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in subjects: "Group Theory"

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Benchmark problems in which equality plays the major role

We have recently heard rumors that researchers are again studying paramodulation (Wos87) in the context of strategy for its control. In part to facilitate such research, and in part to provide test problems for evaluating other approaches to equality-oriented reasoning, we offer in this article a set of benchmark problems in which equality plays the dominant role. The test problems are taken from group theory, Robbins algebra, combinatory logic, and other areas. For each problem, we include app… more

Date: January 1, 1992

Creator: Lusk, E. & Wos, L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Non-rigid molecular group theory and its applications

The use of generalized wreath product groups as representations of symmetry groups of nonrigid molecules is considered. Generating function techniques are outlined for nuclear spin statistics and character tables of the symmetry groups of nonrigid molecules. Several applications of nonrigid molecular group theory to NMR spectroscopy, rovibronic splitting and nuclear spin statistics of nonrigid molecules, molecular beam deflection and electric resonance experiments of weakly bound Van der Waal c… more

Date: June 1, 1982

Creator: Balasubramanian, K.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Dimensions, induces and congruence classes of representations of affine Kac-Moody algebras (with examples for affine E/sub 8/)

Affine generalizations of some familiar notions from the representation theory of semisimple Lie algebras/groups are introduced, described and illustrated. The multiplicity of a weight and the dimension congruence class, and indices of a representation are touched upon. Examples of the highest weight representations of affine E/sub 8/ are considered as a preview of far more extensive results of this type to appear.

Date: January 1, 1986

Creator: Kass, S.N. & Patera, J.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Progress report on research program in elementary particle theory, 1979-1980. [Univ. of Texas at Austin]

A qualitative description is given of research in the following areas: particle physics in relativistic astrophysics and cosmology; phenomenology of weak and electromagnetic interactions; strong interaction physics and quark-parton physics; quantum mechanics, quantum field theory, and fundamental problems; and groups, gauges, and grand unified theories. Reports on this work have already been published, or will be, when it is completed. (RWR)

Date: January 1, 1980

Creator: Sudarshan, E.C.G. & Ne'eman, Y.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Group theoretic approaches to nuclear and hadronic collective motion

Three approaches to nuclear and hadronic collective motion are reviewed, compared and contrasted: the standard symmetry approach as typified by the Interacting Boson Model, the kinematic symmetry group approach of Gell-Mann and Tomonaga, and the recent direct construction by Buck. 50 references.

Date: January 1, 1982

Creator: Biedenharn, L.C.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Fun with E/sub 6/. [Symmetry properties and representations of E/sub 6/]

The exceptional Lie group E/sub 6/ is a candidate local symmetry for a Yang-Mills theory that unifies electromagnetic, weak, and strong interactions. Several ways of incorporating the fermion spectrum are discussed, including an amusing example where some of the known spin 1/2 fermions are composite states of elementary fermions and some scalar particles in the theory. The symmetry properties and the representations of E/sub 6/ are reviewed, the symmetry breaking classified, and the dynamical b… more

Date: January 1, 1980

Creator: Slansky, R.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Special functions and group theory in theoretical physics

The subject of special functions, even where restricted to the narrower subject of special functions in theoretical physics, is far too broad for one to attempt any meaningfully complete survey. We attempt to review the important main themes in the subject and then show how recent advances broadened and extended these themes.

Date: January 1, 1983

Creator: Biedenharn, L. C.; Gustafson, R. A.; Lohe, M. A.; Louck, J. D. & Milne, S. C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Nuclear structure theory. Annual technical progress report, October 1, 1978-September 30, 1979. [Summaries of research activities at Univ. of Rochester]

This report summarizes progress during the past year in the following areas of nuclear structure and reaction theory: Statistical spectroscopy, including: Random matrix methods, with applications to fluctuations in spectra and in strength distributions, and to problems of ergodicity; Group symmetries in spectral-distribution theory; Electromagnetic and ..beta.. transitions. Meson scattering and absorption by nuclei, including: general scattering theory with absorption, multiple scattering theor… more

Date: January 1, 1979

Creator: French, J. B. & Koltun, D. S.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Differential calculus on quantum spaces and quantum groups

A review of recent developments in the quantum differential calculus. The quantum group GL[sub q](n) is treated by considering it as a particular quantum space. Functions on SL[sub q] (n) are defined as a subclass of functions on GL[sub q](n). The case of SO[sub q](n) is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.

