On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

Reevaluating evaluative conditioning: A nonassociative explanation of conditioning effects in the visual evaluative conditioning paradigm

In 2 studies, the authors investigated whether evaluative conditioning (EC) is an associative phenomenon. Experiment 1 compared a standard EC paradigm with nonpaired and no-treatment control conditions. EC effects were obtained only when the conditioned stimulus (CS) and unconditioned stimulus (UCS) were rated as perceptually similar. However, similar EC effects were obtained in both control groups. An earlier failure to obtain EC effects was reanalyzed in Experiment 2. Conditioning-like effects were found when comparing a CS with the most perceptually similar UCSs used in the procedure but not when analyzing a CS rating with respect to the UCS with which it was paired during conditioning. The implications are that EC effects found in many studies are not due to associative learning and that the special characteristics of EC (conditioning without awareness and resistance to extinction) are probably nonassociative artifacts of the EC paradigm

Interaction of a Modulated Electron Beam with a Plasma

The results of a theoretical and experimental investigation of the high-frequency interaction of an electron beam with a plasma are reported. An electron beam, modulated at a microwave frequency, passes through a uniform region of a mercury arc discharge after which it is demodulated. Exponentially growing wave amplification along the electron beam was experimentally observed for the first time at a microwave frequency equal to the plasma frequency. Approximate theories of the effects of 1) plasma-electron collision frequencies, 2) plasma-electron thermal velocities and 3) finite beam diameter, are given. In a second experiment the interaction between a modulated electron beam and a slow electrostatic wave on a plasma column has been studied. A strong interaction occurs when the velocity of the electron beam is approximately equal to the velocity of the wave and the interaction is essentially the same as that which occurs in traveling-wave amplifiers, except that here the plasma colum replaces the usual helical slow-wave circuit. The theory predicting rates of growth is presented and compared with the experimental results

The automated multi-stage substructuring system for NASTRAN

The substructuring capability developed for eventual installation in Level 16 is now operational in a test version of NASTRAN. Its features are summarized. These include the user-oriented, Case Control type control language, the automated multi-stage matrix processing, the independent direct access data storage facilities, and the static and normal modes solution capabilities. A complete problem analysis sequence is presented with card-by-card description of the user input

The nature of turbulence in OMC1 at the star forming scale: observations and simulations

Aim: To study turbulence in the Orion Molecular Cloud (OMC1) by comparing observed and simulated characteristics of the gas motions. Method: Using a dataset of vibrationally excited H2 emission in OMC1 containing radial velocity and brightness which covers scales from 70AU to 30000AU, we present the transversal structure functions and the scaling of the structure functions with their order. These are compared with the predictions of two-dimensional projections of simulations of supersonic hydrodynamic turbulence. Results: The structure functions of OMC1 are not well represented by power laws, but show clear deviations below 2000AU. However, using the technique of extended self-similarity, power laws are recovered at scales down to 160AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence. This is explained as a selection effect of preferentially observing the shocked part of the gas and the scaling can be reproduced using line-of-sight integrated velocity data from subsets of supersonic turbulence simulations. These subsets select regions of strong flow convergence and high density associated with shock structure. Deviations of the structure functions in OMC1 from power laws cannot however be reproduced in simulations and remains an outstanding issue.Comment: 12 pages, 8 figures, accepted A&A. Revised in response to referee. For higher resolution, see http://www.astro.phys.au.dk/~maikeng/sim_paper

Decoherence - Fluctuation Relation and Measurement Noise

We discuss fluctuations in the measurement process and how these fluctuations are related to the dissipational parameter characterising quantum damping or decoherence. On the example of the measuring current of the variable-barrier or QPC problem we show there is an extra noise or fluctuation connected with the possible different outcomes of a measurement. This noise has an enhanced short time component which could be interpreted as due to ``telegraph noise'' or ``wavefunction collapses''. Furthermore the parameter giving the the strength of this noise is related to the parameter giving the rate of damping or decoherence.Comment: 6 pages, no figures, for Okun Festschrift, Physics Report

Higgs boson production with one bottom quark including higher-order soft-gluon corrections

A Higgs boson produced in association with one or more bottom quarks is of great theoretical and experimental interest to the high-energy community. A precise prediction of its total and differential cross-section can have a great impact on the discovery of a Higgs boson with large bottom-quark Yukawa coupling, like the scalar (h^0 and H^0) and pseudoscalar (A^0) Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) in the region of large \tan\beta. In this paper we apply the threshold resummation formalism to determine both differential and total cross-sections for b g \to b\Phi (where \Phi = h^0, H^0), including up to next-to-next-to-next-to-leading order (NNNLO) soft plus virtual QCD corrections at next-to-leading logarithmic (NLL) accuracy. We present results for both the Fermilab Tevatron and the CERN Large Hadron Collider (LHC).Comment: revtex4, 13 pages, 11 figures; new references and additional comment

Inspections To Avert Terrorism: Robustness Under Severe Uncertainty

Protecting against terrorist attacks requires making decisions in a world in which attack probabilities are largely unknown. The potential for very large losses encourages a conservative perspective, in particular toward decisions that are robust. But robustness, in the sense of assurance against extreme outcomes, ordinarily is not the only desideratum in uncertain environments. We adopt Yakov Ben-Haim’s (2001b) model of information gap decision making to investigate the problem of inspecting a number of similar targets when one of the targets may be attacked, but with unknown probability. We apply this to a problem of inspecting a sample of incoming shipping containers for a terrorist weapon. While it is always possible to lower the risk of a successful attack by inspecting more vessels, we show that robustness against the failure to guarantee a minimum level of expected utility might not be monotonic. Robustness modeling based on expected utility and incorporating inspection costs yields decision protocols that are a useful alternative to traditional risk analysis.Terrorism, Robustness, Severe Uncertainty, Port Security

Individual Control of Risk: Seat Belt Use, Subjective Norms and the Theory of Reasoned Action

When faced with a risk for which an inexpensive solution is available, individuals often choose the risk rather than the solution. Protection from certain kinds of risks, e.g., using seat belts or condoms or insulating against radon, is largely under personal control, but individuals often choose not to comply with behaviors which would reduce the risk. The Theory of Reasoned Action (TRA) has been used to predict when individuals will comply. The authors attempted to validate aspects of the TRA by the use of scenarios. Factor analysis of their data supports the theory that intention is a major determinate of behavior but fails to establish the influence of scenarios on subjects\u27 intention to wear seat belts