that the spectroscopic parameters derived for NGC 7027 are consistent with the 11.2 μ m UIR bands observed for other objects. We present density functional theory (DFT) calculations for the frequencies and infrared intensities of C{sub 24}. The DFT results are used to predict a spectral energy distribution (SED) originating from absorption of a 5 eV photon, and characterized by an effective vibrational temperature of 930 K. The C{sub 24} SED is consistent with the entire UIR spectrum and is the dominant contributor to the 11.2 and 12.7 μ m bands.
Creation and annihilation operators for SU(3) in an SO(6,2) model
International Nuclear Information System (INIS)
Bracken, A.J.; MacGibbon, J.H.
1984-01-01
Creation and annihilation operators are defined which are Wigner operators (tensor shift operators) for SU(3). While the annihilation operators are simply boson operators, the creation operators are cubic polynomials in boson operators. Together they generate under commutation the Lie algebra of SO(6,2). A model for SU(3) is defined. The different SU(3) irreducible representations appear explicitly as manifestly covariant, irreducible tensors, whose orthogonality and normalisation properties are examined. Other Wigner operators for SU(3) can be constructed simply as products of the new creation and annihilation operators, or sums of such products. (author)
Energy Technology Data Exchange (ETDEWEB)
Ojeda-Guillén, D., E-mail: dogphysics@gmail.com [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738, México D.F. (Mexico); Mota, R.D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D.F. (Mexico); Granados, V.D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738, México D.F. (Mexico)
2014-08-14
We decouple the Dirac's radial equations in D+1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1,1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1,1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states. - Highlights: • We solve the most general Dirac–Kepler–Coulomb problem. • The eigenfunctions and energy spectrum are obtained in a purely algebraic way. • We construct the radial SU(1,1) coherent states for the Kepler–Coulomb problem.
International Nuclear Information System (INIS)
Ojeda-Guillén, D.; Mota, R.D.; Granados, V.D.
2014-01-01
We decouple the Dirac's radial equations in D+1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1,1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1,1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states. - Highlights: • We solve the most general Dirac–Kepler–Coulomb problem. • The eigenfunctions and energy spectrum are obtained in a purely algebraic way. • We construct the radial SU(1,1) coherent states for the Kepler–Coulomb problem
On basic projective characters of rotation subgroups of Weyl groups of types D6 and D1
International Nuclear Information System (INIS)
Chikunji, J.C.
1990-05-01
The projective representations of the rotation subgroup W + (Φ) have been determined from those of W(Φ) for each root system Φ. This is done by constructing non-trivial central extensions of W + (Φ) via the double coverings of the rotation groups SO(l). This adaptation gives a unified way of obtaining the basic projective representations of W + (Φ) from those of W(Φ). In particular, formulae giving irreducible characters of these representations are explicitly determined in each case. (author). 19 refs, 2 tabs
International Nuclear Information System (INIS)
Reshetnyak, A.
2013-01-01
We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST–BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, (arXiv:1110.5044 [hep-th])]. Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to osp(k|2k) superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spin-tensor field of spin (5/2,3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2,3/2)
Energy Technology Data Exchange (ETDEWEB)
Bellucci, S. [INFN, Laboratori Nazionali di Frascati, Frascati (Italy); Bezerra de Mello, E.R. [Universidade Federal da Parai ba, Departamento de Fisica, 58.059-970, Joao Pessoa, PB (Brazil); Braganca, E. [INFN, Laboratori Nazionali di Frascati, Frascati (Italy); Universidade Federal da Parai ba, Departamento de Fisica, 58.059-970, Joao Pessoa, PB (Brazil); Saharian, A.A. [Yerevan State University, Department of Physics, Yerevan (Armenia)
2016-06-15
We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even function of the chemical potential. The behavior of the expectation values in various asymptotic regions of the parameters are discussed in detail. In particular, we show that for points near the cone apex the vacuum parts dominate. For a massless field with zero chemical potential the fermion condensate and charge density vanish. Simple expressions are derived for the part in the total charge induced by the planar angle deficit and magnetic flux. Combining the results for separate irreducible representations, we also consider the fermion condensate, charge and current densities in parity and time-reversal symmetric models. Possible applications to graphitic nanocones are discussed. (orig.)
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
Vertex operator construction of superconformal ghosts and string field theory
International Nuclear Information System (INIS)
Ezawa, Z.F.; Nakamura, S.; Tezuka, A.
1987-01-01
Superconformal ghosts in string theories are characterized by the SU(1,1) Kac-Moody algebra with central charge -1/2. These ghost fields are constructed as the vertex operators realizing spinor representations of the Kac-Moody algebra. Representations of the canonical commutation relations of the superconformal ghosts are analyzed extensively. All irreducible representations are found to possess only the trivial inner product but for one exceptional case. Consequently, in superstring field theory it is necessary to consider reducible representations in general. Hilbert spaces with a non-trivial inner product are explicitly obtained upon which second quantization of superstring may be carried out. (orig.)
Mixed-symmetry fields in de Sitter space: a group theoretical glance
Energy Technology Data Exchange (ETDEWEB)
Basile, Thomas [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS,Fédération de Recherche 2964 Denis Poisson, Université François Rabelais,Parc de Grandmont, 37200 Tours (France); Groupe de Mécanique et Gravitation, Service de Physique Théorique et Mathématique,Université de Mons - UMONS,20 Place du Parc, 7000 Mons, Belgique (Belgium); Bekaert, Xavier [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS,Fédération de Recherche 2964 Denis Poisson, Université François Rabelais,Parc de Grandmont, 37200 Tours (France); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science,Daejeon (Korea, Republic of); Boulanger, Nicolas [Groupe de Mécanique et Gravitation, Service de Physique Théorique et Mathématique,Université de Mons - UMONS,20 Place du Parc, 7000 Mons, Belgique (Belgium)
2017-05-15
We derive the characters of all unitary irreducible representations of the (d+1)-dimensional de Sitter spacetime isometry algebra so(1,d+1), and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We identify the equivalent of the scalar singleton for the de Sitter (dS) spacetime.
The Developement of A Lattice Structured Database
DEFF Research Database (Denmark)
Bruun, Hans
In this project we have investigated the possibilities to make a system based on the concept algebra described in [3], [4] and [5]. The concept algebra is used for ontology specification and knowledge representation. It is a distributive lattice extended with attribution operations. One of the main...... ideas in this work is to use Birkhoff's representation theorem, so we represent distributive lattices using its dual representation: the partial order of join irreducibles. We show how to construct a concept algebra satisfying a given set of equations. The universal/initial algebra is usually too big...
Irreducible kernels and nonperturbative expansions in a theory with pure m -> m interaction
International Nuclear Information System (INIS)
Iagolnitzer, D.
1983-01-01
Recent results on the structure of the S matrix at the m-particle threshold (m>=2) in a simplified m->m scattering theory with no subchannel interaction are extended to the Green function F on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure of F around s=(mμ) 2 depending on the parity of (m-1) (ν-1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernel U [which is the analogue of the K matrix in the two different parity cases (m-1)(ν-1) odd or even] and related local expansion of F, for (m-1)(ν-1) even, in powers of sigmasup(β)lnsigma(sigma=(mμ) 2 -s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernel U. The links between kernel U and Bethe-Salpeter type kernels G of the theory are exhibited in both parity cases, as also the links between the above expansion of F and local expansions, in the Bethe-Salpeter type framework, of Fsub(lambda) in terms of Feynman-type integrals in which each vertex is a kernel G and which include both dominant and subdominant contributions. (orig.)
Solving Linear Differential Equations
Nguyen, K.A.; Put, M. van der
2010-01-01
The theme of this paper is to 'solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field K. Representations of semi-simple Lie algebras and differential Galo is theory are the main tools. The results extend
Energy Technology Data Exchange (ETDEWEB)
Tsuge, Masashi; Bahou, Mohammed; Lee, Yuan-Pern [Department of Applied Chemistry and Institute of Molecular Sciences, National Chiao Tung University, 1001, Ta-Hsueh Road, Hsinchu 30010, Taiwan (China); Wu, Yu-Jong [National Synchrotron Radiation Research Center, 101, Hsin-Ann Road, Hsinchu 30076, Taiwan (China); Allamandola, Louis, E-mail: tsuge@nctu.edu.tw, E-mail: yplee@mail.nctu.edu.tw [The Astrophysics and Astrochemistry Laboratory, NASA Ames Research Center, Moffett Field, CA 94035 (United States)
2016-07-10
The mid-infrared emission from galactic objects, including reflection nebulae, planetary nebulae, proto-planetary nebulae, molecular clouds, etc, as well as external galaxies, is dominated by the unidentified infrared (UIR) emission bands. Large protonated polycyclic aromatic hydrocarbons (H{sup +}PAHs) were proposed as possible carriers, but no spectrum of an H{sup +}PAH has been shown to exactly match the UIR bands. Here, we report the IR spectrum of protonated ovalene (7-C{sub 32}H{sub 15} {sup +}) measured in a para -hydrogen ( p -H{sub 2}) matrix at 3.2 K, generated by bombarding a mixture of ovalene and p -H{sub 2} with electrons during matrix deposition. Spectral assignments were made based on the expected chemistry and on the spectra simulated with the wavenumbers and infrared intensities predicted with the B3PW91/6-311++G(2d,2p) method. The close resemblance of the observed spectral pattern to that of the UIR bands suggests that protonated ovalene may contribute to the UIR emission, particularly from objects that emit Class A spectra, such as the IRIS reflection nebula, NGC 7023.
Modular structure of local algebras associated with massless free quantum fields
International Nuclear Information System (INIS)
Hislop, P.D.
1984-01-01
The Tomita modular operators and the duality property for the local von Neumann algebras in quantum field models describing free massless particles with arbitrary helicity are studied. It is proved that the representation of the Poincare group in each model extends to a unitary representation SU(2,2), a covering group of the conformal group. An irreducible set of standard linear fields is shown to be covariant with respect to this representation. The von Neumann algebras associated with wedge, double-cone, and lightcone regions generated by these fields are proved to be unitarily equivalent. Using the results of Bisognano and Wichmann, the modular operators for these algebras are obtained in explicit form as conformal transformations and the duality property is proved. In the bose case, it is shown that the double-cone algebras constructed from any irreducible set of linear fields not including the standard fields do not satisfy duality and that any non-standard linear fields are not conformally covariant. A simple proof of duality, independent of the Tomita-Takesaki theory, for the double-cone algebras in the scalar case is also presented
Symmetric analysis, categorization, and optical spectrum of ideal pyramid quantum dots
Li, Wei; Belling, Samuel W.
2017-11-01
Self-assembled quantum dots possess an intrinsic geometric symmetry. Applying group representation theory, we systematically analyze the symmetric properties of the bound states for ideal pyramid quantum dots, which neglect band mixing and strain effects. We label each bound state by its symmetry group’s corresponding irreducible representation and define a concept called the quantum dots’ symmetry category. A class of quantum dots with the same irreducible representation sequence of bound states are characterized as belonging to a specific symmetry category. This category concept generally describes the symmetric order of Hilbert space or wavefunction space. We clearly identify the connection between the symmetry category and the geometry of quantum dots by the symmetry category graph or map. The symmetry category change or transition corresponds to an accidental degeneracy of the bound states. The symmetry category and category transition are observable from the photocurrent spectroscopy or optical spectrum. For simplicity’s sake, in this paper, we only focus on inter-subband transition spectra, but the methodology can be extended to the inter-band transition cases. We predict that from the spectral measurements, the quantum dots’ geometric information may be inversely extracted.
International Union of Radioecology response to the Chernobyl radioecological situation
International Nuclear Information System (INIS)
Cigna, A.; Kirchmann, R.
1997-01-01
International Union of Radioecology (UIR) main objective, as NGO and international scientific association of more than 500 members working in 255 organizations from 37 different countries, is to encourage the exchange of information and expertise in the field of radioecology, particularly in case of major accidental release of radioactive materials, such as the Chernobyl accident (1986 April, 26th) which based the problem of a contamination on a large scale. This primary objective of UIR is not restricted to information on the transfer of important radionuclides in the environment but includes information which can aid in understanding the impact of radiation exposure on populations of living organisms and ecosystems. The response of UIR to the Chernobyl accidental situation occurred in various members taking advantage of the structure and the potential of the organization
Magnetic translation group and classification of states of an itinerant electron
International Nuclear Information System (INIS)
Wal, Andrzej
2006-01-01
We consider an itinerant electron on two-dimensional finite square lattice in a magneticfield. A magnetic translation group (MTG) for this system with the periodic Born- Karman conditions has been introduced. The irreducible representation of MTG is used for classification of energy levels of electron states for this model
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
International Nuclear Information System (INIS)
Aoyama, Shogo
2014-01-01
The Poisson brackets for non-linear σ-models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is shown to satisfy the classical exchange algebra
W-realization of Lie algebras. Application to so(4,2) and Poincare algebras
International Nuclear Information System (INIS)
Barbarin, F.; Ragoucy, E.; Sorba, P.
1996-05-01
The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a 'canonical' differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author)
On the twistor representation of Siegel transformation for superparticles
International Nuclear Information System (INIS)
Volkov, D.V.; Sorokin, D.P.; Tkach, V.I.
1988-01-01
It is shown that an explicit incorporation of twistor variables into the Lagrangian of a massless relativistic particle together with the local supersymmetrization of its proper time leads to a Lagrangian which is invariant under the space-time global supersymmetry. The equivalence of the Siegel symmetry and the local proper-time supersymmetry with a complexified grassmanian parameter is established. The Siegel algebra is formed by an irreducible set of covariant constraints and is closed off shell. 20 refs
Sporadic simple groups and quotient singularities
International Nuclear Information System (INIS)
Cheltsov, I A; Shramov, C A
2013-01-01
We show that if a faithful irreducible representation of a central extension of a sporadic simple group with centre contained in the commutator subgroup gives rise to an exceptional (resp. weakly exceptional but not exceptional) quotient singularity, then that simple group is the Hall-Janko group (resp. the Suzuki group)
The asymptotic spectrum of the N = 4 super-Yang-Mills spin chain
International Nuclear Information System (INIS)
Chen, H.-Y.; Dorey, Nick; Okamura, Keisuke
2007-01-01
In this paper we discuss the asymptotic spectrum of the spin chain description of planar N = 4 SUSY Yang-Mills. The states appearing in the spectrum belong to irreducible representations of the unbroken supersymmetry SU(2 vertical bar 2) x SU(2 vertical bar 2) with non-trivial extra central extensions. The elementary magnon corresponds to the bifundamental representation while boundstates of Q magnons form a certain short representation of dimension 16Q 2 . Generalising the Beisert's analysis of the Q = 1 case, we derive the exact dispersion relation for these states by purely group theoretic means
Factorizations and physical representations
International Nuclear Information System (INIS)
Revzen, M; Khanna, F C; Mann, A; Zak, J
2006-01-01
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the decomposition of M into prime numbers. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (Zak J 1970 Phys. Today 23 51), and related representations termed q 1 q 2 representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M
Cook, D. J.; Schlemmer, S.; Balucani, N.; Wagner, D. R.; Harrison, J. A.; Steiner, B.; Saykally, R. J.
1998-01-01
Single-photon infrared emission spectroscopy (SPIRES) has been used to measure emission spectra from polycyclic aromatic hydrocarbons (PAHs). A supersonic free-jet expansion has been used to provide emission spectra of rotationally cold and vibrationally excited naphthalene and benzene. Under these conditions, the observed width of the 3.3-micrometers (C-H stretch) band resembles the bandwidths observed in experiments in which emission is observed from naphthalene with higher rotational energy. To obtain complete coverage of IR wavelengths relevant to the unidentified infrared bands (UIRs), UV laser-induced desorption was used to generate gas-phase highly excited PAHs. Lorentzian band shapes were convoluted with the monochromator-slit function in order to determine the widths of PAH emission bands under astrophysically relevant conditions. Bandwidths were also extracted from bands consisting of multiple normal modes blended together. These parameters are grouped according to the functional groups mostly involved in the vibration, and mean bandwidths are obtained. These bandwidths are larger than the widths of the corresponding UIR bands. However, when the comparison is limited to the largest PAHs studied, the bandwidths are slightly smaller than the corresponding UIR bands. These parameters can be used to model emission spectra from PAH cations and cations of larger PAHs, which are better candidate carriers of the UIRs.
Directory of Open Access Journals (Sweden)
Sudha Ellison Mathe
2017-08-01
Full Text Available Multiplication in finite fields is used in many applications, especially in cryptography. It is a basic and the most computationally intensive operation from among all such operations. Several systolic multipliers are proposed in the literature that offer low hardware complexity or high speed. In this paper, a bit‐parallel polynomial basis systolic multiplier for generic irreducible polynomials is proposed based on a modified interleaved multiplication method. The hardware complexity and delay of the proposed multiplier are estimated, and a comparison with the corresponding multipliers available in the literature is presented. Of the corresponding multipliers, the proposed multiplier achieves a reduction in the hardware complexity of up to 20% when compared to the best multiplier for m = 163. The synthesis results of application‐specific integrated circuit and field‐programmable gate array implementations of the proposed multiplier are also presented. From the synthesis results, it is inferred that the proposed multiplier achieves low power consumption and low area complexitywhen compared to the best of the corresponding multipliers.
Distinguishing Representations as Origin and Representations as Input: Roles for Individual Cells
Directory of Open Access Journals (Sweden)
Jonathan C.W. Edwards
2016-09-01
Full Text Available It is widely perceived that there is a problem in giving a naturalistic account of mental representation that deals adequately with meaning, interpretation or significance (semantic content. It is suggested here that this problem may arise partly from the conflation of two vernacular senses of representation: representation-as-origin and representation-as-input. The flash of a neon sign may in one sense represent a popular drink, but to function as representation it must provide an input to a ‘consumer’ in the street. The arguments presented draw on two principles – the neuron doctrine and the need for a venue for ‘presentation’ or ‘reception’ of a representation at a specified site, consistent with the locality principle. It is also argued that domains of representation cannot be defined by signal traffic, since they can be expected to include ‘null’ elements based on non-firing cells. In this analysis, mental representations-as-origin are distributed patterns of cell firing. Each firing cell is given semantic value in its own right - some form of atomic propositional significance – since different axonal branches may contribute to integration with different populations of signals at different downstream sites. Representations-as-input are patterns of local co-arrival of signals in the form of synaptic potentials in dendrites. Meaning then draws on the relationships between active and null inputs, forming ‘scenarios’ comprising a molecular combination of ‘premises’ from which a new output with atomic propositional significance is generated. In both types of representation, meaning, interpretation or significance pivots on events in an individual cell. (This analysis only applies to ‘occurrent’ representations based on current neural activity. The concept of representations-as-input emphasises the need for a ‘consumer’ of a representation and the dependence of meaning on the co-relationships involved in an
W-realization of Lie algebras. Application to so(4,2) and Poincare algebras
Energy Technology Data Exchange (ETDEWEB)
Barbarin, F.; Ragoucy, E.; Sorba, P.
1996-05-01
The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a `canonical` differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author). 12 refs.
Introduction to supersymmetry and supergravity
International Nuclear Information System (INIS)
West, P.
1986-01-01
This book gives views of supersymmetry and supergravity. The contents include; alternative approach to supersymmetry algebra; immediate consequences of supersymmetry algebra; Wess-Zumino model. N=1 Super QED. N=1 super Yang Mills theory and the Noether procedure; irreducible representations of supersymmetry; invariance of simple supergravity and theories of extended rigid supersymmetry
Eigenstates of a particle in an array of hexagons with periodic boundary condition
Directory of Open Access Journals (Sweden)
A Nemati
2013-10-01
Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.
Multi-representation based on scientific investigation for enhancing students’ representation skills
Siswanto, J.; Susantini, E.; Jatmiko, B.
2018-03-01
This research aims to implementation learning physics with multi-representation based on the scientific investigation for enhancing students’ representation skills, especially on the magnetic field subject. The research design is one group pretest-posttest. This research was conducted in the department of mathematics education, Universitas PGRI Semarang, with the sample is students of class 2F who take basic physics courses. The data were obtained by representation skills test and documentation of multi-representation worksheet. The Results show gain analysis value of .64 which means some medium improvements. The result of t-test (α = .05) is shows p-value = .001. This learning significantly improves students representation skills.
Rumelhart, David E.; Norman, Donald A.
This paper reviews work on the representation of knowledge from within psychology and artificial intelligence. The work covers the nature of representation, the distinction between the represented world and the representing world, and significant issues concerned with propositional, analogical, and superpositional representations. Specific topics…
Attention and Representational Momentum
Hayes, Amy; Freyd, Jennifer J
1995-01-01
Representational momentum, the tendency for memory to be distorted in the direction of an implied transformation, suggests that dynamics are an intrinsic part of perceptual representations. We examined the effect of attention on dynamic representation by testing for representational momentum under conditions of distraction. Forward memory shifts increase when attention is divided. Attention may be involved in halting but not in maintaining dynamic representations.
LGBT Representations on Facebook : Representations of the Self and the Content
Chu, Yawen
2017-01-01
The topic of LGBT rights has been increasingly discussed and debated over recent years. More and more scholars show their interests in the field of LGBT representations in media. However, not many studies involved LGBT representations in social media. This paper explores LGBT representations on Facebook by analysing posts on an open page and in a private group, including both representations of the self as the identity of sexual minorities, content that is displayed on Facebook and the simila...
Representation Elements of Spatial Thinking
Fiantika, F. R.
