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Minimality of the Special Linear Groups

Description: Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, quotient groups, and subgroups. Minimality of SLn(F) is concluded by appealing to the associated Lie group decomposition as the product of a compact group and an upper triangular group. We also prove the universal minimality of homeomorphism groups of one dimensional manifolds, and we give a new simple proof of the universal minimality of S∞.
Date: December 1997
Creator: Hayes, Diana Margaret
Partner: UNT Libraries

The Eulerian Functions of Cyclic Groups, Dihedral Groups, and P-Groups

Description: In 1935, Philip Hall developed a formula for finding the number of ways of generating the group of symmetries of the icosahedron from a given number of its elements. In doing so, he defined a generalized Eulerian function. This thesis uses Hall's generalized Eulerian function to calculate generalized Eulerian functions for specific groups, namely: cyclic groups, dihedral groups, and p- groups.
Date: August 1992
Creator: Sewell, Cynthia M. (Cynthia Marie)
Partner: UNT Libraries

Restricting Invariants and Arrangements of Finite Complex Reflection Groups

Description: Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Röhrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X is in the lattice of the reflection arrangement of G. The main result characterizes when the restriction mapping is surjective in terms of the exponents of G and C and their reflection arrangements.
Date: August 2015
Creator: Berardinelli, Angela
Partner: UNT Libraries

[A large family group]

Description: Photograph of a large number of family members standing in a group and looking at the camera. A group of trees can be seen behind them. Some of the individuals are children.
Date: [1950..1965]
Creator: Williams, Byrd M. (Byrd Moore), III
Partner: UNT Libraries Special Collections

The Effects of Counseling and Religious Groups upon Selected Personality and Behavioral Variables

Description: This study investigates and evaluates the effects of an eighteen-hour weekend encounter group and three twelve-week groups--a weekly counseling group, a Bible discussion group, and a church attendance group, upon selected personality and behavioral variables, group morale and social integration. Subjects were forty-eight volunteers from a 250-member Protestant, evangelical church in a suburb of a Texas city of five-hundred thousand people. Six men and six women were randomly assigned to each of the four groups. Data analyzed were the pre-, post-, and post-post-experiment scores of the Personal Orientation Inventory, the Sixteen Personality Factor Questionnaire, and the sociometric variables based on Bonney's "Criteria for a Better Group on Sociometric Scales". The .05 level of significance was required for rejection of the null hypotheses. The statistical analyses were accomplished by applying a one-way analysis of co-variance design to the raw scores from the Personal Orientation Inventory, the Sixteen Personality Factor Questionnaire, and two of the three sociometric variables--mutual choices and opposite sex choices. The sociometric variable, choices between upper and lower quarters, was computed with the z formula. The sociometric data, mutuals and opposite sex choices on the encounter group, were further analyzed using the single-factor analysis of variance with repeated measures. It was hypothesized that the participants in the weekend encounter group would show a significantly greater change in self-actualization, positive personality and behavioral changes, social integration and group morale than would the participants in the other groups. It was further hypothesized that the weekly counseling group would show a significantly greater change in the selected variables, social integration and group morale, than would the Bible discussion or church attendance groups. It was also hypothesized that the Bible discussion group would show a significantly greater change in the selected variables, social integration and group morale than would the church attendance group. …
Date: August 1974
Creator: Brendel, Harold J.
Partner: UNT Libraries

Invariance, groups, and non-uniqueness: The discrete case

Description: Lie group methods provide a valuable tool for examininginvariance and non-uniqueness associated with geophysical inverseproblems. The techniques are particularly well suited for the study ofnon-linear inverse problems. Using the infinitesimal generators of thegroup it is possible to move within the null space in an iterativefashion. The key computational step in determining the symmetry groupsassociated with an inverse problem is the singular value decomposition(SVD) of a sparse matrix. I apply the methodology to the eikonal equationand examine the possible solutions associated with a crosswelltomographic experiment. Results from a synthetic test indicate that it ispossible to vary the velocity model significantly and still fit thereference arrival times. the approach is also applied to data fromcorosswell surveys conducted before and after a CO2 injection at the LostHills field in California. The results highlight the fact that a faultcross-cutting the region between the wells may act as a conduit for theflow of water and CO2.
Date: March 24, 2005
Creator: Vasco, D.W.
Partner: UNT Libraries Government Documents Department

New symmetry regions in the IBA and a simplified approach to nuclear phase transitions

Description: The IBA treatment of nuclear symmetries and transition regions is discussed. A new, extensive region of O(6) nuclei near A = 130 is presented and compared with the Pt isotopes. Nearly identical level schemes characterize both regions, including similar relations between the O(6) and O(5) steps in the dynamical symmetry chain decomposition, and similar discrepancies with the O(6) limit. Simple calculations that incorporate a triaxial component as an O(6) symmetry breaking mechanism remove these discrepancies in both regions. The evidence for a new, and perhaps the only, good region of SU(3) symmetry is given and discussed in a context of mixing with non-collective degrees of freedom. Finally, a systematic approach to transition regions is presented in which the key determinant of structure is the product N/sub ..pi../.N/sub ..nu../ of the number of valence proton and neutron bosons. Recognition of this allows an extremely simple treatment of complex transition regions. As an example, calculations for the U(5)..-->..O(6)..-->..SU(3) sequence from A = 120-140, which involve only six constants for the entire region of approx. = 30 nuclei, are discussed. The use of N/sub ..pi../.N/sub ..nu../ plots allows the study of the dissipation of shell and subshell gaps. Results for the A approx. = 100 and A approx. = 150 regions are presented and effective proton-boson numbers are extracted and compared with earlier results from g factor measurements and from microscopic calculations. 43 references.
Date: January 1, 1984
Creator: Carsten, R. F.
Partner: UNT Libraries Government Documents Department

