Conditional Symmetries, the True Degree of Freedom and G.C.T. Invariant Wave functions for the general Bianchi Type II Vacuum Cosmology

The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional configuration space, to a 4-dimensional one, has been achieved by the usage of the information furnished by the quantum form of the linear constraints. Further reduction of the space in which the wave function -obeying the Wheeler-DeWitt equation- lives, is accomplished by unrevealling the extra symmetries of the Hamiltonian. These symmetries appear in the form of -linear in momenta- first integrals of motion. Most of these symmetries, correspond to G.C.T.s through the action of the automorphism group. Thus, a G.C.T. invariant wave function is found, which depends on the only true degree of freedom, i.e. the unique curvature invariant, characterizing the hypersurfaces t=const.Comment: 10 pages, no figures, LaTeX2e Typesetting syste

Organizational energy: A behavioral analysis of human and organizational factors in manufacturing

This paper seeks to explore the behavior and embodied energy involved in the decision-making of information technology/information systems (IT/IS) investments using a case within a small- to medium-sized manufacturing firm. By analyzing decision making within a given case context, this paper describes the nature of the investment through the lens of behavioral economics, causality, input-output (IO) equilibrium, and the general notion of depletion of executive energy function. To explore the interplay between these elements, the authors structure the case context via a morphological field in order to construct a fuzzy cognitive map of decision-making relationships relating to the multidimensional and nonquantifiable problems of IT/IS investment evaluation. Noting the significance of inputs and outputs relating to the investment decision within the case, the authors assess these cognitive interrelationships through the lens of the Leontief IO energy equilibrium model. Subsequently, the authors suggest, through an embodied energy audit, that all such management decisions are susceptible to decision fatigue (so-called 'ego depletion'). The findings of this paper highlight pertinent cognitive and IO paths of the investment decision-making process that will allow others making similar types of investments to learn from and draw parallels from such processes

Dynamical symmetry enhancement near N=2, D=4 gauged supergravity horizons

We show that all smooth Killing horizons with compact horizon sections of 4-dimensional gauged N=2 supergravity coupled to any number of vector multiplets preserve $2 c_1({\cal K})+4 \ell$ supersymmetries, where ${\cal K}$ is a pull-back of the Hodge bundle of the special K\"ahler manifold on the horizon spatial section. We also demonstrate that all such horizons with $c_1({\cal K})=0$ exhibit an SL(2,R) symmetry and preserve either 4 or 8 supersymmetries. If the orbits of the SL(2,R) symmetry are 2-dimensional, the horizons are warped products of AdS2 with the horizon spatial section. Otherwise, the horizon section admits an isometry which preserves all the fields. The proof of these results is centered on the use of index theorem in conjunction with an appropriate generalization of the Lichnerowicz theorem for horizons that preserve at least one supersymmetry. In all $c_1({\cal K})=0$ cases, we specify the local geometry of spatial horizon sections and demonstrate that the solutions are determined by first order non-linear ordinary differential equations on some of the fields.Comment: 60 pages, late

Automorphism Inducing Diffeomorphisms, Invariant Characterization of Homogeneous 3-Spaces and Hamiltonian Dynamics of Bianchi Cosmologies

An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the gauge degrees of freedom are removed and the remaining (gauge invariant) degrees, are the --up to 3-- curvature invariants. An apparent discrepancy between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class A Bianchi Types, occurs due to the existence of the Outer Automorphism Subgroup. This discrepancy is satisfactorily removed by exploiting the quantum version of some classical integrals of motion (conditional symmetries) which are recognized as corresponding to the Outer Automorphisms.Comment: 18 pages, LaTeX2e, no figures, one table, to appear in Communications in Mathematical Physic

Oblique Ion Two-Stream Instability in the Foot Region of a Collisionless Shock

Electrostatic behavior of a collisionless plasma in the foot region of high Mach number perpendicular shocks is investigated through the two-dimensional linear analysis and electrostatic particle-in-cell (PIC) simulation. The simulations are double periodic and taken as a proxy for the situation in the foot. The linear analysis for relatively cold unmagnetized plasmas with a reflected proton beam shows that obliquely propagating Buneman instability is strongly excited. We also found that when the electron temperature is much higher than the proton temperature, the most unstable mode is the highly obliquely propagating ion two-stream instability excited through the resonance between ion plasma oscillations of the background protons and of the beam protons, rather than the ion acoustic instability that is dominant for parallel propagation. To investigate nonlinear behavior of the ion two-stream instability, we have made PIC simulations for the shock foot region in which the initial state satisfies the Buneman instability condition. In the first phase, electrostatic waves grow two-dimensionally by the Buneman instability to heat electrons. In the second phase, highly oblique ion two-stream instability grows to heat mainly ions. This result is in contrast to previous studies based on one-dimensional simulations, for which ion acoustic instability further heats electrons. The present result implies that overheating problem of electrons for shocks in supernova remnants is resolved by considering ion two-stream instability propagating highly obliquely to the shock normal and that multi-dimensional analysis is crucial to understand the particle heating and acceleration processes in shocks.Comment: 20 pages, 9 figures, accepted for publication in Ap

Incomplete Orthogonal Factorization Methods Using Givens Rotations II: Implementation and Results

We present, implement and test a series of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: column-Incomplete Givens Orthogonalization (cIGO-method), which drops entries by position only; column-Threshold Incomplete Givens Orthogonalization (cTIGO-method) which drops entries dynamically by both their magnitudes and positions and where the reduction via Givens rotations is done in a column-wise fashion; and, row-Threshold Incomplete Givens Orthogonalization (r-TIGO-method) which again drops entries dynamically, but only magnitude is now taken into account and reduction is performed in a row-wise fashion. We give comprehensive accounts of how one would code these algorithms using a high level language to ensure efficiency of computation and memory use. The methods are then applied to a variety of square systems and their performance as preconditioners is tested against standard incomplete LU factorization techniques. For rectangular matrices corresponding to least-squares problems, the resulting incomplete factorizations are applied as preconditioners for conjugate gradients for the system of normal equations. A comprehensive discussion about the uses, advantages and shortcomings of these preconditioners is given