2017-04-01
This paper aims to add a reference in revealing spatial thinking. There several definitions of spatial thinking but it is not easy to defining it. We can start to discuss the concept, its basic a forming representation. Initially, the five sense catch the natural phenomenon and forward it to memory for processing. Abstraction plays a role in processing information into a concept. There are two types of representation, namely internal representation and external representation. The internal representation is also known as mental representation; this representation is in the human mind. The external representation may include images, auditory and kinesthetic which can be used to describe, explain and communicate the structure, operation, the function of the object as well as relationships. There are two main elements, representations properties and object relationships. These elements play a role in forming a representation.
An alternative realization of 't Hooft's quantum determinism
Energy Technology Data Exchange (ETDEWEB)
Sadiq, M., E-mail: sadiq@qau.edu.p [Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Ghafoor, F. [Centre for Quantum Physics, COMSATS Institute of Information Technology, Islamabad (Pakistan)
2010-11-15
We present an alternative to 't Hooft's mechanism relating a deterministic system to a 1D quantum oscillator. We argue that it is possible to map 't Hooft's ontological space onto an irreducible representation of a 2D isotropic oscillator. A direct group contraction procedure can then be applied to achieve the correspondence.
Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups
International Nuclear Information System (INIS)
Podles, P.
1995-01-01
We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU(2) and SO(3) groups. (orig.)
Introduction to supersymmetry and supergravity
International Nuclear Information System (INIS)
West, P.
1990-01-01
This book discusses two-dimensional supersymmetry algebras, and their irreducible representations as well as rigid and local (supergravity) theories of supersymmetry both in x-space and superspace. These theories include the actions for the superstring and the heterotic string. A discussion on superconformal algebras in two dimensions and an account of super operator product expansion are included
Coherent transform, quantization, and Poisson geometry
Novikova, E; Itskov, V; Karasev, M V
1998-01-01
This volume contains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.
International Nuclear Information System (INIS)
Ferrie, Christopher; Emerson, Joseph
2008-01-01
Several finite-dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite-dimensional quantum systems. Moreover, we show that any quasi-probability representation is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus. (fast track communication)
DEFF Research Database (Denmark)
Wulf-Andersen, Trine Østergaard
2012-01-01
, and dialogue, of situated participants. The article includes a lengthy example of a poetic representation of one participant’s story, and the author comments on the potentials of ‘doing’ poetic representations as an example of writing in ways that challenges what sometimes goes unasked in participative social...
Understanding representations in design
DEFF Research Database (Denmark)
Bødker, Susanne
1998-01-01
Representing computer applications and their use is an important aspect of design. In various ways, designers need to externalize design proposals and present them to other designers, users, or managers. This article deals with understanding design representations and the work they do in design....... The article is based on a series of theoretical concepts coming out of studies of scientific and other work practices and on practical experiences from design of computer applications. The article presents alternatives to the ideas that design representations are mappings of present or future work situations...... and computer applications. It suggests that representations are primarily containers of ideas and that representation is situated at the same time as representations are crossing boundaries between various design and use activities. As such, representations should be carriers of their own contexts regarding...
Nanopublication beyond the sciences: the PeriodO period gazetteer
Directory of Open Access Journals (Sweden)
Patrick Golden
2016-02-01
Full Text Available The information expressed in humanities datasets is inextricably tied to a wider discursive environment that is irreducible to complete formal representation. Humanities scholars must wrestle with this fact when they attempt to publish or consume structured data. The practice of “nanopublication,” which originated in the e-science domain, offers a way to maintain the connection between formal representations of humanities data and its discursive basis. In this paper we describe nanopublication, its potential applicability to the humanities, and our experience curating humanities nanopublications in the PeriodO period gazetteer.
Clifford Continuous Wavelet Transforms in Ll0,2 and Ll0,3
International Nuclear Information System (INIS)
Bernstein, S.
2008-01-01
We consider Clifford-valued functions defined on R n . From the viewpoint of square integrable group representations a continuous wavelet transform is an irreducible continuous unitary representation of the affin group on the real line but also on R n . We will demonstrate that different Clifford continuous wavelet transforms can be obtained inside the calculus with similar properties than the real valued transform. Nevertheless, the Clifford wavelet transform is neither just a special vector transform nor just a wavelet transform applied to each component of the Clifford-valued function.
Algebra with polynomial commutation relations for Zeeman effect in Coulomb-Dirac field
International Nuclear Information System (INIS)
Karasev, M.V.; Novikova, E.M.
2005-01-01
One studies a model of a particle motion in the field of electromagnetic monopole (the Coulomb-Dirac field) disturbed by homogeneous magnetic and inhomogeneous electric fields. The quantum averaging is followed by occurrence of the integrated system the Hamiltonian of which is represented by the algebra elements with polynomial commutation relations. One forms irreducible representations of the mentioned algebra and its hypergeometric coherent states. One obtains the representation of the eigenfunction of the assumption problem and specifies the asymptotics of eigenvalues in the first order of perturbation theory [ru
Rotational KMS States and Type I Conformal Nets
Longo, Roberto; Tanimoto, Yoh
2018-01-01
We consider KMS states on a local conformal net on S 1 with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.
Standard model of knowledge representation
Yin, Wensheng
2016-09-01
Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.
International Nuclear Information System (INIS)
Davis, J. E.; Eddy, M. J.; Sutton, T. M.; Altomari, T. J.
2007-01-01
Solid modeling computer software systems provide for the design of three-dimensional solid models used in the design and analysis of physical components. The current state-of-the-art in solid modeling representation uses a boundary representation format in which geometry and topology are used to form three-dimensional boundaries of the solid. The geometry representation used in these systems is cubic B-spline curves and surfaces - a network of cubic B-spline functions in three-dimensional Cartesian coordinate space. Many Monte Carlo codes, however, use a geometry representation in which geometry units are specified by intersections and unions of half-spaces. This paper describes an algorithm for converting from a boundary representation to a half-space representation. (authors)
Furman, Wyndol; Collibee, Charlene
2018-01-01
This study examined how representations of parent-child relationships, friendships, and past romantic relationships are related to subsequent romantic representations. Two-hundred 10th graders (100 female; M age = 15.87 years) from diverse neighborhoods in a Western U.S. city were administered questionnaires and were interviewed to assess avoidant and anxious representations of their relationships with parents, friends, and romantic partners. Participants then completed similar questionnaires and interviews about their romantic representations six more times over the next 7.5 years. Growth curve analyses revealed that representations of relationships with parents, friends, and romantic partners each uniquely predicted subsequent romantic representations across development. Consistent with attachment and behavioral systems theory, representations of romantic relationships are revised by representations and experiences in other relationships. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.
A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion
International Nuclear Information System (INIS)
Aldaya, V.; Navarro-Salas, J.
1992-01-01
A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)
A dynamical theory for linearized massive superspin 3/2
International Nuclear Information System (INIS)
Gates, James S. Jr.; Koutrolikos, Konstantinos
2014-01-01
We present a new theory of free massive superspin Y=3/2 irreducible representation of the 4D, N=1 Super-Poincaré group, which has linearized non-minimal supergravity (superhelicity Y=3/2) as it’s massless limit. The new results will illuminate the underlying structure of auxiliary superfields required for the description of higher massive superspin systems
Zero-energy modes, charge conjugation, and fermion number
International Nuclear Information System (INIS)
Sudarshan, E.C.G.; Yajnik, U.A.
1986-01-01
States with a half-integer fermion number occur when a fermionic field coupled to a soliton possesses a zero mode. This paper spells out the circumstances under which one can retain an integer fermion number as also a charge-conjugation-invariant ground state. It is necessary to make the representation reducible but it is kept irreducible by introducing an additional operator
Free massless fermionic fields of arbitrary spin in d-dimensional anti-de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Vasiliev, M A
1988-04-25
Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d-2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.
The hidden SO(4) symmetry of general SU(2) Thirring models
International Nuclear Information System (INIS)
Curci, G.; Paffuti, G.; Rossi, P.
1988-01-01
General four-fermion interactions in two dimensions with SU(2) invariance are shown to possess a hidden SO(4) symmetry. As a consequence physical states belong to irreducible representations of the two commuting O(3) subgroups and their interactions decouple accordingly. Two independent stable trajectories of the renormalization group are shown to exist perturbatively and are consistently reproduced by abelian bosonization. (orig.)
Unitary symmetry, combinatorics, and special functions
Energy Technology Data Exchange (ETDEWEB)
Louck, J.D.
1996-12-31
From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.
Helsy, I.; Maryamah; Farida, I.; Ramdhani, M. A.
2017-09-01
This study aimed to describe the application of teaching materials, analyze the increase in the ability of students to connect the three levels of representation and student responses after application of multiple representations based teaching materials chemistry. The method used quasi one-group pretest-posttest design to 71 students. The results showed the application of teaching materials carried 88% with very good category. A significant increase ability to connect the three levels of representation of students after the application of multiple representations based teaching materials chemistry with t-value > t-crit (11.402 > 1.991). Recapitulation N-gain pretest and posttest showed relatively similar for all groups is 0.6 criterion being achievement. Students gave a positive response to the application of multiple representations based teaching materials chemistry. Students agree teaching materials used in teaching chemistry (88%), and agrees teaching materials to provide convenience in connecting the three levels of representation (95%).
Quantum dressing orbits on compact groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. (Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Sommerfeld Inst.); Stovicek, P. (Prague Univ. (Czechoslovakia). Dept. of Mathematics)
1993-02-01
The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.).
Quantum dressing orbits on compact groups
International Nuclear Information System (INIS)
Jurco, B.; Stovicek, P.
1993-01-01
The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.)
Introduction to computer data representation
Fenwick, Peter
2014-01-01
Introduction to Computer Data Representation introduces readers to the representation of data within computers. Starting from basic principles of number representation in computers, the book covers the representation of both integer and floating point numbers, and characters or text. It comprehensively explains the main techniques of computer arithmetic and logical manipulation. The book also features chapters covering the less usual topics of basic checksums and 'universal' or variable length representations for integers, with additional coverage of Gray Codes, BCD codes and logarithmic repre
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
Takiff superalgebras and conformal field theory
International Nuclear Information System (INIS)
Babichenko, Andrei; Ridout, David
2013-01-01
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an Abelian ideal. When the superalgebra is of affine Kac–Moody type, a generalization of Sugawara’s construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinization of the superalgebra gl( 1|1): its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced. (paper)
DEFF Research Database (Denmark)
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...
Categorification and higher representation theory
Beliakova, Anna
2017-01-01
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse te...
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules
Directory of Open Access Journals (Sweden)
Katy L. Chubb
2018-04-01
Full Text Available A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE.
A Top-Down Account of Linear Canonical Transforms
Directory of Open Access Journals (Sweden)
Kurt Bernardo Wolf
2012-06-01
Full Text Available We contend that what are called Linear Canonical Transforms (LCTs should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel representation found by Collins, Moshinsky and Quesne, and the radial and hyperbolic LCTs introduced thereafter, belong to the discrete and continuous representation series of the Lorentz group in its parabolic subgroup reduction. The reduction by the elliptic and hyperbolic subgroups can also be considered to yield LCTs that act on functions, discrete or continuous in other Hilbert spaces. We gather the summation and integration kernels reported by Basu and Wolf when studiying all discrete, continuous, and mixed representations of the linear group of 2×2 real matrices. We add some comments on why all should be considered canonical.
Schiffler, Ralf
2014-01-01
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
Hilton, Annette; Nichols, Kim
2011-11-01
Understanding bonding is fundamental to success in chemistry. A number of alternative conceptions related to chemical bonding have been reported in the literature. Research suggests that many alternative conceptions held by chemistry students result from previous teaching; if teachers are explicit in the use of representations and explain their content-specific forms and functions, this might be avoided. The development of an understanding of and ability to use multiple representations is crucial to students' understanding of chemical bonding. This paper draws on data from a larger study involving two Year 11 chemistry classes (n = 27, n = 22). It explores the contribution of explicit instruction about multiple representations to students' understanding and representation of chemical bonding. The instructional strategies were documented using audio-recordings and the teacher-researcher's reflection journal. Pre-test-post-test comparisons showed an improvement in conceptual understanding and representational competence. Analysis of the students' texts provided further evidence of the students' ability to use multiple representations to explain macroscopic phenomena on the molecular level. The findings suggest that explicit instruction about representational form and function contributes to the enhancement of representational competence and conceptual understanding of bonding in chemistry. However, the scaffolding strategies employed by the teacher play an important role in the learning process. This research has implications for professional development enhancing teachers' approaches to these aspects of instruction around chemical bonding.
Quantum groups and quantum homogeneous spaces
International Nuclear Information System (INIS)
Kulish, P.P.
1994-01-01
The usefulness of the R-matrix formalism and the reflection equations is demonstrated on examples of the quantum group covariant algebras (quantum homogeneous spaces): quantum Minkowski space-time, quantum sphere and super-sphere. The irreducible representations of some covariant algebras are constructed. The generalization of the reflection equation to super case is given and the existence of the quasiclassical limits is pointed out. (orig.)
The derivation of the conventional basis for the classical Lie algebra generators
International Nuclear Information System (INIS)
Karadayi, H.R.
1982-01-01
The explicit construction of the classical Lie algebra generators in the conventional Gell-Mann basis is derived for all irreducible unitary representations of all classical groups. The main framework is based on a description of the simple roots of the classical Lie algebras such that the inter-relations implied by the Cartan matrix of the group among these simple roots are explicit within this description. (author)
A toy model for higher spin Dirac operators
International Nuclear Information System (INIS)
Eelbode, D.; Van de Voorde, L.
2010-01-01
This paper deals with the higher spin Dirac operator Q 2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight (5/2, 3/2, 1/2,..., 1/2). . This operator acts as a toy model for generalizations of the classical Rarita-Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.
New symmetries for the Dirac equation
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.
1990-06-01
We study through both the matrix and differential-form formalism the SU(4) symmetry relating spin 1/2 particles. Minimal left ideals of the Clifford algebra are shown to be irreducible representations of these particles. Their physical interpretation relies on their mutual relationship via parity, time reversal and their product. The implication of these features on the spectrum proliferation problem on the lattice is emphasized. (author)
Evolved Representation and Computational Creativity
Directory of Open Access Journals (Sweden)
Ashraf Fouad Hafez Ismail
2001-01-01
Full Text Available Advances in science and technology have influenced designing activity in architecture throughout its history. Observing the fundamental changes to architectural designing due to the substantial influences of the advent of the computing era, we now witness our design environment gradually changing from conventional pencil and paper to digital multi-media. Although designing is considered to be a unique human activity, there has always been a great dependency on design aid tools. One of the greatest aids to architectural design, amongst the many conventional and widely accepted computational tools, is the computer-aided object modeling and rendering tool, commonly known as a CAD package. But even though conventional modeling tools have provided designers with fast and precise object handling capabilities that were not available in the pencil-and-paper age, they normally show weaknesses and limitations in covering the whole design process.In any kind of design activity, the design worked on has to be represented in some way. For a human designer, designs are for example represented using models, drawings, or verbal descriptions. If a computer is used for design work, designs are usually represented by groups of pixels (paintbrush programs, lines and shapes (general-purpose CAD programs or higher-level objects like ‘walls’ and ‘rooms’ (purpose-specific CAD programs.A human designer usually has a large number of representations available, and can use the representation most suitable for what he or she is working on. Humans can also introduce new representations and thereby represent objects that are not part of the world they experience with their sensory organs, for example vector representations of four and five dimensional objects. In design computing on the other hand, the representation or representations used have to be explicitly defined. Many different representations have been suggested, often optimized for specific design domains
Operator representations of frames
DEFF Research Database (Denmark)
Christensen, Ole; Hasannasab, Marzieh
2017-01-01
of the properties of the operator T requires more work. For example it is a delicate issue to obtain a representation with a bounded operator, and the availability of such a representation not only depends on the frame considered as a set, but also on the chosen indexing. Using results from operator theory we show......The purpose of this paper is to consider representations of frames {fk}k∈I in a Hilbert space ℋ of the form {fk}k∈I = {Tkf0}k∈I for a linear operator T; here the index set I is either ℤ or ℒ0. While a representation of this form is available under weak conditions on the frame, the analysis...... that by embedding the Hilbert space ℋ into a larger Hilbert space, we can always represent a frame via iterations of a bounded operator, composed with the orthogonal projection onto ℋ. The paper closes with a discussion of an open problem concerning representations of Gabor frames via iterations of a bounded...
Introduction to representation theory
Etingof, Pavel; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex
2011-01-01
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic k...
On Behavioral Equivalence of Rational Representations
Trentelman, Harry L.; Willems, JC; Hara, S; Ohta, Y; Fujioka, H
2010-01-01
This article deals with the equivalence of representations of behaviors of linear differential systems In general. the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel representations and image representations Two kernel
Functional representations for quantized fields
International Nuclear Information System (INIS)
Jackiw, R.
1988-01-01
This paper provides information on Representing transformations in quantum theory bosonic quantum field theories: Schrodinger Picture; Represnting Transformations in Bosonic Quantum Field Theory; Two-Dimensional Conformal Transformations, Schrodinger picture representation, Fock space representation, Inequivalent Schrodinger picture representations; Discussion, Self-Dual and Other Models; Field Theory in de Sitter Space. Fermionic Quantum Field Theories: Schroedinger Picture; Schrodinger Picture Representation for Two-Dimensional; Conformal Transformations; Fock Space Dynamics in the Schrodinger Picture; Fock Space Evaluation of Anomalous Current and Conformal Commutators
The protection of warranties and representations
International Nuclear Information System (INIS)
Spence, C.D.; Thusoo, N.
1999-01-01
Most acquisition contracts within the oil and gas industry consist of representations and warranties. The legal distinction between representations and warranties was explained as follows: a representation is a statement of fact made by the representor before making the contract, but a warranty is a statement of fact which forms part of the terms of the contract. The paper outlines the nature of a representation or warranty and explains why certain warranties are not given. The protection offered by representations and warranties in breach of contract cases is also explained. Suggestions are offered for increasing protection by representations and warranties. 22 refs
Landau levels on the hyperbolic plane
International Nuclear Information System (INIS)
Fakhri, H; Shariati, M
2004-01-01
The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength. (letter to the editor)
Landau levels on the hyperbolic plane
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H [Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran 19395-5531 (Iran, Islamic Republic of); Shariati, M [Department of Physics, Khajeh Nassir-Al-Deen Toosi University of Technology, Tehran 15418 (Iran, Islamic Republic of)
2004-11-05
The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength. (letter to the editor)
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.
Directory of Open Access Journals (Sweden)
Roberto De Rubertis
2012-06-01
Full Text Available This article will discuss about the physiological genesis of representation and then it will illustrate the developments, especially in evolutionary perspective, and it will show how these are mainly a result of accidental circumstances, rather than of deliberate intention of improvement. In particular, it will be argue that the representation has behaved like a meme that has arrived to its own progressive evolution coming into symbiosis with the different cultures in which it has spread, and using in this activity human work “unconsciously”. Finally it will be shown how in this action the geometry is an element key, linked to representation both to construct images using graphics operations and to erect buildings using concrete operations.
Introduction to supersymmetry in particle and nuclear physics
International Nuclear Information System (INIS)
Castanos, O.; Frank, A.; Urrutia, L.
1981-01-01
This book constitutes the proceedings of an International School of Supersymmetry held in Mexico City in 1981. Lectures presented include an introduction to supersymmetry (symmetries in relativistic quantum field theory, supersymmetry in quantum field theory, Dirac matrices and Majorana spinors, supersymmetric Yang-Mills theory, scalar multiplet and auxiliary fields, supergravity, N=1 supersymmetric theories, extended supersymmetry algebras, representations of extended supersymmetry, N=4 supersymmetric Yang-Mills theory, extended supergravity), superfields (irreducible representations and chiral superfields, invariants and ''tensor calculus,'' gauge superfield, N=1 supergravity), grand unification with and without supersymmetry (supersymmetric models), Yang-Mills theories with global and local supersymmetry (Higgs and Superhiggs effect in unified field theories), and supergroups and their representations (fermion and Grassmann numbers, supertrace and superdeterminant, harmonic oscillator representation, the Tilde operator, eigenvalues of Casimir operators, branching rules, Kac-Dynkin diagrams and supertableaux)
Polynomial representations of GLn
Green, James A; Erdmann, Karin
2007-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Polynomial representations of GLN
Green, James A
1980-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Karpilovsky, G
1994-01-01
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory
DEFF Research Database (Denmark)
Rasmussen, Majken Kirkegaard; Petersen, Marianne Graves
2011-01-01
Stereotypic presumptions about gender affect the design process, both in relation to how users are understood and how products are designed. As a way to decrease the influence of stereotypic presumptions in design process, we propose not to disregard the aspect of gender in the design process......, as the perspective brings valuable insights on different approaches to technology, but instead to view gender through a value lens. Contributing to this perspective, we have developed Value Representations as a design-oriented instrument for staging a reflective dialogue with users. Value Representations...
Hard and soft supersymmetry breaking for ‘graphinos’ in uniform magnetic fields
International Nuclear Information System (INIS)
Hernández-Ortíz, S; Raya, A; Murguía, G
2012-01-01
Using irreducible and reducible representations of the Dirac matrices, we study the two- and four-component quantum mechanical supersymmetric (SUSY) theories for ultrarelativistic fermions in (2 + 1) dimensions (‘graphinos’) in a background uniform magnetic field perpendicular to their plane of motion. We then consider ordinary and parity-violating mass terms and identify the former as a soft SUSY breaking term and the latter as the hard SUSY breaking one. (paper)
International Nuclear Information System (INIS)
Rajput, B.S.
1977-01-01
Using the reduced expansions of second quantized electromagnetic vector potential operator in terms of irreducible representations of Pioncare group in the interaction Hamiltonian, the exact matrix elements of interaction of electromagnetic field with a hydrogenic atom have been derived and the contributions of transitions for different combinations of angular momentum quantum numbers to the transition probabilities of various lines in Lyman-, Balmer-, and Paschen-series have been computed. (author)
The symmetric group and its relevance to fermion physics
International Nuclear Information System (INIS)
Harvey, M.