Fermion dynamical symmetry and the nuclear shell model

Description: The interacting boson model (IBM) has been very successful in giving a unified and simple description of the spectroscopic properties of a wide range of nuclei, from vibrational through rotational nuclei. The three basic assumptions of the model are that: (1) the valence nucleons move about a doubly closed core, (2) the collective low-lying states are composed primarily of coherent pairs of neutrons and pairs of protons coupled to angular momentum zero and two, and (3) these coherent pairs are approximated as bosons. In this review we shall show how it is possible to have fermion Hamiltonians which have a class of collective eigenstates composed entirely of monopole and quadrupole pairs of fermions. Hence these models satisfy the assumptions (1) and (2) above but no boson approximation need be made. Thus the Pauli principle is kept in tact. Furthermore the fermion shell model states excluded in the IBM can be classified by the number of fermion pairs which are not coherent monopole or quadrupole pairs. Hence the mixing of these states into the low-lying spectrum can be calculated in a systematic and tractable manner. Thus we can introduce features which are outside the IBM. 11 refs.
Date: January 1, 1985
Creator: Ginocchio, J.N.
Partner: UNT Libraries Government Documents Department

A Topological Uniqueness Result for the Special Linear Groups

Description: The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Date: August 1997
Creator: Opalecky, Robert Vincent
Partner: UNT Libraries

Phase transitions and variant actions in lattice gauge theory

Description: Unexpected phase structure in four dimensional lattice gauge theory based on the groups SO(3) and SU(5) have prompted studies of variations on the Wilson action for SU(2). A rich phase structure related to the decomposition of SU(2) into SO(3) and Z/sub 2/ is found. The scale of asymptotic freedom has a dramatic dependence on the choice of lattice action.
Date: June 1, 1981
Creator: Creutz, M.
Partner: UNT Libraries Government Documents Department

Monte Carlo Renormalization Group: a review

Description: The logic and the methods of Monte Carlo Renormalization Group (MCRG) are reviewed. A status report of results for 4-dimensional lattice gauge theories derived using MCRG is presented. Existing methods for calculating the improved action are reviewed and evaluated. The Gupta-Cordery improved MCRG method is described and compared with the standard one. 71 refs., 8 figs.
Date: January 1, 1985
Creator: Gupta, R.
Partner: UNT Libraries Government Documents Department

The m(A1/sup + +/)/m(E/sup + +/) mass ratio from lattice gauge theory

Description: Evidence is presented that, in the infinite volume continuum limit, the m(A1/sup + +/) and the m(E/sup + +/) mass are almost degenerate. (A slightly lower A1/sup + +/ mass is preferred.) A1/sup + +/ and E/sup + +/ are irreducible representations of the cubic group and supposed to correspond to spin 0/sup + +/ and 2/sup + +/, respectively.
Date: July 30, 1987
Creator: Berg, B. A.
Partner: UNT Libraries Government Documents Department

A unique SU(5) and SO(10) unification with complete dynamical symmetry breaking

Description: A unique asymptotically free, anomaly-free, SU(5) gauge theory is proposed as a possible complete unification of the standard model in which all symmetry-breaking is dynamical. The asymptotic freedom constraint is saturated, removing renormalon divergences and leaving well-defined instanton interactions as the only non-perturbative ingredient of the theory. Consequently, it is argued, topological vacuum polarization of a very heavy, unconventional quantum number, quark sector dominates the dynamics, producing SU(5) symmetry breaking and a three generation low energy spectrum. Electroweak symmetry breaking is due to a chiral condensate of color sextet quarks. The embedding of the theory in a single SO(10) representation is used for the dynamical analysis and may also have physical significance. 22 refs., 5 figs., 2 tabs.
Date: August 1, 1986
Creator: Kang, Kyungsik & White, A.R.
Partner: UNT Libraries Government Documents Department

Symmetries in heavy nuclei and the proton-neutron interaction

Description: The Interacting Boson Approximation (IBA) nuclear structure model can be expressed in terms of the U(6) group, and thereby leads to three dynamical symmetries (or group chains) corresponding to different nuclear coupling schemes and geometrical shapes. The status of the empirical evidence for these three symmetries is reviewed, along with brief comments on the possible existence of supersymmetries in nuclei. The relationships between these symmetries, the nuclear phase transitional regions linking them, and the residual proton-neutron interaction are discussed in terms of a particularly simple scheme for parameterizing the effects of that interaction. 34 refs., 15 figs.
Date: January 1, 1986
Creator: Carsten, R. F.
Partner: UNT Libraries Government Documents Department

Axial asymmetry and the IBM

Description: The intimate relation between the IBM and axial asymmetry, appearing in its dynamical symmetries, in numerical calculations, in bandmixing effects, and in extensions to the model, is discussed.
Date: January 1, 1990
Creator: Carsten, R. F.
Partner: UNT Libraries Government Documents Department

[Two men (singing?) with a microphone and protesters behind them]

Description: A bearded man with a microphone stands with another man in front of protesters with signs. Inmigrantes piden despido de concejal y representación política. Farmers Branch (Texas), 26 ago (EFE). Unas 300 personas protestaron hoy en esta ciudad para exigir al gobierno municipal que despida al concejal que propuso que el inglés sea el idioma oficial y que se sancione a quienes den trabajo a indocumentados. Immigrants ask for dismissal of councilman and political representation. Farmers Branch (Texas), August 26 (EFE). Some 300 persons protested today in this city to demand of the municipal government that it dismiss the councilman who proposed that English be the official language and that those who give employment to undocumented aliens be sanctioned.
Date: August 26, 2006
Creator: Castillo, José L.
Partner: UNT Libraries Special Collections
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