Date: December 10, 1992

Creator: Zumino, B.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Theories of fermion masses

We present grand unified theories in which the quark masses and mixing angles are calculated in terms of the lepton masses through simple group theory. The theories contain no small Yukawa couplings. A favored value of the top quark mass is 35 GeV.

Date: May 1, 1984

Creator: Bagger, J.; Dimopoulos, S.; Georgi, H. & Raby, S.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Some progress in statistical turbulence theory

An examination is made of relationships among several approaches to analytical turbulence theory: approximation by finite sets of moments, renormalized perturbation theory, decimation under symmetry constraints, renormalization-group methods, and the upper-bounding of transport under integral constraints. Most of the discussion assumes isotropic turbulence. Decimation under symmetry constraints plays a unifying role. It promises a rational basis for renormalized perturbation theory and provides… more

Date: January 1, 1987

Creator: Kraichnan, R.H.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Application of group theory to data reduction

The analysis within the framework of a theory of what was observed in experiments is essential to the testing of theories and is fundamental to physics. It is shown in this report how group theory can be used to provide a general method of data reduction whereby only the laws of a particular theory are used in the analysis of observations. This application of group theory involves introducing a group of transformations of the physical system upon which the observations were made. This group of … more

Date: September 1, 1982

Creator: Perey, F.G.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Neutronics Computational Applications of Symmetry Algebras

Lie groups of point transformations and their corresponding symmetry algebras are determined for a general system of second order differential equations, special cases of which include the multigroup diffusion equations and the ''FLIP form'' of the P/sub L/ equations. It is shown how Lie symmetry algebras can be used to motivate, formulate and simplify double sweep algorithms for solving two-point boundary value problems that involve systems of second order differential equations. A matrix Ricc… more

Date: January 1, 1989

Creator: Axford, R. A.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Relationship between the feasible group and the point group of a rigid molecule. [Point group]

The role of the point group in conventional rigid molecule theory is reviewed and its relation to the feasible group discussed. 6 references.

Date: January 1, 1978

Creator: Louck, J.D.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Testing the standard model

We summarize here the results of the standard model group which has studied the ways in which different facilities may be used to test in detail what we now call the standard model, that is SU/sub c/(3) x SU(2) x U(1). The topics considered are: W/sup + -/, Z/sup 0/ mass, width; sin/sup 2/theta/sub W/ and neutral current couplings; W/sup +/W/sup -/, W..gamma..; Higgs; QCD; toponium and naked quarks; glueballs; mixing angles; and heavy ions.

Date: January 1, 1982

Creator: Gordon, H.; Marciano, W. & Williams, H. H.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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First Theory Institute on Computational Differentiation

Computational differentiation (CD) is concerned with tools, techniques, and mathematics for generating, with little human effort, efficient and accurate derivative codes from programs written in such computer languages as C and Fortran. The primary purposes of the meeting were to explore the deep complexity issues that lie at the heart of the computation of derivatives from computer programs and to provide a forum for brainstorming on future research directions, including the applications of au… more

Date: December 31, 1993

Creator: Bischof, Christian H.; Griewank, Andreas & Khademi, Peyvand M.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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The canonical forms of a lattice rule

Much of the elementary theory of lattice rules may, be presented as an elegant application of classical results. These include Kronecker group representation theorem and the Hermite and Smith normal forms of integer matrices. The theory of the canonical form is a case in point. In this paper, some of this theory is treated in a constructive rather than abstract manner. A step-by-step approach that parallels the group theory is described, leading to an algorithm to obtain a canonical form of a r… more