1981-04-01
Notes are given of a series of lectures presented at TRIUMF (Vancouver) during the week of October 17-24, 1980. The lectures, and accompanying notes were designed to give the student a working knowledge of the classification and construction of sets of n-particle states transforming according to a definite irreducible representation of the symmetric group Ssub(n). Applications are given for the classification of quark states of baryons and multibaryons
International Nuclear Information System (INIS)
Ponce, W.A.; Zepeda, A.
1987-08-01
We present the results obtained from our systematic search of a simple Lie group that unifies weak and electromagnetic interactions in a single truly unified theory. We work with fractionally charged quarks, and allow for particles and antiparticles to belong to the same irreducible representation. We found that models based on SU(6), SU(7), SU(8) and SU(10) are viable candidates for simple unification. (author). 23 refs
(Self)-representations on youtube
DEFF Research Database (Denmark)
Simonsen, Thomas Mosebo
This paper examines forms of self-representation on YouTube with specific focus on Vlogs (Video blogs). The analytical scope of the paper is on how User-generated Content on YouTube initiates a certain kind of audiovisual representation and a particular interpretation of reality that can...... be distinguished within Vlogs. This will be analysed through selected case studies taken from a representative sample of empirically based observations of YouTube videos. The analysis includes a focus on how certain forms of representation can be identified as representations of the self (Turkle 1995, Scannell...... 1996, Walker 2005) and further how these forms must be comprehended within a context of technological constrains, institutional structures and social as well as economical practices on YouTube (Burgess and Green 2009, Van Dijck 2009). It is argued that these different contexts play a vital part...
Sinusoidal Representation of Acoustic Signals
Honda, Masaaki
Sinusoidal representation of acoustic signals has been an important tool in speech and music processing like signal analysis, synthesis and time scale or pitch modifications. It can be applicable to arbitrary signals, which is an important advantage over other signal representations like physical modeling of acoustic signals. In sinusoidal representation, acoustic signals are composed as sums of sinusoid (sine wave) with different amplitudes, frequencies and phases, which is based on the timedependent short-time Fourier transform (STFT). This article describes the principles of acoustic signal analysis/synthesis based on a sinusoid representation with focus on sine waves with rapidly varying frequency.
International Nuclear Information System (INIS)
Segre, G.; Arthur Weldon, H.
1980-01-01
The general problem of conservation of strangeness and other quark flavors by the exchange of several neutral Higgs mesons is investigated in SU (2)/sub L/ x U (1). We find that the horizontal symmetries necessary to enforce this conservation conflict with the known Cabibbo mixing. In particular, if the quarks form an irreducible representation of the horizontal symmetry, the mixing angles are all trivial (i.e. 0 or π/2); if they form a reducible representation, it is possible to have some nontrivial mixing angles, but only if there are several unmixed generations of quarks with exactly the same relative pattern of masses and mixings
Breakdown of maximality conjecture in continuous phase transitions
International Nuclear Information System (INIS)
Mukamel, D.; Jaric, M.V.
1983-04-01
A Landau-Ginzburg-Wilson model associated with a single irreducible representation which exhibits an ordered phase whose symmetry group is not a maximal isotropy subgroup of the symmetry group of the disordered phase is constructed. This example disproves the maximality conjecture suggested in numerous previous studies. Below the (continuous) transition, the order parameter points along a direction which varies with the temperature and with the other parameters which define the model. An extension of the maximality conjecture to reducible representations was postulated in the context of Higgs symmetry breaking mechanism. Our model can also be extended to provide a counter example in these cases. (author)
Remarks on the history of the terms "object representation" and "self representation".
May, Ulrike
2005-01-01
This paper reconstructs the history of the term "object representation" and "self representation". It seeks to show that "Objektrepräsentanz" was introduced by Fenichel in 1926, following on from Radó, in order to be able to integrate identification (and the superego) into metapsychology. Freud himself never used "Objektrepräsentanz". Fenichel's pioneering role is not discernible in the English literature mainly because of the diverging approaches used in the translation of this term (object representative versus object representation). It is generally acknowledged that "self representation" was first used by Hartmann but this paper suggests that it actually played a more crucial role in Jacobson's work than it did in Hartmann's. In addition, this paper sees the terms of self and object representation as a reflection of the paradigm change in the 1920s that ensued after the publication of Freud's "The Ego and the Id". In tracing the history of the terms, the significance of the Berlin Psychoanalytical Institute in the 1920s emerges as do the Berlin roots of the works written in the USA in the 1950s and 1960s by Edith Jacobson. She received her analytical training in Berlin. Fenichel was her analyst, Radó was one of her teachers, and she was closely involved with the work of her fellow analysts there.
Role of multiorbital effects in the magnetic phase diagram of iron pnictides
Christensen, Morten H.; Scherer, Daniel D.; Kotetes, Panagiotis; Andersen, Brian M.
2017-07-01
We elucidate the pivotal role of the band structure's orbital content in deciding the type of commensurate magnetic order stabilized within the itinerant scenario of iron pnictides. Recent experimental findings in the tetragonal magnetic phase attest to the existence of the so-called charge and spin ordered density wave over the spin-vortex crystal phase, the latter of which tends to be favored in simplified band models of itinerant magnetism. Here we show that employing a multiorbital itinerant Landau approach based on realistic band structures can account for the experimentally observed magnetic phase, and thus shed light on the importance of the orbital content in deciding the magnetic order. In addition, we remark that the presence of a hole pocket centered at the Brillouin zone's M point favors a magnetic stripe rather than a tetragonal magnetic phase. For inferring the symmetry properties of the different magnetic phases, we formulate our theory in terms of magnetic order parameters transforming according to irreducible representations of the ensuing D4 h point group. The latter method not only provides transparent understanding of the symmetry-breaking schemes but also reveals that the leading instabilities always belong to the {A1 g,B1 g} subset of irreducible representations, independently of their C2 or C4 nature.
The fusion rules for the Temperley–Lieb algebra and its dilute generalization
International Nuclear Information System (INIS)
Belletête, Jonathan
2015-01-01
The Temperley–Lieb (TL) family of algebras is well known for its role in building integrable lattice models. Even though a proof is still missing, it is agreed that these models should go to conformal field theories in the thermodynamic limit and that the limiting vector space should carry a representation of the Virasoro algebra. The fusion rules are a notable feature of the Virasoro algebra. One would hope that there is an analogous construction for the TL family. Such a construction was proposed by Read and Saleur (2007 Nucl. Phys. B 777 316) and partially computed by Gainutdinov and Vasseur (2013 Nucl. Phys. B 868 223–70) using the bimodule structure over the TL algebras and the quantum group Uq (sl2).We use their definition for the dilute Temperley–Lieb (dTL) family, a generalization of the original TL family. We develop a new way of computing fusion by using induction and show its power by obtaining fusion rules for both dTL and TL. We recover those computed by Gainutdivov and Vasseur and new ones that were beyond their scope. In particular, we identify a set of irreducible TL- or dTL-representations whose behavior under fusion is that of some irreducibles of the minimal models of conformal field theory. (paper)
Multiple representations in physics education
Duit, Reinders; Fischer, Hans E
2017-01-01
This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementati...
The holomorphicity of the gauge coupling constant in supersymmetric gauge theories
International Nuclear Information System (INIS)
Li, H.
1993-01-01
Holomorphicity is the analytical dependence of the gauge coupling function, f = 1/g 2 + Θ/8π 2 , on the chiral fields in supergravity and supersymmetric gauge theories. The holomorphic property of 1/g 2 in supersymmetric gauge theories is studied by calculating its dependence on the mass matrix. The general representations of the mass matrix allowed by the constraints of gauge invariance is considered, and calculate the one- and two-loop corrections to 1/g 2 for both super QED and super Yang-Mills theories. For the massive mass matrix it is shown that one- and two-loop corrections to the gauge coupling constant are holomorphic. The reason for two-loop holomorphicity is that the second order logarithmic terms cancel out. For the mass matrix with at least one zero mode, it is recognized that there are two distinct cases which we call pseudo massive and intrinsically massless. For the case of pseudo mass matrix, the reducible representation of the gauge group is (i) complex with equal numbers of irreducible representations and their conjugates, (ii) real, or (iii) pseudo-real. Even though there are massless modes, it is found that the dependence of the gauge coupling constant on the mass matrix is holomorphic. This holomorphicity follows because the mass matrix can be perturbed to regularize the infrared divergence. For the case of intrinsically massless mass matrix, a reducible complex representation with unequal numbers of irreducible representations and their conjugates. The author shows that loop corrections to the gauge coupling constant are non-holomorphic. The reason is an infrared momentum cutoff is used which spins holomorphicity. The results show that, for the pseudo massive case, even though there is an infrared divergence, the one- and two-loop corrections are still holomorphic. Hence, it is concluded that non-holomorphicity is caused by the unbalanced numbers of families and antifamilies in the complex representation
Alternative approach to nuclear data representation
International Nuclear Information System (INIS)
Pruet, J.; Brown, D.; Beck, B.; McNabb, D.P.
2006-01-01
This paper considers an approach for representing nuclear data that is qualitatively different from the approach currently adopted by the nuclear science community. Specifically, we examine a representation in which complicated data is described through collections of distinct and self-contained simple data structures. This structure-based representation is compared with the ENDF and ENDL formats, which can be roughly characterized as dictionary-based representations. A pilot data representation for replacing the format currently used at LLNL is presented. Examples are given as is a discussion of promises and shortcomings associated with moving from traditional dictionary-based formats to a structure-rich or class-like representation
On the phase space representations. 1
International Nuclear Information System (INIS)
Polubarinov, I.V.
1978-01-01
The Dirac representation theory deals usually with the amplitude formalism of the quantum theory. An introduction is given into a theory of some other representations, which are applicable in the density matrix formalism and can naturally be called phase space representations (PSR). They use terms of phase space variables (x and p simultaneously) and give a description, close to the classical phase space description. Definitions and algebraic properties are given in quantum mechanics for such PSRs as the Wigner representation, coherent state representation and others. Completeness relations of a matrix type are used as a starting point. The case of quantum field theory is also outlined
Mobilities and Representations
DEFF Research Database (Denmark)
Thelle, Mikkel
2017-01-01
to consider how they and their peers are currently confronting representations of mobility. This is particularly timely given the growing academic focus on practices, material mediation, and nonrepresentational theories, as well as on bodily reactions, emotions, and feelings that, according to those theories......As the centerpiece of the eighth T2M yearbook, the following interview about representations of mobility signals a new and exciting focus area for Mobility in History. In future issues we hope to include reviews that grapple more with how mobilities have been imagined and represented in the arts......, literature, and film. Moreover, we hope the authors of future reviews will reflect on the ways they approached those representations. Such commentaries would provide valuable methodological insights, and we hope to begin that effort with this interview. We have asked four prominent mobility scholars...
Post-representational cartography
Directory of Open Access Journals (Sweden)
Rob Kitchin
2010-03-01
Full Text Available Over the past decade there has been a move amongst critical cartographers to rethink maps from a post-representational perspective – that is, a vantage point that does not privilege representational modes of thinking (wherein maps are assumed to be mirrors of the world and automatically presumes the ontological security of a map as a map, but rather rethinks and destabilises such notions. This new theorisation extends beyond the earlier critiques of Brian Harley (1989 that argued maps were social constructions. For Harley a map still conveyed the truth of a landscape, albeit its message was bound within the ideological frame of its creator. He thus advocated a strategy of identifying the politics of representation within maps in order to circumnavigate them (to reveal the truth lurking underneath, with the ontology of cartographic practice remaining unquestioned.
Generalized oscillator representations for Calogero Hamiltonians
International Nuclear Information System (INIS)
Tyutin, I V; Voronov, B L
2013-01-01
This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)
Equivalence of rational representations of behaviors
Gottimukkala, Sasanka; Fiaz, Shaik; Trentelman, H.L.
This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel
Cohen, Adam S; Sasaki, Joni Y; German, Tamsin C
2015-03-01
Does theory of mind depend on a capacity to reason about representations generally or on mechanisms selective for the processing of mental state representations? In four experiments, participants reasoned about beliefs (mental representations) and notes (non-mental, linguistic representations), which according to two prominent theories are closely matched representations because both are represented propositionally. Reaction times were faster and accuracies higher when participants endorsed or rejected statements about false beliefs than about false notes (Experiment 1), even when statements emphasized representational format (Experiment 2), which should have favored the activation of representation concepts. Experiments 3 and 4 ruled out a counterhypothesis that differences in task demands were responsible for the advantage in belief processing. These results demonstrate for the first time that understanding of mental and linguistic representations can be dissociated even though both may carry propositional content, supporting the theory that mechanisms governing theory of mind reasoning are narrowly specialized to process mental states, not representations more broadly. Extending this theory, we discuss whether less efficient processing of non-mental representations may be a by-product of mechanisms specialized for processing mental states. Crown Copyright © 2014. Published by Elsevier B.V. All rights reserved.
A generalized wavelet extrema representation
Energy Technology Data Exchange (ETDEWEB)
Lu, Jian; Lades, M.
1995-10-01
The wavelet extrema representation originated by Stephane Mallat is a unique framework for low-level and intermediate-level (feature) processing. In this paper, we present a new form of wavelet extrema representation generalizing Mallat`s original work. The generalized wavelet extrema representation is a feature-based multiscale representation. For a particular choice of wavelet, our scheme can be interpreted as representing a signal or image by its edges, and peaks and valleys at multiple scales. Such a representation is shown to be stable -- the original signal or image can be reconstructed with very good quality. It is further shown that a signal or image can be modeled as piecewise monotonic, with all turning points between monotonic segments given by the wavelet extrema. A new projection operator is introduced to enforce piecewise inonotonicity of a signal in its reconstruction. This leads to an enhancement to previously developed algorithms in preventing artifacts in reconstructed signal.
Madden, Sean Patrick
This study examined the role of multiple representations of chemical phenomena, specifically, the temperature-pressure relationship of ideal gases, in the problem solving strategies of college chemistry students. Volunteers included students enrolled in a first semester general chemistry course at a western university. Two additional volunteers from the same university were asked to participate and serve as models of greater sophistication. One was a senior chemistry major; another was a junior science writing major. Volunteers completed an initial screening task involving multiple representations of concentration and dilution concepts. Based on the results of this screening instrument a smaller set of subjects were asked to complete a think aloud session involving multiple representations of the temperature-pressure relationship. Data consisted of the written work of the volunteers and transcripts from videotaped think aloud sessions. The data were evaluated by the researcher and two other graduate students in chemical education using a coding scheme (Kozma, Schank, Coppola, Michalchik, and Allen. 2000). This coding scheme was designed to identify essential features of representational competence and differences in uses of multiple representations. The results indicate that students tend to have a strong preference for one type of representation. Students scoring low on representational competence, as measured by the rubric, ignored important features of some representations or acknowledged them only superficially. Students scoring higher on representational competence made meaningful connections among representations. The more advanced students, those who rated highly on representational competence, tended to use their preferred representation in a heuristic manner to establish meaning for other representations. The more advanced students also reflected upon the problem at greater length before beginning work. Molecular level sketches seemed to be the most
DEFF Research Database (Denmark)
Photography not only represents space. Space is produced photographically. Since its inception in the 19th century, photography has brought to light a vast array of represented subjects. Always situated in some spatial order, photographic representations have been operatively underpinned by social...... to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...... possibilities, and genre distinctions. Presenting several distinct ways of producing space photographically, this book opens a new and important field of inquiry for photography research....
Facilitating Mathematical Practices through Visual Representations
Murata, Aki; Stewart, Chana
2017-01-01
Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…
Application of group theory to proper vibrations in an electric circuit
Hosoya, Masahiko; 細谷, 将彦
2010-01-01
Group-theoretical analysis is first presented to three-dimensional behavior of an electric circuit. All the modes of proper vibration are found and assigned to each irreducible representation of symmetrical group of the circuit without solving its circuit equations. In order that an electromagnetic radiation from the outside may induce each vibration, a selection rule which is similar to that in infrared absorption must be fulfilled. The circuit may be used as a directive antenna.
Link invariant and $G_2$ web space
Sakamoto, Takuro; Yonezawa, Yasuyoshi
2017-01-01
In this paper, we reconstruct Kuperberg’s $G_2$ web space [5, 6]. We introduce a new web diagram (a trivalent graph with only double edges) and new relations between Kuperberg’s web diagrams and the new web diagram. Using the web diagrams, we give crossing formulas for the $R$-matrices associated to some irreducible representations of $U_q(G_2)$ and calculate $G_2$ quantum link invariants for generalized twist links.
International Nuclear Information System (INIS)
French, J.B.
1974-01-01
The concepts of statistical behavior and symmetry are presented from the point of view of many body spectroscopy. Remarks are made on methods for the evaluation of moments, particularly widths, for the purpose of giving a feeling for the types of mathematical structures encountered. Applications involving ground state energies, spectra, and level densities are discussed. The extent to which Hamiltonian eigenstates belong to irreducible representations is mentioned. (4 figures, 1 table) (U.S.)
Magnetic phase transitions with incommensurate structures in systems with coupled order parameters
International Nuclear Information System (INIS)
Izyumov, Yu.A.; Laptev, V.M.; Petrov, S.B.
1984-01-01
Modulated magnetic phases are investigated for the case when symmetry does not allow linear by gradients Lifshits invariants and magnetic momenta are converted by two irreducible representations. Possible phase diagrams with participation of incommensurable phases are plotted on the base of Ginsburg-Landau functional for 2 bound parameters of the order. The role of the highest harmonics in spatial distribution of the order parameters is clarified on the example of magnetic phase transitions in Er
From large N nonplanar anomalous dimensions to open spring theory
Energy Technology Data Exchange (ETDEWEB)
Mello Koch, Robert de, E-mail: robert@neo.phys.wits.ac.za [National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics University of Witwatersrand, Wits, 2050 (South Africa); Kemp, Garreth, E-mail: Garreth.Kemp@students.wits.ac.za [National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics University of Witwatersrand, Wits, 2050 (South Africa); Smith, Stephanie, E-mail: Stephanie.Smith@students.wits.ac.za [National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics University of Witwatersrand, Wits, 2050 (South Africa)
2012-05-23
In this Letter we compute the nonplanar one-loop anomalous dimension of restricted Schur polynomials that have a bare dimension of O(N). This is achieved by mapping the restricted Schur polynomials into states of a specific U(p) irreducible representation. In this way the dilatation operator is mapped into a u(p) valued operator and, as a result, can easily be diagonalized. The resulting spectrum is reproduced by a model of springs between masses.
Quantum dynamics and breakdown of classical realism in nonlinear oscillators
International Nuclear Information System (INIS)
Gat, Omri
2007-01-01
The leading nonclassical term in the quantum dynamics of nonlinear oscillators is calculated in the Moyal quasi-trajectory representation. The irreducibility of the quantum dynamics to phase-space trajectories is quantified by the discrepancy of the canonical quasi-flow and the quasi-flow of a general observable. This discrepancy is shown to imply the breakdown of classical realism that can give rise to a dynamical violation of Bell's inequalities. (fast track communication)
On the total character of finite groups
Directory of Open Access Journals (Sweden)
Sunil Kumar Prajapati
2014-09-01
Full Text Available For a finite group $G$, we study the total character $tau_G$ afforded by the direct sum of all the non-isomorphic irreducible complex representations of $G$. We resolve for several classes of groups (the Camina $p$-groups, the generalized Camina $p$-groups, the groups which admit $(G,Z(G$ as a generalized Camina pair, the problem of existence of a polynomial $f(x in mathbb{Q}[x]$ such that $f(chi = tau_G$ for some irreducible character $chi$ of $G$. As a consequence, we completely determine the $p$-groups of order at most $p^5$ (with $p$ odd which admit such a polynomial. We deduce the characterization that these are the groups $G$ for which $Z(G$ is cyclic and $(G,Z(G$ is a generalized Camina pair and, we conjecture that this holds good for $p$-groups of any order.
Procedural Media Representation
Henrysson, Anders
2002-01-01
We present a concept for using procedural techniques to represent media. Procedural methods allow us to represent digital media (2D images, 3D environments etc.) with very little information and to render it photo realistically. Since not all kind of content can be created procedurally, traditional media representations (bitmaps, polygons etc.) must be used as well. We have adopted an object-based media representation where an object can be represented either with a procedure or with its trad...
The abstract representations in speech processing.
Cutler, Anne
2008-11-01
Speech processing by human listeners derives meaning from acoustic input via intermediate steps involving abstract representations of what has been heard. Recent results from several lines of research are here brought together to shed light on the nature and role of these representations. In spoken-word recognition, representations of phonological form and of conceptual content are dissociable. This follows from the independence of patterns of priming for a word's form and its meaning. The nature of the phonological-form representations is determined not only by acoustic-phonetic input but also by other sources of information, including metalinguistic knowledge. This follows from evidence that listeners can store two forms as different without showing any evidence of being able to detect the difference in question when they listen to speech. The lexical representations are in turn separate from prelexical representations, which are also abstract in nature. This follows from evidence that perceptual learning about speaker-specific phoneme realization, induced on the basis of a few words, generalizes across the whole lexicon to inform the recognition of all words containing the same phoneme. The efficiency of human speech processing has its basis in the rapid execution of operations over abstract representations.
Interactions between visual working memory representations.
Bae, Gi-Yeul; Luck, Steven J
2017-11-01
We investigated whether the representations of different objects are maintained independently in working memory or interact with each other. Observers were shown two sequentially presented orientations and required to reproduce each orientation after a delay. The sequential presentation minimized perceptual interactions so that we could isolate interactions between memory representations per se. We found that similar orientations were repelled from each other whereas dissimilar orientations were attracted to each other. In addition, when one of the items was given greater attentional priority by means of a cue, the representation of the high-priority item was not influenced very much by the orientation of the low-priority item, but the representation of the low-priority item was strongly influenced by the orientation of the high-priority item. This indicates that attention modulates the interactions between working memory representations. In addition, errors in the reported orientations of the two objects were positively correlated under some conditions, suggesting that representations of distinct objects may become grouped together in memory. Together, these results demonstrate that working-memory representations are not independent but instead interact with each other in a manner that depends on attentional priority.
National Research Council Canada - National Science Library
Little, Daniel
2006-01-01
...). The reason this is so is due to hierarchies that we take for granted. By hierarchies I mean that there is a layer of representation of us as individuals, as military professional, as members of a military unit and as citizens of an entire nation...
L-functions and the oscillator representation
Rallis, Stephen
1987-01-01
These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N
Denis, Michel; Beschin, Nicoletta; Logie, Robert H; Della Sala, Sergio
2002-03-01
In the majority of investigations of representational neglect, patients are asked to report information derived from long-term visual knowledge. In contrast, studies of perceptual neglect involve reporting the contents of relatively novel scenes in the immediate environment. The present study aimed to establish how representational neglect might affect (a) immediate recall of recently perceived, novel visual layouts, and (b) immediate recall of novel layouts presented only as auditory verbal descriptions. These conditions were contrasted with reports from visual perception and a test of immediate recall of verbal material. Data were obtained from 11 neglect patients (9 with representational neglect), 6 right hemisphere lesion control patients with no evidence of neglect, and 15 healthy controls. In the perception, memory following perception, and memory following layout description conditions, the neglect patients showed poorer report of items depicted or described on the left than on the right of each layout. The lateralised error pattern was not evident in the non-neglect patients or healthy controls, and there was no difference among the three groups on immediate verbal memory. One patient showed pure representational neglect, with ceiling performance in the perception condition, but with lateralised errors for memory following perception or following verbal description. Overall, the results indicate that representational neglect does not depend on the presence of perceptual neglect, that visual perception and visual mental representations are less closely linked than has been thought hitherto, and that visuospatial mental representations have similar functional characteristics whether they are derived from visual perception or from auditory linguistic descriptive inputs.
Kato, Yasuhiko; Kamii, Constance; Ozaki, Kyoko; Nagahiro, Mariko
2002-01-01
Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…
Hohenberg-Kohn theorem and non-V-representable densities
International Nuclear Information System (INIS)
Englisch, H.; Englisch, R.
1983-01-01
In the density-functional formalism of Hohenberg and Kohn, the variation is only allowed over the one-particle densities which are pure-state-V-representable (PS-V-representable). Levy and Lieb proved that not every ensemble-V-representable (E-V-representable) density is PS-V-representable. Since we show that the Hohenberg-Kohn formalism can be extended to a variation over E-V-representable densities for degenerated ground states, Levy's and Lieb's result is not a counterexample to the universality of the Hohenberg-Kohn theorem. The question whether every N-representable density is E-V-representable has remained open so far. Presenting examples of non-E-V-representable densities we answer this question in the negative. Thus the value of Levy's functional for the calculation of ground-state energies is obvious, since this functional only requires the N-representability of the densities. Therefore we transfer two approaches for the calculation of excited-state energies into the framework of Levy's formalism. (orig.)
Cohen-Macaulay representations
Leuschke, Graham J
2012-01-01
This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Au...
International Nuclear Information System (INIS)
Gruber, B.; Thomas, M.S.
1980-01-01
In this article the symmetry chains for the atomic shell model are classified in such a way that they lead from the group SU(4l+2) to its subgroup SOsub(J)(3). The atomic configurations (nl)sup(N) transform like irreducible representations of the group SU(4l+2), while SOsub(J)(3) corresponds to total angular momentum in SU(4l+2). The defining matrices for the various embeddings are given for each symmetry chain that is obtained. These matrices also define the projection onto the weight subspaces for the corresponding subsymmetries and thus relate the various quantum numbers and determine the branching of representations. It is shown in this article that three (interrelated) symmetry chains are obtained which correspond to L-S coupling, j-j coupling, and a seniority dependent coupling. Moreover, for l<=6 these chains are complete, i.e., there are no other chains but these. In articles to follow, the symmetry chains that lead from the group SO(8l+5) to SOsub(J)(3) will be discussed, with the entire atomic shell transforming like an irreducible representation of SO(8l+5). The transformation properties of the states of the atomic shell will be determined according to the various symmetry chains obtained. The symmetry lattice discussed in this article forms a sublattice of the larger symmetry lattice with SO(8l+5) as supergroup. Thus the transformation properties of the states of the atomic configurations, according to the various symmetry chains discussed in this article, will be obtained too. (author)
Zumsteg, Zachary S; Zelefsky, Michael J; Woo, Kaitlin M; Spratt, Daniel E; Kollmeier, Marisa A; McBride, Sean; Pei, Xin; Sandler, Howard M; Zhang, Zhigang
2017-11-01
To improve on the existing risk-stratification systems for prostate cancer. This was a retrospective investigation including 2 248 patients undergoing dose-escalated external beam radiotherapy (EBRT) at a single institution. We separated National Comprehensive Cancer Network (NCCN) intermediate-risk prostate cancer into 'favourable' and 'unfavourable' groups based on primary Gleason pattern, percentage of positive biopsy cores (PPBC), and number of NCCN intermediate-risk factors. Similarly, NCCN high-risk prostate cancer was stratified into 'standard' and 'very high-risk' groups based on primary Gleason pattern, PPBC, number of NCCN high-risk factors, and stage T3b-T4 disease. Patients with unfavourable-intermediate-risk (UIR) prostate cancer had significantly inferior prostate-specific antigen relapse-free survival (PSA-RFS, P prostate cancer-specific mortality (PCSM, P prostate cancer. Similarly, patients with very high-risk (VHR) prostate cancer had significantly worse PSA-RFS (P prostate cancer. Moreover, patients with FIR and low-risk prostate cancer had similar outcomes, as did patients with UIR and SHR prostate cancer. Consequently, we propose the following risk-stratification system: Group 1, low risk and FIR; Group 2, UIR and SHR; and Group 3, VHR. These groups have markedly different outcomes, with 8-year distant metastasis rates of 3%, 9%, and 29% (P < 0.001) for Groups 1, 2, and 3, respectively, and 8-year PCSM of 1%, 4%, and 13% (P < 0.001) after EBRT. This modified stratification system was significantly more accurate than the three-tiered NCCN system currently in clinical use for all outcomes. Modifying the NCCN risk-stratification system to group FIR with low-risk patients and UIR with SHR patients, results in modestly improved prediction of outcomes, potentially allowing better personalisation of therapeutic recommendations. © 2017 The Authors BJU International © 2017 BJU International Published by John Wiley & Sons Ltd.
Operator representation for effective realistic interactions
Energy Technology Data Exchange (ETDEWEB)
Weber, Dennis; Feldmeier, Hans; Neff, Thomas [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany)
2013-07-01
We present a method to derive an operator representation from the partial wave matrix elements of effective realistic nucleon-nucleon potentials. This method allows to employ modern effective interactions, which are mostly given in matrix element representation, also in nuclear many-body methods requiring explicitly the operator representation, for example ''Fermionic Molecular Dynamics'' (FMD). We present results for the operator representation of effective interactions obtained from the Argonne V18 potential with the Uenitary Correlation Operator Method'' (UCOM) and the ''Similarity Renormalization Group'' (SRG). Moreover, the operator representation allows a better insight in the nonlocal structure of the potential: While the UCOM transformed potential only shows a quadratic momentum dependence, the momentum dependence of SRG transformed potentials is beyond such a simple polynomial form.
ABJM Wilson loops in arbitrary representations
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Honda, Masazumi [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.
ABJM Wilson loops in arbitrary representations
International Nuclear Information System (INIS)
Hatsuda, Yasuyuki; Moriyama, Sanefumi; Okuyama, Kazumi
2013-06-01
We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.
Mental Representation and Motor Imagery Training
Directory of Open Access Journals (Sweden)
Thomas eSchack
2014-05-01
Full Text Available Research in sports, dance and rehabilitation has shown that Basic Action Concepts (BACs are fundamental building blocks of mental action representations. BACs are based on chunked body postures related to common functions for realizing action goals. In this paper, we outline issues in research methodology and an experimental method, SDA-M (structural dimensional analysis of mental representation, to assess action-relevant representational structures that reflect the organization of BACs. The SDA-M reveals a strong relationship between cognitive representation and performance if complex actions are performed. We show how the SDA-M can improve motor imagery training and how it contributes to our understanding of coaching processes. The SDA-M capitalizes on the objective measurement of individual mental movement representations before training and the integration of these results into the motor imagery training. Such motor imagery training based on mental representations has been applied successfully in professional sports such as golf, volleyball, gymnastics, windsurfing, and recently in the rehabilitation of patients who have suffered a stroke.
Off-shell representations of maximally-extended supersymmetry
International Nuclear Information System (INIS)
Cox, P.H.
1985-01-01
A general theorem on the necessity of off-shell central charges in representations of maximally-extended supersymmetry (number of spinor charges - 4 x largest spin) is presented. A procedure for building larger and higher-N representations is also explored; a (noninteracting) N=8, maximum spin 2, off-shell representation is achieved. Difficulties in adding interactions for this representation are discussed
Spatially variant morphological restoration and skeleton representation.
Bouaynaya, Nidhal; Charif-Chefchaouni, Mohammed; Schonfeld, Dan
2006-11-01
The theory of spatially variant (SV) mathematical morphology is used to extend and analyze two important image processing applications: morphological image restoration and skeleton representation of binary images. For morphological image restoration, we propose the SV alternating sequential filters and SV median filters. We establish the relation of SV median filters to the basic SV morphological operators (i.e., SV erosions and SV dilations). For skeleton representation, we present a general framework for the SV morphological skeleton representation of binary images. We study the properties of the SV morphological skeleton representation and derive conditions for its invertibility. We also develop an algorithm for the implementation of the SV morphological skeleton representation of binary images. The latter algorithm is based on the optimal construction of the SV structuring element mapping designed to minimize the cardinality of the SV morphological skeleton representation. Experimental results show the dramatic improvement in the performance of the SV morphological restoration and SV morphological skeleton representation algorithms in comparison to their translation-invariant counterparts.
Distorted representation in visual tourism research
DEFF Research Database (Denmark)
Jensen, Martin Trandberg
2016-01-01
how photographic materialities, performativities and sensations contribute to new tourism knowledges. While highlighting the potential of distorted representation, the paper posits a cautionary note in regards to the influential role of academic journals in determining the qualities of visual data....... The paper exemplifies distorted representation through three impressionistic tales derived from ethnographic research on the European rail travel phenomenon: interrail.......Tourism research has recently been informed by non-representational theories to highlight the socio-material, embodied and heterogeneous composition of tourist experiences. These advances have contributed to further reflexivity and called for novel ways to animate representations...
When data representation compromise data security
DEFF Research Database (Denmark)
Simonsen, Eivind Ortind; Dahl, Mads Ronald
WHEN DATA REPRESENTATION COMPROMISE DATA SECURITY The workflow of transforming data into informative representations makes extensive usage of computers and software. Scientists have a conventional tradition for producing publications that include tables and graphs as data representations....... These representations can be used for multiple purposes such as publications in journals, teaching and conference material. But when created, stored and distributed in a digital form there is a risk of compromising data security. Data beyond the once used specifically to create the representation can be included...... on the internet over many years? A new legislation proposed in 2012 by the European Commission on protection of personal data will be implemented from 2015. The new law will impose sanction options ranging from a warning to a fine up to 100.000.000 EUR. We argue that this new law will lead to especially...
The representations of Lie groups and geometric quantizations
International Nuclear Information System (INIS)
Zhao Qiang
1998-01-01
In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. (orig.)
Exact results for the many-body problem in one dimension with repulsive delta-function interaction
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group S/sub N/. For some R's this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation
Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds
International Nuclear Information System (INIS)
Rusokov, B.Y.
1990-01-01
Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including non-orientable one. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities' point of view, non-orientability of the manifold is equivalent to its non-compactness
On Analog of Fourier Transform in Interior of the Light Cone
Directory of Open Access Journals (Sweden)
Tatyana Shtepina
2014-01-01
Full Text Available We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.
Identical particles, exotic statistics and braid groups
International Nuclear Information System (INIS)
Imbo, T.D.; Sudarshan, E.C.G.; Shah Imbo, C.
1990-01-01
The inequivalent quantizations of a system of n identical particles on a manifold M, dim M≥2, are in 1-1 correspondence with irreducible unitary representations of the braid group B n (M). The notion of the statistics of the particles is made precise. We give various examples where all the possible statistics for the system are determined, and find instances where the particles obey statistics different from the well-studied Bose, Fermi para- and θ-statistics. (orig.)
Boundary states in c=-2 logarithmic conformal field theory
International Nuclear Information System (INIS)
Bredthauer, Andreas; Flohr, Michael
2002-01-01
Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with central charge c=-2 in detail, we show that our method leads to consistent results. In particular, it allows to define boundary states corresponding to both, indecomposable representations as well as their irreducible subrepresentations
Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector
Emmanuel-Costa, D.; Osland, P.; Rebelo, M.N.
2016-02-23
We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability.
Invariant approach to CP in unbroken Δ(27
Directory of Open Access Journals (Sweden)
Gustavo C. Branco
2015-10-01
Full Text Available The invariant approach is a powerful method for studying CP violation for specific Lagrangians. The method is particularly useful for dealing with discrete family symmetries. We focus on the CP properties of unbroken Δ(27 invariant Lagrangians with Yukawa-like terms, which proves to be a rich framework, with distinct aspects of CP, making it an ideal group to investigate with the invariant approach. We classify Lagrangians depending on the number of fields transforming as irreducible triplet representations of Δ(27. For each case, we construct CP-odd weak basis invariants and use them to discuss the respective CP properties. We find that CP violation is sensitive to the number and type of Δ(27 representations.
Group-theoretical method in the many-beam theory of electron diffraction
International Nuclear Information System (INIS)
Kogiso, Motokazu; Takahashi, Hidewo.
1977-01-01
A group-theoretical method is developed for the many-beam dynamical theory of the symmetric Laue case. When the incident wave is directed so that the Laue point lies on a symmetric position in the reciprocal lattice, the dispersion matrix in the fundamental equation can be reduced to a block diagonal form. The transformation matrix is composed of column vectors belonging to irreducible representations of the group of the incident wave vector. Without performing reduction, the reduced form of the dispersion matrix is determined from characters of representations. Practical application is made to the case of symmorphic crystals, where general reduced forms and all solvable examples are given in terms of some geometrical factors of reciprocal lattice arrangements. (auth.)
Energy Technology Data Exchange (ETDEWEB)
Mishra, Ajay; Li, Aigen [Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 (United States); Jiang, B. W., E-mail: amishra@mail.missouri.edu, E-mail: lia@missouri.edu, E-mail: bjiang@bnu.edu.cn [Department of Astronomy, Beijing Normal University, Beijing 100875 (China)
2015-03-20
The mysterious “21 μm” emission feature seen almost exclusively in the short-lived protoplanetary nebula (PPN) phase of stellar evolution remains unidentified since its discovery two decades ago. This feature is always accompanied by the equally mysterious, unidentified “30 μm” feature and the so-called “unidentified infrared” (UIR) features at 3.3, 6.2, 7.7, 8.6, and 11.3 μm which are generally attributed to polycyclic aromatic hydrocarbon (PAH) molecules. The 30 μm feature is commonly observed in all stages of stellar evolution from the asymptotic giant branch through PPN to the planetary nebula phase. We explore the interrelations among the mysterious 21, 30 μm, and UIR features of the 21 μm sources. We derive the fluxes emitted in the observed UIR, 21, and 30 μm features from published Infrared Space Observatory or Spitzer/IRS spectra. We find that none of these spectral features correlate with each other. This argues against a common carrier (e.g., thiourea) for both the 21 μm feature and the 30 μm feature. This also does not support large PAH clusters as a possible carrier for the 21 μm feature.
Social representations about cancer
Directory of Open Access Journals (Sweden)
Andreja Cirila Škufca
2003-09-01
Full Text Available In this article we are presenting the results of the comparison study on social representations and causal attributions about cancer. We compared a breast cancer survivors group and control group without own experience of cancer of their own. Although social representations about cancer differ in each group, they are closely related to the concept of suffering, dying and death. We found differences in causal attribution of cancer. In both groups we found a category of risky behavior, which attributes a responsibility for a disease to an individual. Besides these factors we found predominate stress and psychological influences in cancer survivors group. On the other hand control group indicated factors outside the ones control e.g. heredity and environmental factors. Representations about a disease inside person's social space are important in co-shaping the individual process of coping with own disease. Since these representations are not always coherent with the knowledge of modern medicine their knowledge and appreciation in the course of treatment is of great value. We find the findingss of applied social psychology important as starting points in the therapeutic work with patients.
Realization and elimination in rational representations of behaviors
Gottimukkala, Sasanka V.; Trentelman, Hendrikus; Fiaz, Shaik
This article deals with the relationship between rational representations of linear differential systems and their state representations. In particular we study the relationship between rational representations on the one hand, and output nulling and driving variable representations on the other. In
Exploring the Structure of Spatial Representations
Madl, Tamas; Franklin, Stan; Chen, Ke; Trappl, Robert; Montaldi, Daniela
2016-01-01
It has been suggested that the map-like representations that support human spatial memory are fragmented into sub-maps with local reference frames, rather than being unitary and global. However, the principles underlying the structure of these ‘cognitive maps’ are not well understood. We propose that the structure of the representations of navigation space arises from clustering within individual psychological spaces, i.e. from a process that groups together objects that are close in these spaces. Building on the ideas of representational geometry and similarity-based representations in cognitive science, we formulate methods for learning dissimilarity functions (metrics) characterizing participants’ psychological spaces. We show that these learned metrics, together with a probabilistic model of clustering based on the Bayesian cognition paradigm, allow prediction of participants’ cognitive map structures in advance. Apart from insights into spatial representation learning in human cognition, these methods could facilitate novel computational tools capable of using human-like spatial concepts. We also compare several features influencing spatial memory structure, including spatial distance, visual similarity and functional similarity, and report strong correlations between these dimensions and the grouping probability in participants’ spatial representations, providing further support for clustering in spatial memory. PMID:27347681
Two-Dimensional Theory of Scientific Representation
Directory of Open Access Journals (Sweden)
A Yaghmaie
2013-03-01
Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.
Using Integer Manipulatives: Representational Determinism
Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla
2016-01-01
Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…
International agreements on commercial representation
Slanař, Jan
2014-01-01
The purpose of the thesis is to describe the possibilities for fixing the position of a company in the market through contracts for commercial representation with a focus to finding legal and economic impact on the company that contracted for exclusive representation.
Massless particles, electromagnetism, and Rieffel induction
International Nuclear Information System (INIS)
Landsman, N.P.; Wiedemann, U.A.
1994-06-01
The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincare groups is re-examined in the massless case. In the situation relevant to physics, it is found that these are related by Marsden-Weinstein reduction with respect to a gauge group. An analogous phenomenon is observed for classical massless relativistic particles. This symplectic reduction procedure can be ('second') quantized using a generalization of the Rieffel induction technique in operator algebra theory, which is carried through in detail for electromagnetism. Starting from the so-called Fermi representation of the field algebra generated by the free abelian gauge field, we construct a new ('rigged') sesquilinear form on the representation space, which is positive semi-definite, and given in terms of a Gaussian weak distribution (promeasure) on the gauge group (taken to be a Hilbert Lie group). This eventually constructs the algebra of observables of quantum electromagnetism (directly in its vacuum representation) as a representation of the so-called algebra of weak observables induced by the trivial representation of the gauge group. (orig.)
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Impossibility Theorem in Proportional Representation Problem
International Nuclear Information System (INIS)
Karpov, Alexander
2010-01-01
The study examines general axiomatics of Balinski and Young and analyzes existed proportional representation methods using this approach. The second part of the paper provides new axiomatics based on rational choice models. New system of axioms is applied to study known proportional representation systems. It is shown that there is no proportional representation method satisfying a minimal set of the axioms (monotonicity and neutrality).
DEFF Research Database (Denmark)
Mullins, Michael
Contemporary communicational and informational processes contribute to the shaping of our physical environment by having a powerful influence on the process of design. Applications of virtual reality (VR) are transforming the way architecture is conceived and produced by introducing dynamic...... elements into the process of design. Through its immersive properties, virtual reality allows access to a spatial experience of a computer model very different to both screen based simulations as well as traditional forms of architectural representation. The dissertation focuses on processes of the current...... representation? How is virtual reality used in public participation and how do virtual environments affect participatory decision making? How does VR thus affect the physical world of built environment? Given the practical collaborative possibilities of immersive technology, how can they best be implemented...
Congruence properties of induced representations
DEFF Research Database (Denmark)
Mayer, Dieter; Momeni, Arash; Venkov, Alexei
In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg's character. We show that the well known congruence properties of Selberg's character are equivalent to the congruence properties of the induced representations...
Knowledge Representation: A Brief Review.
Vickery, B. C.