Date: December 31, 1992

Creator: Lyness, J. N.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Benchmark problems in which equality plays the major role

We have recently heard rumors that researchers are again studying paramodulation [Wos87] in the context of strategy for its control. In part to facilitate such research, and in part to provide test problems for evaluating other approaches to equality-oriented reasoning, we offer in this article a set of benchmark problems in which equality plays the dominant role. The test problems are taken from group theory, Robbins algebra, combinatory logic, and other areas. For each problem, we include app… more

Date: May 1, 1992

Creator: Lusk, E. & Wos, L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Lower bounds for identifying subset members with subset queries

An instance of a group testing problem is a set of objects {Omicron}and an unknown subset P of {Omicron}.The task is to determine P by using queries of the type ``does P intersect ``Q``, where Q is a subset of {Omicron}. This problem occurs in areas such as fault detection, multiaccess communications, optimal search, blood testing and chromosome mapping. Consider the two stage algorithm for solving a group testing problem where in the first stage, a predetermined set of queries, are asked in pa… more

Date: April 1, 1994

Creator: Knill, E.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Physical realisation of n greater than or equal to 4 vector models

Renormalization group analysis of several n greater than or equal to 4 systems was performed. The first-order transitions in Cr, Eu, UO/sub 2/, MnO, and TbP can be explained by noting that the Hamiltonians have no stable fixed-points in 4-epsilon dimensions. The phase transitions in TbAu/sub 2/, DyC/sub 2/, Tb, Ho, Dy, TbD/sub 2/, Nd, MnS/sub 2/, and K/sub 2/IrCl/sub 6/ are described by n greater than or equal to 4 Hamiltonians with a stable fixed point; critical exponents corresponding to this… more

Date: January 1, 1976

Creator: Mukamel, D.; Krinsky, S. & Bak, P.

Item Type: Article

Partner: UNT Libraries Government Documents Department

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Use of group theory in the interpretation of infrared and Raman spectra. [Tables, vibrational spectroscopy]

Application of the mathematical theory of groups to the symmetry of molecules is a powerful method which permits the prediction, classification, and qualitative description of many molecular properties. In the particular case of vibrational molecular spectroscopy, applications of group theory lead to simple methods for the prediction of the number of bands to be found in the infrared and Raman spectra, their shape and polarization, and the qualitative description of the normal modes with which … more

Date: January 1, 1977

Creator: Silberman, E. & Morgan, H. W.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Di-hedral symmetry and charge conjugation

The charge conjugation C and the parity P are assumed to generate a finite group without assuming any apriori commutation or anti-commutation relation. The group then generated is the di-hedral group D/sub n/ (n being even) which has two dimensional irreducible representations. This implies that we could have in principle, elementary particles with parity and charge-conjugation doublet structure.

Date: January 1, 1976

Creator: Okubo, S.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Multigroup constants for charged particle elastic nuclear (plus interference) scattering of light isotopes. [Reaction rates, transfer matrices, tables]

Multi-group averaged reaction rates and transfer matrices were calculated for charged particle induced elastic nuclear (plus interference) scattering. Results are presented using a ten group structure for all twenty-five permutations of projectile and target for the following charged particles: p, d, t, /sup 3/He and alpha. Transfer matrices are presented in a simplified form for both incident projectile and the knock-ons; these matrices explicitly conserve energy.

Date: August 26, 1977

Creator: Cullen, D. E. & Perkins, S. T.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Differential calculus on quantum spaces and quantum groups

A review of recent developments in the quantum differential calculus. The quantum group GL{sub q}(n) is treated by considering it as a particular quantum space. Functions on SL{sub q} (n) are defined as a subclass of functions on GL{sub q}(n). The case of SO{sub q}(n) is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.

Date: December 10, 1992

Creator: Zumino, B.

Item Type: Article

Partner: UNT Libraries Government Documents Department