1986-01-01
Reviews different structures and techniques of knowledge representation: structure of database records and files, data structures in computer programming, syntatic and semantic structure of natural language, knowledge representation in artificial intelligence, and models of human memory. A prototype expert system that makes use of some of these…
Vietnamese Document Representation and Classification
Nguyen, Giang-Son; Gao, Xiaoying; Andreae, Peter
Vietnamese is very different from English and little research has been done on Vietnamese document classification, or indeed, on any kind of Vietnamese language processing, and only a few small corpora are available for research. We created a large Vietnamese text corpus with about 18000 documents, and manually classified them based on different criteria such as topics and styles, giving several classification tasks of different difficulty levels. This paper introduces a new syllable-based document representation at the morphological level of the language for efficient classification. We tested the representation on our corpus with different classification tasks using six classification algorithms and two feature selection techniques. Our experiments show that the new representation is effective for Vietnamese categorization, and suggest that best performance can be achieved using syllable-pair document representation, an SVM with a polynomial kernel as the learning algorithm, and using Information gain and an external dictionary for feature selection.
International Nuclear Information System (INIS)
Swope, W.C.; Schaefer, H.F. III; Yarkony, D.R.
1980-01-01
The use of Clebsch--Gordan-type coupling coefficients for finite point groups is applied to the problem of constructing symmetrized N-electron wave functions (configurations) for use by the Hartree--Fock SCF and CI methods of determining electronic wave functions for molecular systems. The configurations are eigenfunctions of electronic spin operators, and transform according to a particular irreducible representation of the relevant group of spatial operations which leave the Born--Oppenheimer Hamiltonian invariant. The method proposed for constructing the configurations involves a genealogical coupling procedure. It is particularly useful for studies of molecules which belong to a group which has multiply degenerate irreducible representations. The advantage of the method is that it results in configurations which are real linear combinations of determinants of real symmetry orbitals. This procedure for constructing configurations also allows for the identification of configurations which have no matrix element of the Hamiltonian with a reference configuration. It is therefore possible to construct a Hartree--Fock interacting space of configurations which can speed the convergence of a CI wave function. The coupling method is applied to a study of the ground and two excited electronic states of BH 3 in its D/sub 3h/ geometry. The theoretical approach involved Hartree--Fock SCF calculations followed by single and double substitution CI calculations, both of which employed double-zeta plus polarization quality basis sets
Tippett, Christine Diane
Scientific knowledge is constructed and communicated through a range of forms in addition to verbal language. Maps, graphs, charts, diagrams, formulae, models, and drawings are just some of the ways in which science concepts can be represented. Representational competence---an aspect of visual literacy that focuses on the ability to interpret, transform, and produce visual representations---is a key component of science literacy and an essential part of science reading and writing. To date, however, most research has examined learning from representations rather than learning with representations. This dissertation consisted of three distinct projects that were related by a common focus on learning from visual representations as an important aspect of scientific literacy. The first project was the development of an exploratory framework that is proposed for use in investigations of students constructing and interpreting multimedia texts. The exploratory framework, which integrates cognition, metacognition, semiotics, and systemic functional linguistics, could eventually result in a model that might be used to guide classroom practice, leading to improved visual literacy, better comprehension of science concepts, and enhanced science literacy because it emphasizes distinct aspects of learning with representations that can be addressed though explicit instruction. The second project was a metasynthesis of the research that was previously conducted as part of the Explicit Literacy Instruction Embedded in Middle School Science project (Pacific CRYSTAL, http://www.educ.uvic.ca/pacificcrystal). Five overarching themes emerged from this case-to-case synthesis: the engaging and effective nature of multimedia genres, opportunities for differentiated instruction using multimodal strategies, opportunities for assessment, an emphasis on visual representations, and the robustness of some multimodal literacy strategies across content areas. The third project was a mixed
Women and political representation.
Rathod, P B
1999-01-01
A remarkable progress in women's participation in politics throughout the world was witnessed in the final decade of the 20th century. According to the Inter-Parliamentary Union report, there were only eight countries with no women in their legislatures in 1998. The number of women ministers at the cabinet level worldwide doubled in a decade, and the number of countries without any women ministers dropped from 93 to 48 during 1987-96. However, this progress is far from satisfactory. Political representation of women, minorities, and other social groups is still inadequate. This may be due to a complex combination of socioeconomic, cultural, and institutional factors. The view that women's political participation increases with social and economic development is supported by data from the Nordic countries, where there are higher proportions of women legislators than in less developed countries. While better levels of socioeconomic development, having a women-friendly political culture, and higher literacy are considered favorable factors for women's increased political representation, adopting one of the proportional representation systems (such as a party-list system, a single transferable vote system, or a mixed proportional system with multi-member constituencies) is the single factor most responsible for the higher representation of women.
General regression and representation model for classification.
Directory of Open Access Journals (Sweden)
Jianjun Qian
Full Text Available Recently, the regularized coding-based classification methods (e.g. SRC and CRC show a great potential for pattern classification. However, most existing coding methods assume that the representation residuals are uncorrelated. In real-world applications, this assumption does not hold. In this paper, we take account of the correlations of the representation residuals and develop a general regression and representation model (GRR for classification. GRR not only has advantages of CRC, but also takes full use of the prior information (e.g. the correlations between representation residuals and representation coefficients and the specific information (weight matrix of image pixels to enhance the classification performance. GRR uses the generalized Tikhonov regularization and K Nearest Neighbors to learn the prior information from the training data. Meanwhile, the specific information is obtained by using an iterative algorithm to update the feature (or image pixel weights of the test sample. With the proposed model as a platform, we design two classifiers: basic general regression and representation classifier (B-GRR and robust general regression and representation classifier (R-GRR. The experimental results demonstrate the performance advantages of proposed methods over state-of-the-art algorithms.
Lifts of matroid representations over partial fields
Pendavingh, R.A.; Zwam, van S.H.M.
2010-01-01
There exist several theorems which state that when a matroid is representable over distinct fields F1,...,Fk , it is also representable over other fields. We prove a theorem, the Lift Theorem, that implies many of these results. First, parts of Whittle's characterization of representations of
The semantic representation of prejudice and stereotypes.
Bhatia, Sudeep
2017-07-01
We use a theory of semantic representation to study prejudice and stereotyping. Particularly, we consider large datasets of newspaper articles published in the United States, and apply latent semantic analysis (LSA), a prominent model of human semantic memory, to these datasets to learn representations for common male and female, White, African American, and Latino names. LSA performs a singular value decomposition on word distribution statistics in order to recover word vector representations, and we find that our recovered representations display the types of biases observed in human participants using tasks such as the implicit association test. Importantly, these biases are strongest for vector representations with moderate dimensionality, and weaken or disappear for representations with very high or very low dimensionality. Moderate dimensional LSA models are also the best at learning race, ethnicity, and gender-based categories, suggesting that social category knowledge, acquired through dimensionality reduction on word distribution statistics, can facilitate prejudiced and stereotyped associations. Copyright © 2017 Elsevier B.V. All rights reserved.
Computability and Representations of the Zero Set
P.J. Collins (Pieter)
2008-01-01
htmlabstractIn this note we give a new representation for closed sets under which the robust zero set of a function is computable. We call this representation the component cover representation. The computation of the zero set is based on topological index theory, the most powerful tool for finding
Factorial representations of path groups
International Nuclear Information System (INIS)
Albeverio, S.; Hoegh-Krohn, R.; Testard, D.; Vershik, A.
1983-11-01
We give the reduction of the energy representation of the group of mappings from I = [ 0,1 ], S 1 , IRsub(+) or IR into a compact semi simple Lie group G. For G = SU(2) we prove the factoriality of the representation, which is of type III in the case I = IR
Scientific Representation and Science Learning
Matta, Corrado
2014-01-01
In this article I examine three examples of philosophical theories of scientific representation with the aim of assessing which of these is a good candidate for a philosophical theory of scientific representation in science learning. The three candidate theories are Giere's intentional approach, Suárez's inferential approach and Lynch and…
Anharmonic potential in the oscillator representation
International Nuclear Information System (INIS)
Dineykhan, M.; Efimov, G.V.
1994-01-01
In the non relativistic and relativized Schroedinger equation the Wick ordering method called the oscillator representation is proposed to calculate the energy spectrum for a wide class of potentials allowing the existence of a bound state. The oscillator representation method gives a unique regular way to describe and calculate the energy levels of ground as well as orbital and radial excitation states for a wide class of potentials. The results of the zeroth approximation oscillator representation are in good agreement with the exact values for the anharmonic potentials. The oscillator representation method was applied to the relativized Schroedinger equation too. The perturbation series converges fairly fast, i.e., the highest perturbation corrections over the interaction Hamiltonian are small enough. 29 refs.; 4 tabs. (author)
Line group techniques in description of the structural phase transitions in some superconductors
Energy Technology Data Exchange (ETDEWEB)
Meszaros, C.; Bankuti, J. [Roland Eoetvoes Univ., Budapest (Hungary); Balint, A. [Univ. of Agricultural Sciences, Goedoello (Hungary)
1994-12-31
The main features of the theory of line groups, and their irreducible representations are briefly discussed, as well as the most important applications of them. A new approach in the general symmetry analysis of the modulated systems is presented. It is shown, that the line group formalism could be a very effective tool in the examination of the structural phase transitions in High Temperature Superconductors. As an example, the material YBa{sub 2}Cu{sub 3}O{sub 7-x} is discussed briefly.
Discrete symmetries in the Weyl expansion for quantum billiards
International Nuclear Information System (INIS)
Pavloff, N.
1994-01-01
2 and 3 dimensional quantum billiards with discrete symmetries are considered. The boundary condition is either Dirichlet or Neumann. The first terms of the Weyl expansion are derived for the level density projected onto the irreducible representations of the symmetry group. The formulae require only the knowledge of the character table of the group and the geometrical properties (such as surface, perimeter etc.) of sub-parts of the billiard invariant under a group transformation. (author). 17 refs., 1 fig., 1 tab
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
Self-duality in generalized Lorentz superspaces
International Nuclear Information System (INIS)
Devchand, C.; Nuyts, J.
1996-12-01
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspace are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures. (author). 4 refs
Quantization of a relativistic particle on the SL(2.R) manifold based on Hamiltonian reduction
International Nuclear Information System (INIS)
Jorjadze, G.; O'Raifeartaigh, L.; Tsutsui, I.
1994-07-01
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2.R) group manifold. Applied to the cotangent bundle of SL(2.R). the method of Hamiltonian reduction allows us to split the reduced system into two coadjoint orbits of the group. We find that the Hilbert space consists of states given by the discrete series of the unitary irreducible representations of SL(2.R). and with a positive-definite, discrete spectrum. (author)
Physical Consequences of Mathematical Principles
Directory of Open Access Journals (Sweden)
Comay E.
2009-10-01
Full Text Available Physical consequences are derived from the following mathematical structures: the variational principle, Wigner’s classifications of the irreducible representations of the Poincar ́ e group and the duality invariance of the homogeneous Maxwell equations. The analysis is carried out within the validity domain of special relativity. Hierarchical re- lations between physical theories are used. Some new results are pointed out together with their comparison with experimental data. It is also predicted that a genuine Higgs particle will not be detected.
Robustness of regularities for energy centroids in the presence of random interactions
International Nuclear Information System (INIS)
Zhao, Y.M.; Arima, A.; Yoshida, N.; Ogawa, K.; Yoshinaga, N.; Kota, V. K. B.
2005-01-01
In this paper we study energy centroids such as those with fixed spin and isospin and those with fixed irreducible representations for both bosons and fermions, in the presence of random two-body and/or three-body interactions. Our results show that regularities of energy centroids of fixed-spin states reported in earlier works are very robust in these more complicated cases. We suggest that these behaviors might be intrinsic features of quantum many-body systems interacting by random forces
(Self)-representations on youtube
Simonsen, Thomas Mosebo
2011-01-01
This paper examines forms of self-representation on YouTube with specific focus on Vlogs (Video blogs). The analytical scope of the paper is on how User-generated Content on YouTube initiates a certain kind of audiovisual representation and a particular interpretation of reality that can be distinguished within Vlogs. This will be analysed through selected case studies taken from a representative sample of empirically based observations of YouTube videos. The analysis includes a focus on how ...
Shared Representations and the Translation Process
DEFF Research Database (Denmark)
Schaeffer, Moritz; Carl, Michael
2015-01-01
The purpose of the present chapter is to investigate automated processing during translation. We provide evidence from a translation priming study which suggests that translation involves activation of shared lexico-semantic and syntactical representations, i.e., the activation of features of both...... source and target language items which share one single cognitive representation. We argue that activation of shared representations facilitates automated processing. The chapter revises the literal translation hypothesis and the monitor model (Ivir 1981; Toury 1995; Tirkkonen-Condit 2005), and re...
Shared Representations and the Translation Process
DEFF Research Database (Denmark)
Schaeffer, Moritz; Carl, Michael
2013-01-01
The purpose of the present paper is to investigate automated processing during translation. We provide evidence from a translation priming study which suggests that translation involves activation of shared lexico-semantic and syntactical representations, i.e., the activation of features of both...... source and target language items which share one single cognitive representation. We argue that activation of shared representations facilitates automated processing. The paper revises the literal translation hypothesis and the monitor model (Ivir 1981; Toury 1995; Tirkkonen-Condit 2005), and re...
Representation and redistribution in federations.
Dragu, Tiberiu; Rodden, Jonathan
2011-05-24
Many of the world's most populous democracies are political unions composed of states or provinces that are unequally represented in the national legislature. Scattered empirical studies, most of them focusing on the United States, have discovered that overrepresented states appear to receive larger shares of the national budget. Although this relationship is typically attributed to bargaining advantages associated with greater legislative representation, an important threat to empirical identification stems from the fact that the representation scheme was chosen by the provinces. Thus, it is possible that representation and fiscal transfers are both determined by other characteristics of the provinces in a specific country. To obtain an improved estimate of the relationship between representation and redistribution, we collect and analyze provincial-level data from nine federations over several decades, taking advantage of the historical process through which federations formed and expanded. Controlling for a variety of country- and province-level factors and using a variety of estimation techniques, we show that overrepresented provinces in political unions around the world are rather dramatically favored in the distribution of resources.
Representations for Supporting Students' Context Awareness
DEFF Research Database (Denmark)
Demetriadis, Stavros N.; Papadopoulos, Pantelis M.
2005-01-01
The context of the specific situation where knowledge is applied affects significantly the problem solving process by forcing people to negotiate and reconsider the priorities of their mental representations and problem solving operators, in relation to this process. In this work we argue...... that students’ context awareness can significantly be enhanced by the use of appropriate external representations which guide them to activate context inducing cognitive processes. By embedding such representations in a case based learning environment we expect to guide students’ processing of the rich...... in contextual information material, in a way that improves both their context awareness and metacontextual competence. After presenting a context model, we discuss the design of such representations based on this model and explain why we expect that their use in a learning situation would enhance context...
On the Benefits of Divergent Search for Evolved Representations
DEFF Research Database (Denmark)
Lehman, Joel; Risi, Sebastian; Stanley, Kenneth O
2012-01-01
Evolved representations in evolutionary computation are often fragile, which can impede representation-dependent mechanisms such as self-adaptation. In contrast, evolved representations in nature are robust, evolvable, and creatively exploit available representational features. This paper provide...
Quantum Hamiltonian reduction and conformal field theories
International Nuclear Information System (INIS)
Bershadsky, M.
1991-01-01
It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity
Spectral representations of neutron-star equations of state
International Nuclear Information System (INIS)
Lindblom, Lee
2010-01-01
Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral representations are also efficient, in the sense that only a few spectral coefficients are generally required to represent neutron-star equations of state quiet accurately. This accuracy and efficiency is illustrated by constructing spectral fits to a large collection of 'realistic' neutron-star equations of state.
Mazman, Alper
2010-01-01
The main focus of this thesis is the representation of jazz music and its musicians, and the ways in which American (black and white) critics, novelists, and musicians interpret this music from the development of bebop to free jazz. My aim is to reveal the complexities of the dialogue between white and black representations of jazz, as well as among the self-representations of African American musicians. To this end, I discuss the discourses of jazz that are embedded within the broader cultur...
A polygon soup representation for free viewpoint video
Colleu, T.; Pateux, S.; Morin, L.; Labit, C.
2010-02-01
This paper presents a polygon soup representation for multiview data. Starting from a sequence of multi-view video plus depth (MVD) data, the proposed representation takes into account, in a unified manner, different issues such as compactness, compression, and intermediate view synthesis. The representation is built in two steps. First, a set of 3D quads is extracted using a quadtree decomposition of the depth maps. Second, a selective elimination of the quads is performed in order to reduce inter-view redundancies and thus provide a compact representation. Moreover, the proposed methodology for extracting the representation allows to reduce ghosting artifacts. Finally, an adapted compression technique is proposed that limits coding artifacts. The results presented on two real sequences show that the proposed representation provides a good trade-off between rendering quality and data compactness.
METHODS FOR THE REPRESENTATION OF THE HELICOIDAL SURFACE
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SCURTU Liviu-Iacob
2017-05-01
Full Text Available In this paper there are presented the graphical methods to determine the parameters of an helicoidal stairs. The first part of this paper shows the used methods to generate the helicoidal curves using descriptive geometry methods. It has represented the state of the art of the generation of a helical surface studies. The second part of this study shows the helical stairs surface representation using descriptive geometry methods. For the representation of the helicoidal stairs are used two projections, the front and top view. A method of the stairs representation is solved using CAD modelling dedicated software. Following the helical surface representation in both methods, has been achieved a comparative study by using two representation methods. Conclusions about these two representation methods are presented in the end of this paper.
Locally analytic vectors in representations of locally
Emerton, Matthew J
2017-01-01
The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various "radii of analyticity"). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.
Pioneers of representation theory
Curtis, Charles W
1999-01-01
The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927). Burnside soon developed his own approach to representations of finite groups. In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory. They were soon joined in this enterprise by Issai Schur (1875-1941) and some years later, by Richard Brauer (1901-1977). These mathematicians' pioneering research is the subject of this book. It presents an account of the early history of representation theory through an analysis of the published work of the principals and others with whom the principals' work was interwoven. Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject. An introductor...
On Representation in Information Theory
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Joseph E. Brenner
2011-09-01
Full Text Available Semiotics is widely applied in theories of information. Following the original triadic characterization of reality by Peirce, the linguistic processes involved in information—production, transmission, reception, and understanding—would all appear to be interpretable in terms of signs and their relations to their objects. Perhaps the most important of these relations is that of the representation-one, entity, standing for or representing some other. For example, an index—one of the three major kinds of signs—is said to represent something by being directly related to its object. My position, however, is that the concept of symbolic representations having such roles in information, as intermediaries, is fraught with the same difficulties as in representational theories of mind. I have proposed an extension of logic to complex real phenomena, including mind and information (Logic in Reality; LIR, most recently at the 4th International Conference on the Foundations of Information Science (Beijing, August, 2010. LIR provides explanations for the evolution of complex processes, including information, that do not require any entities other than the processes themselves. In this paper, I discuss the limitations of the standard relation of representation. I argue that more realistic pictures of informational systems can be provided by reference to information as an energetic process, following the categorial ontology of LIR. This approach enables naïve, anti-realist conceptions of anti-representationalism to be avoided, and enables an approach to both information and meaning in the same novel logical framework.
Directory of Open Access Journals (Sweden)
Suci Furwati
2017-08-01
Full Text Available Abstract: Students who have good conceptual acquisition will be able to represent the concept by using multi representation. This study aims to determine the improvement of students' understanding of the concept of Newton's Law material, and the quality of representation used in solving problems on Newton's Law material. The results showed that the concept acquisition of students increased from the average of 35.32 to 78.97 with an effect size of 2.66 (strong and N-gain of 0.68 (medium. The quality of each type of student representation also increased from level 1 and level 2 up to level 3. Key Words: concept aquisition, represetation quality, multi representation learning, Newton’s Law Abstrak: Siswa yang memiliki penguasaan konsep yang baik akan mampu merepresentasikan konsep dengan menggunakan multi representasi. Penelitian ini bertujuan untuk mengetahui peningkatan pemahaman konsep siswa SMP pada materi Hukum Newton, dan kualitas representasi yang digunakan dalam menyelesaikan masalah pada materi Hukum Newton. Hasil penelitian menunjukkan bahwa penguasaan konsep siswa meningkat dari rata-rata 35,32 menjadi 78,97 dengan effect size sebesar 2,66 (kuat dan N-gain sebesar 0,68 (sedang. Kualitas tiap jenis representasi siswa juga mengalami peningkatan dari level 1 dan level 2 naik menjadi level 3. Kata kunci: hukum Newton, kualitas representasi, pemahaman konsep, pembelajaran multi representasi
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Condensed matter optical spectroscopy an illustrated introduction
Ionita, Iulian
2014-01-01
Molecular Symmetry and the Symmetry GroupsSymmetry Elements and Symmetry OperationsPoint Groups and Molecular SymmetrySymmetry Classification of MoleculesMatrix Representation of Symmetry TransformationGroup RepresentationsProperties of Irreducible RepresentationsTables of CharactersSymmetry of Crystals and Space GroupsRotation Groups and OperatorsExamples of SymmetryStudy QuestionsReferencesCrystal Field TheoryStates and Energies of Free Atoms and IonsOptical Spectra of Ionic CrystalsImpurities in Crystal Lattice: Splitting of Levels and Terms in Lattice SymmetryWeak Crystalline Field of Octahedral SymmetryEffect of a Weak Crystalline Field of Lower SymmetriesSplitting of Multielectron dn Configurations in the Crystalline FieldJahn-Teller EffectConstruction of Energy-Level DiagramsTanabe-Sugano DiagramsExample of the Co IonLimitations of the Crystal Field TheoryStudy QuestionsReferencesSymmetry and Molecular Orbitals TheoryMolecular OrbitalsHybridization Scheme for σ OrbitalsHybridization Scheme for π Orbi...
The three-dimensional origin of the classifying algebra
International Nuclear Information System (INIS)
Fuchs, Juergen; Schweigert, Christoph; Stigner, Carl
2010-01-01
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra. We show how this algebra arises naturally from the three-dimensional geometry of factorization of correlators of bulk fields on the disk. This allows us to derive explicit expressions for the structure constants of the classifying algebra as invariants of ribbon graphs in the three-manifold S 2 xS 1 . Our result unravels a precise relation between intertwiners of the action of the mapping class group on spaces of conformal blocks and boundary conditions in rational conformal field theories.
Twisted spin Sutherland models from quantum Hamiltonian reduction
International Nuclear Information System (INIS)
Feher, L; Pusztai, B G
2008-01-01
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems associated with arbitrary finite-dimensional irreducible representations of the group by using the symmetry induced by twisted conjugations are described in detail. These systems generically yield integrable Sutherland-type many-body models with spin, which are called twisted spin Sutherland models if the underlying twisted conjugations are built on non-trivial Dynkin diagram automorphisms. The spectra of these models can be calculated, in principle, by solving certain Clebsch-Gordan problems, and the result is presented for the models associated with the symmetric tensorial powers of the defining representation of SU(N)
Representations of G+++ and the role of space-time
International Nuclear Information System (INIS)
Kleinschmidt, A.; West, P.
2004-01-01
We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++ . In particular, for E 8 +++ , this applies to all its fundamental representations. However, there are some important examples, such as A N-3 +++ , where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++ . Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions. (author)
48 CFR 2009.570-4 - Representation.
2010-10-01
... type required by the organizational conflicts of interest representation provisions has previously been... ACQUISITION PLANNING CONTRACTOR QUALIFICATIONS Organizational Conflicts of Interest 2009.570-4 Representation... whether situations or relationships exist which may constitute organizational conflicts of interest with...
Public Library Representations and Internet Appropriations
Directory of Open Access Journals (Sweden)
Paula Sequeiros
2013-11-01
Full Text Available May the changes in the representations of the public library be propitiated by readers' appropriations of the Internet? To answer this question, a theoretically-driven and empirically-based research was developed in a public library in Portugal, combining the analysis of documents uses, the ethnography of space and Internet use, of social relations developed while reading, with the analysis of representations of the public library. No clear-cut association emerged between social-demographics or user profiles, and representations, in general. No disruptive Internet "impact" was found: Internet use may contribute to reinforce traditional representations of the library, while it may also update and democratise other representations. If the library and the Internet are represented as synonymous, the former does not make sense without the latter; but an Internet widespread and intensive use conflicts with the image of an institution dedicated to high-brow culture. Changes in uses of the public library are, instead, clearly associated with new types of readers, which in their turn reflect changes in urban social composition. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs1401141
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
The ARES High-level Intermediate Representation
Energy Technology Data Exchange (ETDEWEB)
Moss, Nicholas David [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-03-03
The LLVM intermediate representation (IR) lacks semantic constructs for depicting common high-performance operations such as parallel and concurrent execution, communication and synchronization. Currently, representing such semantics in LLVM requires either extending the intermediate form (a signi cant undertaking) or the use of ad hoc indirect means such as encoding them as intrinsics and/or the use of metadata constructs. In this paper we discuss a work in progress to explore the design and implementation of a new compilation stage and associated high-level intermediate form that is placed between the abstract syntax tree and when it is lowered to LLVM's IR. This highlevel representation is a superset of LLVM IR and supports the direct representation of these common parallel computing constructs along with the infrastructure for supporting analysis and transformation passes on this representation.
Diabatic and adiabatic representations for atomic collision processes
International Nuclear Information System (INIS)
Delos, J.B.; Thorson, W.R.
1979-01-01
A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity-dependent couplings in slow collisions, including the effects of electron-translation factors (ETF's). We compare the couplings arising from atomic representations and atomic ETF's with those arising from molecular representations and ''switching function'' ETF's. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then show that an acceptable general definition of a diabatic representation is provided by the condition P+A=0, where P is the usual nonadiabatic coupling matrix and A represents corrections to it arising from electron translation factors (ETF's). Two distinct types of diabatic representation result, depending on the definition taken for A. States that undergo no deformation are called F diabatic; those that have no velocity-dependent couplings are called M diabatic. Finally, we discuss the properties of representations that are partially diabatic and partially adiabatic, and we give some rules for the construction of representations that should be nearly optimal for describing many types of collision processes
Representations of Multiple-Valued Logic Functions
Stankovic, Radomir S
2012-01-01
Compared to binary switching functions, multiple-valued functions offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible.Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for ap
Death representation of caregivers in hospice.
Andruccioli, Jessica; Russo, Maria Maffia; Bruschi, Angela; Pedrabissi, Luigi; Sarti, Donatella; Monterubbianesi, Maria Cristina; Rossi, Sabina; Rocconi, Sabina; Raffaeli, William
2012-11-01
In this study, we investigated caregiver's death representation in hospice. The results presented here are a further analysis of the data collected in our previous study, concerning the evaluation of the caregiver in hospice. The data analysis of 24 caregivers of patients hospitalized in Rimini Hospice (Italy) underlined that caregivers avoiding death representation of the patient admitted to hospice had fewer protective factors (52.3%) and more risk factors (47.7%) than caregivers nonavoiding (66.5% and 33.5%, respectively). Caregivers avoiding death representation, moreover, experienced a greater distress (58%) than those nonavoiding (42%).
2006-09-01
two weeks to arrive. Source: http://beergame.mit.edu/ Permission Granted – MIT Supply Chain Forum 2005 Professor Sterman –Sloan School of...Management - MITSource: http://web.mit.edu/jsterman/www/ SDG /beergame.html Rules of Engagement The MIT Beer Game Simulation 04-04 Slide Number 10 Professor...Sterman –Sloan School of Management - MITSource: http://web.mit.edu/jsterman/www/ SDG /beergame.html What is the Significance of Representation
Social representations of female orgasm.
Lavie-Ajayi, Maya; Joffe, Hélène
2009-01-01
This study examines women's social representations of female orgasm. Fifty semi-structured interviews were conducted with British women. The data were thematically analysed and compared with the content of female orgasm-related writing in two women's magazines over a 30-year period. The results indicate that orgasm is deemed the goal of sex with emphasis on its physiological dimension. However, the women and the magazines graft onto this scientifically driven representation the importance of relational and emotive aspects of orgasm. For the women, particularly those who experience themselves as having problems with orgasm, the scientifically driven representations induce feelings of failure, but are also resisted. The findings highlight the role played by the social context in women's subjective experience of their sexual health.
Exploration of solids based on representation systems
Directory of Open Access Journals (Sweden)
Publio Suárez Sotomonte
2011-01-01
Full Text Available This article refers to some of the findings of a research project implemented as a teaching strategy to generate environments for the learning of platonic and archimedean solids, with a group of eighth grade students. This strategy was based on the meaningful learning approach and on the use of representation systems using the ontosemiotic approach in mathematical education, as a framework for the construction of mathematical concepts. This geometry teaching strategy adopts the stages of exploration, representation-modeling, formal construction and study of applications. It uses concrete, physical and tangible materials for origami, die making, and structures for the construction of threedimensional solids considered external tangible solid representation systems, as well as computer based educational tools to design dynamic geometry environments as intangible external representation systems.These strategies support both the imagination and internal systems of representation, fundamental to the comprehension of geometry concepts.
Court representation in Russia before 1917 (historical aspect
Directory of Open Access Journals (Sweden)
Konstantin V. Ilyashenko
2015-12-01
Full Text Available Objective basing on the research and analysis of the legislation historical legal sources and other materials to study the process of formation and development of the institution of legal representation in Russia before 1917. Methods the theoretical basis of research is the works of Russian scientists on various aspects of formation development and functioning of the institution of legal representation in Russia from ancient times till 1917. The methodological basis of the research is general scientific methods historical formallogical system and general logical methods analysis synthesis induction and deduction synthesis analogy abstraction. Historicallegal formallegal logicallegal comparative legal methods were applied in the study. The author used the retrospective approach to the study of the issues of legal representation in Russia. Results basing on analysis of normative legal acts regulating relations in the sphere of judicial representation and various doctrinal sources the author has examined the process of the formation and development of the legal representation institution in Russia before 1917 raised the question of providing legal assistance in prerevolutionary Russia. An analogy is drawn between the prerevolutionary legal regulation of the legal representation institution and the modern legislation regulating this legal institution. The conclusion is made about the inadequacy of prerevolutionary legislation regulating relations in the sphere of judicial representation as well as the modern legal regulation of relations in this sphere. It is established that the judicial reform of 1864 improved regulation in this sphere but still did not solve all the problems in this area. The relevance of the study is due to the topicality and the constitutional importance of legal representation for the entire Russian society the need to examine the origins of this legal phenomenon as well as the fact that the institution of legal representation
Uniformly bounded representations of the Lorentz groups
International Nuclear Information System (INIS)
Brega, A.O.
1982-01-01
For the Lorentz group G = SO/sub e/(n + 1, 1)(ngreater than or equal to 2) the author constructs a family of uniformly bounded representations by means of analytically continuing a certain normalization of the unitary principal series. The method the author uses relies on an analysis of various operators under a Mellin transform and extends earlier work of E.N. Wilson. In a series of papers Kunze and Stein initiated the theory of uniformly bounded representations of semisimple Lie groups; the starting point is the unitary principal series T(sigma,s) obtained in a certain subgroup M of G and a purely imaginary number s. From there Kunze and Stein constructed families of representations R(sigma,s) depending analytically on a parameter s in a domain D of C containing the imaginary axis which are unitarily equilvalent to T(sigma,s) for s contained in the set of imaginary numbers and whose operator norms are uniformly bounded for each s in D. In the case of the Lorentz groups SO/sub e/(n + 1, 1)(ngreater than or equal to2) and the trivial representation 1 of M, E.N. Wilson obtained such a family R(1,s) for the domain D = [s contained in the set of C: absolute value Re(s) Vertical Bar2]. For this domain D and for any representation sigma of M the author provides a family R(sigma,s) of uniformly bounded representations analytically continuing T(sigma,s), thereby generalizing Wilson's work. The author has also investigated certain symmetry properties of the representations R(sigma,s) under the action of the Weyl group. The trivial representation is Weyl group invariant and the family R(1,s) obtained by Wilson satisfies R(1,s) = R(1,-s) reflecting this. Obtained was the analogous result R(sigma,s) = R(sigma,-s) for some well known representations sigma that are Weyl group invariant. This involves the explicit computation of certain constants arising in the Fourier transforms of intertwining operators
Octonionic matrix representation and electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Chanyal, B. C. [Kumaun University, S. S. J. Campus, Almora (India)
2014-12-15
Keeping in mind the important role of octonion algebra, we have obtained the electromagnetic field equations of dyons with an octonionic 8 x 8 matrix representation. In this paper, we consider the eight - dimensional octonionic space as a combination of two (external and internal) four-dimensional spaces for the existence of magnetic monopoles (dyons) in a higher-dimensional formalism. As such, we describe the octonion wave equations in terms of eight components from the 8 x 8 matrix representation. The octonion forms of the generalized potential, fields and current source of dyons in terms of 8 x 8 matrix are discussed in a consistent manner. Thus, we have obtained the generalized Dirac-Maxwell equations of dyons from an 8x8 matrix representation of the octonion wave equations in a compact and consistent manner. The generalized Dirac-Maxwell equations are fully symmetric Maxwell equations and allow for the possibility of magnetic charges and currents, analogous to electric charges and currents. Accordingly, we have obtained the octonionic Dirac wave equations in an external field from the matrix representation of the octonion-valued potentials of dyons.
Additive and polynomial representations
Krantz, David H; Suppes, Patrick
1971-01-01
Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz
Energy Technology Data Exchange (ETDEWEB)
Hoff da Silva, J.M.; Rogerio, R.J.B. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Villalobos, C.H.C. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2017-07-15
A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein-Dirac system that provides the spacetime generated by a fermion. (orig.)
Klink, William H.; Schweiger, Wolfgang
2018-03-01
This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.
Para-bosons and Para-fermions in Quantum Mechanics
International Nuclear Information System (INIS)
Cattani, M.S.D.; Fernandes, N.C.
1982-01-01
Within the framework of the ordinary quantum mechanics, a detailed study of the energy eigenfunctions of N identical particles using the irreducible representations of the permutation group in the Hilbert space is performed. It is shown that the para-states, as occurs with the boson and fermion states, are compatible with the postulates of quantum mechanics and with the principle of indistinguishability. A mathematical support for the existence of para-bosons and para-fermions is given. Gentile's quantum statistics is, in a certain sense, justified. (Author) [pt
The weak-scale hierarchy and discrete symmetries
International Nuclear Information System (INIS)
Haba, Naoyuki; Matsuoka, Takeo; Hattori, Chuichiro; Matsuda, Masahisa; Mochinaga, Daizo.
1996-01-01
In the underlying Planck scale theory, we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak-scale hierarchy under control. Under the discrete symmetry the μ-problem and the tadpole problem can be solved simultaneously without relying on some fine-tuning of parameters. Instead, it is required that doublet Higgs and color-triplet Higgs fields reside in different irreducible representations of the gauge symmetry group at the Planck scale and that they have distinct charges of the discrete symmetry group. (author)
Conformal theories, grassmannians and soliton hierarchies. Pt. 1
International Nuclear Information System (INIS)
De Concini, C.; Fucito, F.; Tirozzi, B.
1989-01-01
We formulate conformal field theories on the infinite-dimensional grassmannian manifold. Besides recovering the known results for the central charge and correlation functions of the b-c system this formalism immediately lends itself to further generalization. The grassmannian manifold is in fact an ad hoc model for the geometrical interpretation of the irreducible representations of an infinite-dimensional Kac-Moody algebra which, in turn, admit an intertwining action of a Virasoro algebra. We further give a proof of bosonization from a purely grassmannian point of view. (orig.)
The Interaction between Semantic Representation and Episodic Memory.
Fang, Jing; Rüther, Naima; Bellebaum, Christian; Wiskott, Laurenz; Cheng, Sen
2018-02-01
The experimental evidence on the interrelation between episodic memory and semantic memory is inconclusive. Are they independent systems, different aspects of a single system, or separate but strongly interacting systems? Here, we propose a computational role for the interaction between the semantic and episodic systems that might help resolve this debate. We hypothesize that episodic memories are represented as sequences of activation patterns. These patterns are the output of a semantic representational network that compresses the high-dimensional sensory input. We show quantitatively that the accuracy of episodic memory crucially depends on the quality of the semantic representation. We compare two types of semantic representations: appropriate representations, which means that the representation is used to store input sequences that are of the same type as those that it was trained on, and inappropriate representations, which means that stored inputs differ from the training data. Retrieval accuracy is higher for appropriate representations because the encoded sequences are less divergent than those encoded with inappropriate representations. Consistent with our model prediction, we found that human subjects remember some aspects of episodes significantly more accurately if they had previously been familiarized with the objects occurring in the episode, as compared to episodes involving unfamiliar objects. We thus conclude that the interaction with the semantic system plays an important role for episodic memory.
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Computer simulation as representation of knowledge in education
International Nuclear Information System (INIS)
Krekic, Valerija Pinter; Namestovski, Zolt
2009-01-01
According to Aebli's operative method (1963) and Bruner's (1974) theory of representation the development of the process of thinking in teaching has the following phases - levels of abstraction: manipulation with specific things (specific phase), iconic representation (figural phase), symbolic representation (symbolic phase). Modern information technology has contributed to the enrichment of teaching and learning processes, especially in the fields of natural sciences and mathematics and those of production and technology. Simulation appears as a new possibility in the representation of knowledge. According to Guetzkow (1972) simulation is an operative representation of reality from a relevant aspect. It is about a model of an objective system, which is dynamic in itself. If that model is material it is a simple simulation, if it is abstract it is a reflective experiment, that is a computer simulation. This present work deals with the systematization and classification of simulation methods in the teaching of natural sciences and mathematics and of production and technology with special retrospective view on computer simulations and exemplar representation of the place and the role of this modern method of cognition. Key words: Representation of knowledge, modeling, simulation, education
Inequivalent coherent state representations in group field theory
Kegeles, Alexander; Oriti, Daniele; Tomlin, Casey
2018-06-01
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.
Social representation of the kinesiotherapist profession
Directory of Open Access Journals (Sweden)
Beatrice ABALAŞE
2017-03-01
Full Text Available The scientific approach is focused on identifying the social representation of the profession of physical therapist referring to mental images of social reality to a group consensus meeting. The goal of research identifies social representation of the profession of physical therapist, on the premise that students of the Faculty of Physical Education and Sport have made a social representation of the profession of physical therapist in accordance with the description of the occupation of COR. Working method was based on the questionnaire. Interpretation of results, the first two items of the questionnaire was done through word association technique, developed by P. Verges (1 and an alternative method for determining the structure and organization of elements representation proposed by. C. Havârneanu (2. Qualitative analysis reveals that students’ specialization Physical Therapy and Special Motricity believes that a therapist uses therapy as a strategy to work, and it must be applied professionally. Respondents considered, as shown in the data collected, that this profession is subject to skills, education, cognitive baggage, all sending to knowledge, experience and passion. The core refers to the complex representation obtained thanks cognitive process by which individuals or groups in familiar transforms abstract and it integrates knowledge of their system.
Czech Academy of Sciences Publication Activity Database
Koťátko, Petr
2014-01-01
Roč. 21, č. 3 (2014), s. 282-302 ISSN 1335-0668 Institutional support: RVO:67985955 Keywords : representation * proposition * truth-conditions * belief-ascriptions * reference * externalism * fiction Subject RIV: AA - Philosophy ; Religion
How initial representations shape coupled learning processes
DEFF Research Database (Denmark)
Puranam, Phanish; Swamy, M.
2016-01-01
Coupled learning processes, in which specialists from different domains learn how to make interdependent choices among alternatives, are common in organizations. We explore the role played by initial representations held by the learners in coupled learning processes using a formal agent-based model....... We find that initial representations have important consequences for the success of the coupled learning process, particularly when communication is constrained and individual rates of learning are high. Under these conditions, initial representations that generate incorrect beliefs can outperform...... one that does not discriminate among alternatives, or even a mix of correct and incorrect representations among the learners. We draw implications for the design of coupled learning processes in organizations. © 2016 INFORMS....
Technology Focus: Multi-Representational Approaches to Equation Solving
Garofalo, Joe; Trinter, Christine
2009-01-01
Most mathematical functions can be represented in numerous ways. The main representations typically addressed in school, often referred to as "the big three," are graphical, algebraic, and numerical representations, but there are others as well (e.g., diagrams, words, simulations). These different types of representations "often illuminate…
Integral Representations of the Catalan Numbers and Their Applications
Directory of Open Access Journals (Sweden)
Feng Qi
2017-08-01
Full Text Available In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.
Improving Representational Competence with Concrete Models
Stieff, Mike; Scopelitis, Stephanie; Lira, Matthew E.; DeSutter, Dane
2016-01-01
Representational competence is a primary contributor to student learning in science, technology, engineering, and math (STEM) disciplines and an optimal target for instruction at all educational levels. We describe the design and implementation of a learning activity that uses concrete models to improve students' representational competence and…
Connectivity in the regular polytope representation
Thompson, R.J.; Van Oosterom, P.J.M.
2009-01-01
In order to be able to draw inferences about real world phenomena from a representation expressed in a digital computer, it is essential that the representation should have a rigorously correct algebraic structure. It is also desirable that the underlying algebra be familiar, and provide a close
Dynamic representations on the interactive whiteboard
van der Meij, Hans; van der Meij, Jan; de Vries, Erica; Scheiter, Katharina
2012-01-01
In this study we assessed whether presenting dynamic representations on an IWB would lead to better learning gains compared to presenting static representations. Participants were 7-8 year old primary school children learning about views (N = 151) and the water cycle (N = 182). The results showed
ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES
RUSCHENDORF, L; DEVALK, [No Value
We construct a.s. nonlinear regression representations of general stochastic processes (X(n))n is-an-element-of N. As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive
Coordinate, Momentum and Dispersion operators in Phase space representation
International Nuclear Information System (INIS)
Rakotoson, H.; Raoelina Andriambololona; Ranaivoson, R.T.R.; Raboanary, R.
2017-07-01
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works. We begin in the introduction section with a recall about the concept of representation of operators on wave function spaces. Then, we show that in the case of the phase space representation the coordinate and momentum operators can be represented either with differential operators or with matrices. The explicit expressions of both the differential operators and matrices representations are established. Multidimensional generalization of the obtained results are performed and phase space representation of dispersion operators are given.
Violence against women: adolescents’ social representations
Directory of Open Access Journals (Sweden)
Ana Márcia de Almeida Rezende
2018-02-01
Full Text Available Violence against women in affectionate intimate relationships is a serious problem that causes damages to its victims. In the social imaginary there are ways of thinking and representations that tend to trivialize this type of violence, considering it a natural practice. In this sense, this article brings a study that aimed to know the social representations elaborated by adolescents on violence against women in affectionate relationships. Data were collected through a semi-structured interview conducted with 22 adolescents, and analyzed through the content analysis technique (BARDIN, 2011. The results revealed that the adolescents represent violence against women objectified in an everyday phenomenon, which happens even in their families. They have also elaborated social representations anchored in patriarchy, in which men use violence as means to dominate partners. It was observed the need for preventive work that would make adolescents aware of patriarchal ideologies present in the society, helping them to construct social representations based on respect and gender equity.
Paired structures in knowledge representation
DEFF Research Database (Denmark)
Montero, J.; Bustince, H.; Franco de los Ríos, Camilo
2016-01-01
In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here...... of the relationships between several existing knowledge representation formalisms, providing a basis from which more expressive models can be later developed....
Weighted Discriminative Dictionary Learning based on Low-rank Representation
International Nuclear Information System (INIS)
Chang, Heyou; Zheng, Hao
2017-01-01
Low-rank representation has been widely used in the field of pattern classification, especially when both training and testing images are corrupted with large noise. Dictionary plays an important role in low-rank representation. With respect to the semantic dictionary, the optimal representation matrix should be block-diagonal. However, traditional low-rank representation based dictionary learning methods cannot effectively exploit the discriminative information between data and dictionary. To address this problem, this paper proposed weighted discriminative dictionary learning based on low-rank representation, where a weighted representation regularization term is constructed. The regularization associates label information of both training samples and dictionary atoms, and encourages to generate a discriminative representation with class-wise block-diagonal structure, which can further improve the classification performance where both training and testing images are corrupted with large noise. Experimental results demonstrate advantages of the proposed method over the state-of-the-art methods. (paper)
Numerical Magnitude Representations Influence Arithmetic Learning
Booth, Julie L.; Siegler, Robert S.
2008-01-01
This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…
Representations of the Magnitudes of Fractions
Schneider, Michael; Siegler, Robert S.
2010-01-01
We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However,…
A Possible Neural Representation of Mathematical Group Structures.
Pomi, Andrés
2016-09-01
Every cognitive activity has a neural representation in the brain. When humans deal with abstract mathematical structures, for instance finite groups, certain patterns of activity are occurring in the brain that constitute their neural representation. A formal neurocognitive theory must account for all the activities developed by our brain and provide a possible neural representation for them. Associative memories are neural network models that have a good chance of achieving a universal representation of cognitive phenomena. In this work, we present a possible neural representation of mathematical group structures based on associative memory models that store finite groups through their Cayley graphs. A context-dependent associative memory stores the transitions between elements of the group when multiplied by each generator of a given presentation of the group. Under a convenient election of the vector basis mapping the elements of the group in the neural activity, the input of a vector corresponding to a generator of the group collapses the context-dependent rectangular matrix into a virtual square permutation matrix that is the matrix representation of the generator. This neural representation corresponds to the regular representation of the group, in which to each element is assigned a permutation matrix. This action of the generator on the memory matrix can also be seen as the dissection of the corresponding monochromatic subgraph of the Cayley graph of the group, and the adjacency matrix of this subgraph is the permutation matrix corresponding to the generator.
Moreno, Roxana; Ozogul, Gamze; Reisslein, Martin
2011-01-01
In 3 experiments, we examined the effects of using concrete and/or abstract visual problem representations during instruction on students' problem-solving practice, near transfer, problem representations, and learning perceptions. In Experiments 1 and 2, novice students learned about electrical circuit analysis with an instructional program that…
Visual representation of spatiotemporal structure
Schill, Kerstin; Zetzsche, Christoph; Brauer, Wilfried; Eisenkolb, A.; Musto, A.
1998-07-01
The processing and representation of motion information is addressed from an integrated perspective comprising low- level signal processing properties as well as higher-level cognitive aspects. For the low-level processing of motion information we argue that a fundamental requirement is the existence of a spatio-temporal memory. Its key feature, the provision of an orthogonal relation between external time and its internal representation, is achieved by a mapping of temporal structure into a locally distributed activity distribution accessible in parallel by higher-level processing stages. This leads to a reinterpretation of the classical concept of `iconic memory' and resolves inconsistencies on ultra-short-time processing and visual masking. The spatial-temporal memory is further investigated by experiments on the perception of spatio-temporal patterns. Results on the direction discrimination of motion paths provide evidence that information about direction and location are not processed and represented independent of each other. This suggests a unified representation on an early level, in the sense that motion information is internally available in form of a spatio-temporal compound. For the higher-level representation we have developed a formal framework for the qualitative description of courses of motion that may occur with moving objects.
Relations between grand unified and monopole theories
International Nuclear Information System (INIS)
Olive, D.I.
1983-01-01
Two kinds of interrelationships between GUTs and monopole theories are discussed: how the duality conjectures could have a bearing on understanding GUTs, and how some of the mathematical technology used in monopole studies can yield simple (Dynkin) diagrammatic rules for some of the common GUT group theory calculations. A compact notation for semisimple Lie algebras is supplied by Dynkin diagrams. Minimal fundamental weights are seen to define minimal representations into which matter may be placed, and also define a special direction for the adjoint Higgs field. Minimal weights play a special role, therefore, both in defining matter multiplets and in symmetry breaking. After considering gauge groups G broken down to U(1) X K/Z (with K semisimple) by an adjoint representation (AR) Higgs, it is asked how the representations of G will look when decomposed into irreducible representations of U(1) X K, by proving two theorems as given. The point is pedagogical: using concepts like the Weyl group, practical calculations can be performed with simple Dynkin diagrams
A representation independent propagator. Pt. 1. Compact Lie groups
International Nuclear Information System (INIS)
Tome, W.A.
1995-01-01
Conventional path integral expressions for propagators are representation dependent. Rather than having to adapt each propagator to the representation in question, it is shown that for compact Lie groups it is possible to introduce a propagator that is representation independent. For a given set of kinematical variables this propagator is a single function independent of any particular choice of fiducial vector, which monetheless, correctly propagates each element of the coherent state representation associated with these kinematical variables. Although the configuration space is in general curved, nevertheless the lattice phase-space path integral for the representation independent propagator has the form appropriate to flat space. To illustrate the general theory a representation independent propagator is explicitly constructed for the Lie group SU(2). (orig.)
The heterogeneity of mental representation: Ending the imagery debate.
Pearson, Joel; Kosslyn, Stephen M
2015-08-18
The possible ways that information can be represented mentally have been discussed often over the past thousand years. However, this issue could not be addressed rigorously until late in the 20th century. Initial empirical findings spurred a debate about the heterogeneity of mental representation: Is all information stored in propositional, language-like, symbolic internal representations, or can humans use at least two different types of representations (and possibly many more)? Here, in historical context, we describe recent evidence that humans do not always rely on propositional internal representations but, instead, can also rely on at least one other format: depictive representation. We propose that the debate should now move on to characterizing all of the different forms of human mental representation.
Naturalising Representational Content
Shea, Nicholas
2014-01-01
This paper sets out a view about the explanatory role of representational content and advocates one approach to naturalising content – to giving a naturalistic account of what makes an entity a representation and in virtue of what it has the content it does. It argues for pluralism about the metaphysics of content and suggests that a good strategy is to ask the content question with respect to a variety of predictively successful information processing models in experimental psychology and cognitive neuroscience; and hence that data from psychology and cognitive neuroscience should play a greater role in theorising about the nature of content. Finally, the contours of the view are illustrated by drawing out and defending a surprising consequence: that individuation of vehicles of content is partly externalist. PMID:24563661
Drawings as Representations of Children's Conceptions
Ehrlen, Karin
2009-01-01
Drawings are often used to obtain an idea of children's conceptions. Doing so takes for granted an unambiguous relation between conceptions and their representations in drawings. This study was undertaken to gain knowledge of the relation between children's conceptions and their representation of these conceptions in drawings. A theory of…
Student Teachers' Knowledge about Chemical Representations
Taskin, Vahide; Bernholt, Sascha; Parchmann, Ilka
2017-01-01
Chemical representations serve as a communication tool not only in exchanges between scientists but also in chemistry lessons. The goals of the present study were to measure the extent of student teachers' knowledge about chemical representations, focusing on chemical formulae and structures in particular, and to explore which factors related to…
Knowledge representation and use. II. Representations
Energy Technology Data Exchange (ETDEWEB)
Lauriere, J L
1982-03-01
The use of computers is less and less restricted to numerical and data processing. On the other hand, current software mostly contains algorithms on universes with complete information. The paper discusses a different family of programs: expert systems are designed as aids in human reasoning in various specific areas. Symbolic knowledge manipulation, uncertain and incomplete deduction capabilities, natural communication with humans in non-procedural ways are their essential features. This part is mainly a reflection and a debate about the various modes of acquisition and representation of human knowledge. 32 references.
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)
Non-commutative flux representation for loop quantum gravity
Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.
2011-09-01
The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.
Noel, Yves; D'arco, Philippe; Demichelis, Raffaella; Zicovich-Wilson, Claudio M; Dovesi, Roberto
2010-03-01
Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented. (c) 2009 Wiley Periodicals, Inc.
Representational momentum in memory for pitch.
Freyd, J J; Kelly, M H; DeKay, M L
1990-11-01
When a visual pattern is displayed at successively different orientations such that a rotation or translation is implied, an observer's memory for the final position is displaced forward. This phenomenon of representational momentum shares some similarities with physical momentum. For instance, the amount of memory shift is proportional to the implied velocity of the inducing display; representational momentum is specifically proportional to the final, not the average, velocity; representational momentum follows a continuous stopping function for the first 250 ms or so of the retention interval. In a previous paper (Kelly & Freyd, 1987) we demonstrated a forward memory asymmetry using implied changes in pitch, for subjects without formal musical training. In the current paper we replicate our earlier finding and show that the forward memory asymmetry occurs for subjects with formal musical training as well (Experiment 1). We then show the structural similarity between representational momentum in memory for pitch with previous reports of parametric effects using visual stimuli. We report a velocity effect for auditory momentum (Experiment 2), we demonstrate specifically that the velocity effect depends on the implied acceleration (Experiment 3), and we show that the stopping function for auditory momentum is qualitatively the same as that for visual momentum (Experiment 4). We consider the implications of these results for theories of mental representation.
In defense of abstract conceptual representations.
Binder, Jeffrey R
2016-08-01
An extensive program of research in the past 2 decades has focused on the role of modal sensory, motor, and affective brain systems in storing and retrieving concept knowledge. This focus has led in some circles to an underestimation of the need for more abstract, supramodal conceptual representations in semantic cognition. Evidence for supramodal processing comes from neuroimaging work documenting a large, well-defined cortical network that responds to meaningful stimuli regardless of modal content. The nodes in this network correspond to high-level "convergence zones" that receive broadly crossmodal input and presumably process crossmodal conjunctions. It is proposed that highly conjunctive representations are needed for several critical functions, including capturing conceptual similarity structure, enabling thematic associative relationships independent of conceptual similarity, and providing efficient "chunking" of concept representations for a range of higher order tasks that require concepts to be configured as situations. These hypothesized functions account for a wide range of neuroimaging results showing modulation of the supramodal convergence zone network by associative strength, lexicality, familiarity, imageability, frequency, and semantic compositionality. The evidence supports a hierarchical model of knowledge representation in which modal systems provide a mechanism for concept acquisition and serve to ground individual concepts in external reality, whereas broadly conjunctive, supramodal representations play an equally important role in concept association and situation knowledge.
Personal neglect-a disorder of body representation?
Baas, Ulrike; de Haan, Bianca; Grässli, Tanja; Karnath, Hans-Otto; Mueri, René; Perrig, Walter J; Wurtz, Pascal; Gutbrod, Klemens
2011-04-01
The cognitive mechanisms underlying personal neglect are not well known. One theory postulates that personal neglect is due to a disorder of contralesional body representation. In the present study, we have investigated whether personal neglect is best explained by impairments in the representation of the contralesional side of the body, in particular, or a dysfunction of the mental representation of the contralesional space in general. For this, 22 patients with right hemisphere cerebral lesions (7 with personal neglect, 15 without personal neglect) and 13 healthy controls have been studied using two experimental tasks measuring representation of the body and extrapersonal space. In the tasks, photographs of left and right hands as well as left and right rear-view mirrors presented from the front and the back had to be judged as left or right. Our results show that patients with personal neglect made more errors when asked to judge stimuli of left hands and left rear-view mirrors than either patients without personal neglect or healthy controls. Furthermore, regression analyses indicated that errors in interpreting left hands were the best predictor of personal neglect, while other variables such as extrapersonal neglect, somatosensory or motor impairments, or deficits in left extrapersonal space representation had no predictive value of personal neglect. These findings suggest that deficient body representation is the major mechanism underlying personal neglect. Copyright © 2011 Elsevier Ltd. All rights reserved.
Supervised Filter Learning for Representation Based Face Recognition.
Directory of Open Access Journals (Sweden)
Chao Bi
Full Text Available Representation based classification methods, such as Sparse Representation Classification (SRC and Linear Regression Classification (LRC have been developed for face recognition problem successfully. However, most of these methods use the original face images without any preprocessing for recognition. Thus, their performances may be affected by some problematic factors (such as illumination and expression variances in the face images. In order to overcome this limitation, a novel supervised filter learning algorithm is proposed for representation based face recognition in this paper. The underlying idea of our algorithm is to learn a filter so that the within-class representation residuals of the faces' Local Binary Pattern (LBP features are minimized and the between-class representation residuals of the faces' LBP features are maximized. Therefore, the LBP features of filtered face images are more discriminative for representation based classifiers. Furthermore, we also extend our algorithm for heterogeneous face recognition problem. Extensive experiments are carried out on five databases and the experimental results verify the efficacy of the proposed algorithm.
An Axiomatic Representation of System Dynamics
Baianu, I
2004-01-01
An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.
Power, privilege and disadvantage: Intersectionality theory and political representation
Directory of Open Access Journals (Sweden)
Eline Severs
2017-06-01
Full Text Available This article critically reviews the extant literature on social group representation and clarifies the advantages of intersectionality theory for studying political representation. It argues that the merit of intersectionality theory can be found in its ontology of power. Intersectionality theory is founded on a relational conception of political power that locates the constitution of power relations within social interactions, such as political representation. As such, intersectionality theory pushes scholarship beyond studying representation inequalities —that are linked to presumably stable societal positions— to also consider the ways in which political representation (recreates positions of privilege and disadvantage.
Directory of Open Access Journals (Sweden)
Anatoliy Klimyk
2007-02-01
Full Text Available In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group $G$ of rank $n$. Up to a sign, values of antisymmetric orbit functions are repeated on copies of the fundamental domain $F$ of the affine Weyl group (determined by the initial Weyl group in the entire Euclidean space $E_n$. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in $E_n$, vanishing on the boundary of the fundamental domain $F$. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group $G$. They also determine a transform on a finite set of points of $F$ (the discrete antisymmetric orbit function transform. Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.
Discrimination and the aim of proportional representation
DEFF Research Database (Denmark)
Lippert-Rasmussen, Kasper
2008-01-01
Many organizations, companies, and so on are committed to certain representational aims as regards the composition of their workforce. One motivation for such aims is the assumption that numerical underrepresentation of groups manifests discrimination against them. In this article, I articulate...... representational aims in a way that best captures this rationale. My main claim is that the achievement of such representational aims is reducible to the elimination of the effects of wrongful discrimination on individuals and that this very important concern is, in principle, compatible with the representation...... of discrimination against numerically overrepresented groups, or overlook the innocently different ambitions of some numerically underrepresented groups. In relation to the latter point, I appeal to the fact that many luck egalitarians think justice should be ambition sensitive (but endowment insensitive). Also...
Quantum kinematic theory of a point charge in a constant magnetic field
International Nuclear Information System (INIS)
Krause, J.
1996-01-01
A group-theoretic quantization method is applied to the open-quote open-quote complete symmetry group close-quote close-quote describing the motion of a point charge in a constant magnetic field. Within the regular ray representation, the Schroedinger operator is obtained as the Casimir operator of the extended Lie algebra. Configuration ray representations of the complete group cast the Schroedinger operator into the familiar space-time differential operator. Next, open-quote open-quote group quantization close-quote close-quote yields the superselection rules, which produce irreducible configuration ray representations. In this way, the Schroedinger operator becomes diagonalized, together with the angular momentum. Finally, the evaluation of an invariant integral, over the group manifold, gives rise to the Feynman propagation kernel left-angle t',x'|t,x right-angle of the system. Everything stems from the assumed symmetry group. Neither canonical quantization nor the path-integral method is used in the present analysis. copyright 1996 The American Physical Society
Operator algebras for general one-dimensional quantum mechanical potentials with discrete spectrum
International Nuclear Information System (INIS)
Wuensche, Alfred
2002-01-01
We define general lowering and raising operators of the eigenstates for one-dimensional quantum mechanical potential problems leading to discrete energy spectra and investigate their associative algebra. The Hamilton operator is quadratic in these lowering and raising operators and corresponding representations of operators for action and angle are found. The normally ordered representation of general operators using combinatorial elements such as partitions is derived. The introduction of generalized coherent states is discussed. Linear laws for the spacing of the energy eigenvalues lead to the Heisenberg-Weyl group and general quadratic laws of level spacing to unitary irreducible representations of the Lie group SU(1, 1) that is considered in detail together with a limiting transition from this group to the Heisenberg-Weyl group. The relation of the approach to quantum deformations is discussed. In two appendices, the classical and quantum mechanical treatment of the squared tangent potential is presented as a special case of a system with quadratic level spacing
Representations of Disability: School and Its Cultural Effects
Medeghini, Roberto; Fornasa, Walter; Vadalà, Giuseppe
School plays a significant role in cultural production where representations of difference and disability are very important: educational and pedagogical practices (implicit and explicit) help to form cultural and social representations of the world and, consequently, to confirm some stereotypes too. In this regard the study of social representations linked in with disability assumes some importance: in fact disability becomes a difference excluded from educational and social dynamics as well as from full participation in citizenship. This research will try to draw some dominant social representations about differences and disability, through analysis of young university students stories and memories.
Functional representations of integrable hierarchies
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2006-01-01
We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which 'functional representations' of particular hierarchies (such as KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as 'noncommutative' analogues of 'Fay identities' for the KP hierarchy
Phase space representations for spin23
International Nuclear Information System (INIS)
Polubarinov, I.V.
1991-01-01
General properties of spin matrices and density ones are considered for any spin s. For spin 2 3 phase space representations are constructed. Representations, similar to the Bell one, for the correlator of projections of two spins 2 3 in the singlet state are found. Quantum analogs of the Bell inequality are obtained. 14 refs
Preon representations and composite models
International Nuclear Information System (INIS)
Kang, Kyungsik
1982-01-01
This is a brief report on the preon models which are investigated by In-Gyu Koh, A. N. Schellekens and myself and based on complex, anomaly-free and asymptotically free representations of SU(3) to SU(8), SO(4N+2) and E 6 with no more than two different preons. Complete list of the representations that are complex anomaly-free and asymptotically free has been given by E. Eichten, I.-G. Koh and myself. The assumptions made about the ground state composites and the role of Fermi statistics to determine the metaflavor wave functions are discussed in some detail. We explain the method of decompositions of tensor products with definite permutation properties which has been developed for this purpose by I.-G. Koh, A.N. Schellekens and myself. An example based on an anomaly-free representation of the confining metacolor group SU(5) is discussed
An introduction to quiver representations
Derksen, Harm
2017-01-01
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is su...
Vivid Representations and Their Effects
Directory of Open Access Journals (Sweden)
Kengo Miyazono
2018-04-01
Full Text Available Sinhababu’s Humean Nature contains many interesting and important ideas, but in this short commentary I focus on the idea of vivid representations. Sinhababu inherits his idea of vivid representations from Hume’s discussions, in particular his discussion of calm and violent passions. I am sympathetic to the idea of developing Hume’s insight that has been largely neglected by philosophers. I believe that Sinhababu and Hume are on the right track. What I do in this short commentary is to raise some questions about the details. The aim of asking these questions is not to challenge Sinhababu’s proposal (at least his main ideas, but rather to point at some interesting issues arising out of his proposal. The questions are about (1 the nature of vividness, (2 the effects of vivid representations, and (3 Sinhababu’s account of alief cases.
SLE local martingales in logarithmic representations
International Nuclear Information System (INIS)
Kytölä, Kalle
2009-01-01
A space of local martingales of SLE-type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases, not much is known about this representation. The purpose of this paper is to exhibit examples of representations where L 0 is not diagonalizable—a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation to the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE κ=6 describing the exploration path in critical percolation and its relation to the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of κ, thus at all central charges and not only at specific rational values
Majority members' feelings about political representation of muslim immigrants
Verkuyten, Maykel; Hindriks, Paul; Coenders, Marcel
2016-01-01
In three survey experimental studies among national samples of the native Dutch, we examined feelings towards Muslim immigrants' political party representation. The strategy of disengagement (reject political representation) was evaluated most positively, followed by the descriptive representation
On the equivalence of GPD representations
International Nuclear Information System (INIS)
Müller, Dieter; Semenov-Tian-Shansky, Kirill
2016-01-01
Phenomenological representations of generalized parton distributions (GPDs) implementing the non-trivial field theoretical requirements are employed in the present day strategies for extracting of hadron structure information encoded in GPDs from the observables of hard exclusive reactions. Showing out the equivalence of various GPD representations can help to get more insight into GPD properties and allow to build up flexible GPD models capable of satisfactory description of the whole set of available experimental data. Below we review the mathematical aspects of establishing equivalence between the the double partial wave expansion of GPDs in the conformal partial waves and in the t-channel SO(3) partial waves and the double distribution representation of GPDs
Understanding as Integration of Heterogeneous Representations
Martínez, Sergio F.
2014-03-01
The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding.
Lebedieva, Tetiana; Gubanov, Victor; Dovbeshko, Galyna; Pidhirnyi, Denys
2015-12-01
Different notations of graphene irreducible representations and optical modes could be found in the literature. The goals of this paper are to identify the correspondence between available notations, to calculate the optical modes of graphene in different points of the Brillouin zone, and to compare them with experimental data obtained by Raman and coherent anti-Stokes Raman scattering (CARS) spectroscopy. The mechanism of the resonance enhancement of vibration modes of the molecules adsorbed on graphene in CARS experiments is proposed. The possibility of appearance of the discrete breathing modes is discussed.
Tensor harmonic analysis on homogenous space
International Nuclear Information System (INIS)
Wrobel, G.
1997-01-01
The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)
International Nuclear Information System (INIS)
Filippov, G.F.; Ovcharenko, V.I.; Teryoshin, Yu.V.
1980-01-01
For near-magnetic nuclei, the matrix elements of the central exchange nucleon-nucleon interaction potential energy operator between the generating functions of the total basis of the Sn are obtained. The basis states are highest weigt vectorsp(2,R) irreducible representatio of the SO(3) irredicible representation and in addition, have a definite O(A-1) symmetry. The Sp(2,R) basis generating matrix elements simplify essentially the problem of calculating the spectrum of collective excitations of the atomic nucleus over an intrinsic function of definite O(A-1) symmetry
Three particle Poincare states and SU(6) x SU(3) as a classification group for baryons
International Nuclear Information System (INIS)
Buccella, F.; Sciarrino, A.; Sorba, P.
1975-05-01
A complete set of democratic quantum numbers is introduced to classify the states of an irreducible unitary representation (IUR) of the Poincare group obtained from the decomposition of the direct products of three I.U.R. Such states are identified with the baryon states constituted of three free relativistic quarks. The transformation from current to constituent quarks is then easily reobtained. Moreover, the group SU(6) x SU(3) appears naturally as a collinear classification group for baryons. Results similar to those of the symmetric harmonic oscillator quark model are obtained [fr
Group covariant protocols for quantum string commitment
International Nuclear Information System (INIS)
Tsurumaru, Toyohiro
2006-01-01
We study the security of quantum string commitment (QSC) protocols with group covariant encoding scheme. First we consider a class of QSC protocol, which is general enough to incorporate all the QSC protocols given in the preceding literatures. Then among those protocols, we consider group covariant protocols and show that the exact upperbound on the binding condition can be calculated. Next using this result, we prove that for every irreducible representation of a finite group, there always exists a corresponding nontrivial QSC protocol which reaches a level of security impossible to achieve classically
Note on twisted elliptic genus of K3 surface
International Nuclear Information System (INIS)
Eguchi, Tohru; Hikami, Kazuhiro
2011-01-01
We discuss the possibility of Mathieu group M 24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M 24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M 24 . In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.
Directory of Open Access Journals (Sweden)
Wakako Nakai
2007-07-01
Full Text Available We study the Jacobi-Trudi-type determinant which is conjectured to be the $q$-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type $C_n$. Like the $D_n$ case studied by the authors recently, applying the Gessel-Viennot path method with an additional involution and a deformation of paths, we obtain an expression by a positive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.
On the irreps of the N-extended supersymmetric quantum mechanics and their fusion graphs
International Nuclear Information System (INIS)
Toppan, Francesco.
2006-12-01
In this talk we review the classification of the irreducible representations of the algebra of the N-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060, proving the agreement of the results here contained with those in hep-th/0511274. We further show that the fusion algebra of the 1D N-extended supersymmetric vacua introduced in hep-th/0511274 admits a graphical presentation. The N = 2 graphs are here explicitly presented for the first time. (author)
Instanton induced compactification and fermion chirality
International Nuclear Information System (INIS)
Randjbar-Daemi, S.; Strathdee, J.
1983-07-01
The question of fermion chirality in Kaluza-Klein theories with coupling to Yang-Mills fields is discussed. The argument is illustrated in eight dimensions where an SU(2) Yang-Mills field assumes the 1-instanton form on the internal space. This serves not only to trigger spontaneous compactification of the internal space but will ensure the emergence of nsub(L)-nsub(R)=2/3t(t+1) (2t+1) zero modes in an irreducible 8-spinor belonging to the (2t+1)-dimensional representation of SU(2). (author)
SU(3) versus deformed Hartree-Fock state
International Nuclear Information System (INIS)
Johnson, Calvin W.; Stetcu, Ionel; Draayer, J.P.
2002-01-01
Deformation is fundamental to understanding nuclear structure. We compare two ways to efficiently realize deformation for many-fermion wave functions, the leading SU(3) irreducible representation and the angular-momentum-projected Hartree-Fock state. In the absence of single-particle spin-orbit splitting the two are nearly identical. With realistic forces, however, the difference between the two is nontrivial, with the angular-momentum-projected Hartree-Fock state better approximating an 'exact' wave function calculated in the fully interacting shell model. The difference is driven almost entirely by the single-particle spin-orbit splitting
Constructing visual representations
DEFF Research Database (Denmark)
Huron, Samuel; Jansen, Yvonne; Carpendale, Sheelagh
2014-01-01
tangible building blocks. We learned that all participants, most of whom had little experience in visualization authoring, were readily able to create and talk about their own visualizations. Based on our observations, we discuss participants’ actions during the development of their visual representations......The accessibility of infovis authoring tools to a wide audience has been identified as a major research challenge. A key task in the authoring process is the development of visual mappings. While the infovis community has long been deeply interested in finding effective visual mappings......, comparatively little attention has been placed on how people construct visual mappings. In this paper, we present the results of a study designed to shed light on how people transform data into visual representations. We asked people to create, update and explain their own information visualizations using only...
Bridge: Intelligent Tutoring with Intermediate Representations
1988-05-01
Research and Development Center and Psychology Department University of Pittsburgh Pittsburgh, PA. 15260 The Artificial Intelligence and Psychology...problem never introduces more than one unfamiliar plan. Inteligent Tutoring With Intermediate Representations - Bonar and Cunniigbam 4 You must have a... Inteligent Tutoring With ntermediate Representations - Bonar and Cunningham 7 The requirements are specified at four differcnt levels, corresponding to
Symmetry analysis in neutron diffraction studies of magnetic structures. IV
International Nuclear Information System (INIS)
Izyumov, Yu.A.; Naish, V.E.; Petrov, S.B.
1979-01-01
By analyzing the exchange Hamiltonian, the authors develop the technique of determining the magnetic structures liable to occur in a crystal. The technique rests on Bertaut's idea that the exchange eigenfunction corresponds to some magnetic structure. A technically simple and efficient method of diagonalizing the exchange matrix is worked out using the devices of space group representation theory. A method is presented to find the magnetic structures with equal exchange energy (exchange multiplets). The occcurrence of exchange multiplets results from the additional invariance of the exchange Hamiltonian under rotation of all the spins. The degeneracy within the exchange multiplet may be the reason why some magnetic structures arise not according to one irreducible representation of the space group. The theory is illustrated with reference to an example of the magnetic structure of spinels. (Auth.)
Usage of semantic representations in recognition memory.
Nishiyama, Ryoji; Hirano, Tetsuji; Ukita, Jun
2017-11-01
Meanings of words facilitate false acceptance as well as correct rejection of lures in recognition memory tests, depending on the experimental context. This suggests that semantic representations are both directly and indirectly (i.e., mediated by perceptual representations) used in remembering. Studies using memory conjunction errors (MCEs) paradigms, in which the lures consist of component parts of studied words, have reported semantic facilitation of rejection of the lures. However, attending to components of the lures could potentially cause this. Therefore, we investigated whether semantic overlap of lures facilitates MCEs using Japanese Kanji words in which a whole-word image is more concerned in reading. Experiments demonstrated semantic facilitation of MCEs in a delayed recognition test (Experiment 1), and in immediate recognition tests in which participants were prevented from using phonological or orthographic representations (Experiment 2), and the salient effect on individuals with high semantic memory capacities (Experiment 3). Additionally, analysis of the receiver operating characteristic suggested that this effect is attributed to familiarity-based memory judgement and phantom recollection. These findings indicate that semantic representations can be directly used in remembering, even when perceptual representations of studied words are available.
Poincaré Embeddings for Learning Hierarchical Representations
CERN. Geneva
2018-01-01
Abstracts: Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically do not account for this property. In this talk, I will discuss a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability. &...
Representations of Lie algebras and partial differential equations
Xu, Xiaoping
2017-01-01
This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students. Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certai...
[Social and cultural representations in epilepsy awareness].
Arborio, Sophie
2015-01-01
Representations relating to epilepsy have evolved over the centuries, but the manifestations of epilepsy awaken archaic images linked to death, violence and disgust. Indeed, the generalised epileptic seizure symbolises a rupture with the surrounding environment, "informs it", through the loss of social codes which it causes. The social and cultural context, as well as medical knowledge, influences the representations of the disease. As a result, popular knowledge is founded on the social and cultural representations of a given era, in a given society. Copyright © 2015 Elsevier Masson SAS. All rights reserved.
Theory of the unitary representations of compact groups
International Nuclear Information System (INIS)
Burzynski, A.; Burzynska, M.
1979-01-01
An introduction contains some basic notions used in group theory, Lie group, Lie algebras and unitary representations. Then we are dealing with compact groups. For these groups we show the problem of reduction of unitary representation of Wigner's projection operators, Clebsch-Gordan coefficients and Wigner-Eckart theorem. We show (this is a new approach) the representations reduction formalism by using superoperators in Hilbert-Schmidt space. (author)
Stochastic Analysis of Gaussian Processes via Fredholm Representation
Directory of Open Access Journals (Sweden)
Tommi Sottinen
2016-01-01
Full Text Available We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations, and maximum likelihood estimations.
Representations of Nets of C*-Algebras over S 1
Ruzzi, Giuseppe; Vasselli, Ezio
2012-11-01
In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over S 1 admits faithful representations, and when the net is covariant under Diff( S 1), it admits representations covariant under any amenable subgroup of Diff( S 1).
Representational constraints on children's suggestibility.
Ceci, Stephen J; Papierno, Paul B; Kulkofsky, Sarah
2007-06-01
In a multistage experiment, twelve 4- and 9-year-old children participated in a triad rating task. Their ratings were mapped with multidimensional scaling, from which euclidean distances were computed to operationalize semantic distance between items in target pairs. These children and age-mates then participated in an experiment that employed these target pairs in a story, which was followed by a misinformation manipulation. Analyses linked individual and developmental differences in suggestibility to children's representations of the target items. Semantic proximity was a strong predictor of differences in suggestibility: The closer a suggested distractor was to the original item's representation, the greater was the distractor's suggestive influence. The triad participants' semantic proximity subsequently served as the basis for correctly predicting memory performance in the larger group. Semantic proximity enabled a priori counterintuitive predictions of reverse age-related trends to be confirmed whenever the distance between representations of items in a target pair was greater for younger than for older children.
Digital models for architectonical representation
Directory of Open Access Journals (Sweden)
Stefano Brusaporci
2011-12-01
Full Text Available Digital instruments and technologies enrich architectonical representation and communication opportunities. Computer graphics is organized according the two phases of visualization and construction, that is modeling and rendering, structuring dichotomy of software technologies. Visualization modalities give different kinds of representations of the same 3D model and instruments produce a separation between drawing and image’s creation. Reverse modeling can be related to a synthesis process, ‘direct modeling’ follows an analytic procedure. The difference between interactive and not interactive applications is connected to the possibilities offered by informatics instruments, and relates to modeling and rendering. At the same time the word ‘model’ describes different phenomenon (i.e. files: mathematical model of the building and of the scene; raster representation and post-processing model. All these correlated different models constitute the architectonical interpretative model, that is a simulation of reality made by the model for improving the knowledge.
Asymptotical representation of discrete groups
International Nuclear Information System (INIS)
Mishchenko, A.S.; Mohammad, N.
1995-08-01
If one has a unitary representation ρ: π → U(H) of the fundamental group π 1 (M) of the manifold M then one can do may useful things: 1. To construct a natural vector bundle over M; 2. To construct the cohomology groups with respect to the local system of coefficients; 3. To construct the signature of manifold M with respect to the local system of coefficients; and others. In particular, one can write the Hirzebruch formula which compares the signature with the characteristic classes of the manifold M, further based on this, find the homotopy invariant characteristic classes (i.e. the Novikov conjecture). Taking into account that the family of known representations is not sufficiently large, it would be interesting to extend this family to some larger one. Using the ideas of A.Connes, M.Gromov and H.Moscovici a proper notion of asymptotical representation is defined. (author). 7 refs
Minimal representations and Freudenthal triple systems
International Nuclear Information System (INIS)
Olive, D.
2004-01-01
Unitary representations of noncompact Lie groups have long been sought in physics. The first nice concrete construction was found by Dirac in connection with the anti-de Sitter group. Some subsequent generalizations will be described, in particular the minimal representation thought to be relevant to realising duality in supergravity superstring theories. A relation to Freudenthal triple systems will be described. (author)
Pattern of mathematic representation ability in magnetic electricity problem
Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.
2018-03-01
The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.
Concepts, ontologies, and knowledge representation
Jakus, Grega; Omerovic, Sanida; Tomažic, Sašo
2013-01-01
Recording knowledge in a common framework that would make it possible to seamlessly share global knowledge remains an important challenge for researchers. This brief examines several ideas about the representation of knowledge addressing this challenge. A widespread general agreement is followed that states uniform knowledge representation should be achievable by using ontologies populated with concepts. A separate chapter is dedicated to each of the three introduced topics, following a uniform outline: definition, organization, and use. This brief is intended for those who want to get to know
Employee Representation and Board Size in the Nordic Countries
DEFF Research Database (Denmark)
Thomsen, Steen; Rose, Caspar; Kronborg, Dorte
2016-01-01
Several European countries have mandatory employee representation on company boards, but the consequences for corporate governance are debated. We use employee representation rules in the otherwise quite similar Nordic countries (Denmark, Finland, Norway, and Sweden) to elicit information...... on shareholder preferences for employee representation and board size. We find that shareholders tend to choose board structures that minimize the proportion of employee representatives. In Denmark and Norway employee representation depends on board size, and shareholders choose board sizes that minimize...
Content-adaptive pyramid representation for 3D object classification
DEFF Research Database (Denmark)
Kounalakis, Tsampikos; Boulgouris, Nikolaos; Triantafyllidis, Georgios
2016-01-01
In this paper we introduce a novel representation for the classification of 3D images. Unlike most current approaches, our representation is not based on a fixed pyramid but adapts to image content and uses image regions instead of rectangular pyramid scales. Image characteristics, such as depth...... and color, are used for defining regions within images. Multiple region scales are formed in order to construct the proposed pyramid image representation. The proposed method achieves excellent results in comparison to conventional representations....
28 CFR 301.304 - Representation of claimant.
2010-07-01
... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Representation of claimant. 301.304 Section 301.304 Judicial Administration FEDERAL PRISON INDUSTRIES, INC., DEPARTMENT OF JUSTICE INMATE ACCIDENT COMPENSATION Compensation for Work-Related Physical Impairment or Death § 301.304 Representation...
Statutory representation of an entrepreneur in business transactions
Jareš, Jiří
2012-01-01
1 1. Summary This dissertation deals with statutory representation of an entrepreneur. At the start are defined key concepts as entrepreneur, entrepreneurship, in case of legal persons described particular legal forms, difference between acting of physical and legal persons. In the next part are described ways of acting of entrepreneur, direct and indirect representation, contractual and legal representation, There is also explained the difference between acting and decision-making. There is ...
LOCALLY REFINED SPLINES REPRESENTATION FOR GEOSPATIAL BIG DATA
Directory of Open Access Journals (Sweden)
T. Dokken
2015-08-01
Full Text Available When viewed from distance, large parts of the topography of landmasses and the bathymetry of the sea and ocean floor can be regarded as a smooth background with local features. Consequently a digital elevation model combining a compact smooth representation of the background with locally added features has the potential of providing a compact and accurate representation for topography and bathymetry. The recent introduction of Locally Refined B-Splines (LR B-splines allows the granularity of spline representations to be locally adapted to the complexity of the smooth shape approximated. This allows few degrees of freedom to be used in areas with little variation, while adding extra degrees of freedom in areas in need of more modelling flexibility. In the EU fp7 Integrating Project IQmulus we exploit LR B-splines for approximating large point clouds representing bathymetry of the smooth sea and ocean floor. A drastic reduction is demonstrated in the bulk of the data representation compared to the size of input point clouds. The representation is very well suited for exploiting the power of GPUs for visualization as the spline format is transferred to the GPU and the triangulation needed for the visualization is generated on the GPU according to the viewing parameters. The LR B-splines are interoperable with other elevation model representations such as LIDAR data, raster representations and triangulated irregular networks as these can be used as input to the LR B-spline approximation algorithms. Output to these formats can be generated from the LR B-spline applications according to the resolution criteria required. The spline models are well suited for change detection as new sensor data can efficiently be compared to the compact LR B-spline representation.
Characterizing representational learning: A combined simulation and tutorial on perturbation theory
Directory of Open Access Journals (Sweden)
Antje Kohnle
2017-11-01
Full Text Available Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them (“representational competence” is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students’ spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.
Characterizing representational learning: A combined simulation and tutorial on perturbation theory
Kohnle, Antje; Passante, Gina
2017-12-01
Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them ("representational competence") is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students' spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.
Representation of Aloneness in Forever Alone Guy Comic Strips
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Pricillia Chandra
2017-01-01
Full Text Available This study aims to discuss the representation of aloneness in Forever Alone Guy comic strips. The purpose of this research is to find out how the meaning of aloneness is constructed in the representation of Forever Alone Guy through the theory of representation described by Stuart Hall (1997, 2013. In the theory suggested by Hall, it is described that there are two ways to be done in creating representation. Those ways are through language/sign and mental representation. The mental representation is the only way used in this research with a reason that this analysis focuses to the stigmas attached to the concept of aloneness. The analysis shows that the construction of meaning is done through embedding clusters of negative stigmas to the three entities: single, alone and lonely. Thus, through the analysis, it can be concluded that the dominant meaning which represents being single and alone as the ‘imperfect’ condition plays an important role in the construction of the meaning
Features of common representations of suiciders in young people
Directory of Open Access Journals (Sweden)
I. B. Bovina
2013-04-01
Full Text Available We discuss the first phase results of a research project dedicated to study of suicide representations in youth. In the framework of structural approach to social representations, we study features of structure and content of social representations of suiciders in two groups of young people (the criterion for group allocation was their acquaintance with people who has suicide attempts. Our sample (N = 106 consisted of representatives of several youth groups (students and working youths with specialized secondary, higher or incomplete higher education, aged 18 to 35 years (M = 23,48 years, SD = 4,36 years: 67 women and 39 men. The 1st group includes respondents personally acquainted with suicide attempters (44 respondents, the 2nd group – respondents without such experience. The subject of research were common representations of suiciders. We tested assumptions about the specificity of protective functions of social representations, as well as consistency of representations in the two groups of respondents.
The Koslowski-Sahlmann representation: quantum configuration space
Campiglia, Miguel; Varadarajan, Madhavan
2014-09-01
The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.
Context Representation and Fusion: Advancements and Opportunities
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Asad Masood Khattak
2014-05-01
Full Text Available The acceptance and usability of context-aware systems have given them the edge of wide use in various domains and has also attracted the attention of researchers in the area of context-aware computing. Making user context information available to such systems is the center of attention. However, there is very little emphasis given to the process of context representation and context fusion which are integral parts of context-aware systems. Context representation and fusion facilitate in recognizing the dependency/relationship of one data source on another to extract a better understanding of user context. The problem is more critical when data is emerging from heterogeneous sources of diverse nature like sensors, user profiles, and social interactions and also at different timestamps. Both the processes of context representation and fusion are followed in one way or another; however, they are not discussed explicitly for the realization of context-aware systems. In other words most of the context-aware systems underestimate the importance context representation and fusion. This research has explicitly focused on the importance of both the processes of context representation and fusion and has streamlined their existence in the overall architecture of context-aware systems’ design and development. Various applications of context representation and fusion in context-aware systems are also highlighted in this research. A detailed review on both the processes is provided in this research with their applications. Future research directions (challenges are also highlighted which needs proper attention for the purpose of achieving the goal of realizing context-aware systems.
Spectral representation of infimum of bounded quantum observables
International Nuclear Information System (INIS)
Shen Jun; Wu Junde
2009-01-01
In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a logic order on bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova [Math Slovaca 57, 589 (2007)] proved that for each subset D of S(H), the infimum of D exists with respect to the logic order. In 2008, Liu and Wu [J. Math. Phys. 49, 073521 (2008)] found a representation of the infimum A and B for A,B is an element of S(H), and by using the limit methods, they gave out a representation for the infimum of D. But, that representation is complicated. In this paper, we present a simpler spectral representation for the infimum of D with respect to the logic order.
On network representations of antennas inside resonating environments
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F. Gronwald
2007-06-01
Full Text Available We discuss network representations of dipole antennas within electromagnetic cavities. It is pointed out that for a given configuration these representations are not unique. For an efficient evaluation a network representation should be chosen such that it involves as few network elements as possible. The field theoretical analogue of this circumstance is the possibility to express electromagnetic cavities' Green's functions by representations which exhibit different convergence properties. An explicit example of a dipole antenna within a rectangular cavity clarifies the corresponding interrelation between network theory and electromagnetic field theory. As an application, current spectra are calculated for the case that the antenna is nonlinearly loaded and subject to a two-tone excitation.
A Social Representations Perspective on Information Systems Implementation
DEFF Research Database (Denmark)
Gal, Uri; Berente, Nicholas
2008-01-01
Abstract: Purpose - The purpose of this paper is to advocate a "social representations" approach to the study of socio-cognitive processes during information systems (IS) implementation as an alternative to the technological frames framework. Design/methodology/approach - The paper demonstrates how......, it may lead to symptomatic explanations of IS implementation. Alternatively, using the theory of social representations can offer more fundamental causal explanations of IS implementation processes. Research limitations/implications - IS researchers are encouraged to use a social representations approach...... social representations theory can improve research outcomes by applying it to three recent studies that employed the technological frames framework. Findings - It is found that because the technological frames framework is overly technologically centered, temporally bounded, and individually focused...