An Elliptical Galaxy Luminosity Function and Velocity Dispersion Sample of Relevance for Gravitational Lensing Statistics

We have selected 42 elliptical galaxies from the literature and estimated their velocity dispersions at the effective radius (\sigma_{\re}) and at 0.54 effective radii (\vff). We find by a dynamical analysis that the normalized velocity dispersion of the dark halo of an elliptical galaxy \vdm is roughly \sigma_{\re} multiplied by a constant, which is almost independent of the core radius or the anisotropy parameter of each galaxy. Our sample analysis suggests that \vdm^{*} lies in the range 178-198 km s$^{-1}$. The power law relation we find between the luminosity and the dark matter velocity dispersion measured in this way is (L/L^{*}) = (\vdm/\vdm^{*})^\gamma, where $\gamma$ is between 2-3. These results are of interest for strong gravitational lensing statistics studies. In order to determine the value of \vdm^{*}, we calculate \mstar in the same \bt band in which \vdm^{*} has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes \bt between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters \mstar = -19.66 + 5$\cdot\log_{10}h \pm 0.30$, $\alpha = 0.15 \pm 0.55$, and the normalization constant $\phi^{*} = (1.34 \pm 0.30) \times 10^{-3} h^{3}$ Mpc$^{-3}$, with the Hubble constant \hnot = 100 $h$ km s$^{-1}$ Mpc$^{-1}$. This normalization implies that morphology type E galaxies make up (10.8 $\pm$ 1.2) per cent of all galaxies.Comment: 18 pages latex, with ps figs included. accepted by New Astronomy (revised to incorporate referees comments

Comparisons between Nimbus 6 satellite and rawinsonde soundings for several geographical areas

Good agreement between satellite and weighted (linearly interpolated) rawinsonde temperature and temperature derived parameters was found in most instances with the poorest agreement either near the tropopause region or near the ground. However, satellite moisture data are highly questionable. The smallest discrepancy between satellite and weighted mean rawinsonde temperature and parameters derived from temperature was found over water and the largest discrepancy was found over mountains. Cumulative frequency distributions show that discrepancies between satellite and rawinsonde data can be represented by a normal distribution except for dew point temperature

Using fractals and power laws to predict the location of mineral deposits

Around the world the mineral exploration industry is interested in getting that small increase in probability measure on the earth's surface of where the next large undiscovered deposit might be found. In particular WMC Resources Ltd has operations world wide looking for just that edge in the detection of very large deposits of, for example, gold. Since the pioneering work of Mandelbrot, geologists have been familiar with the concept of fractals and self similarity over a few orders of magnitude for geological features. This includes the location and size of deposits within a particular mineral province. Fractal dimensions have been computed for such provinces and similarities of these aggregated measures between provinces have been noted. This paper explores the possibility of making use of known information to attempt the inverse process. That is, from lesser dimensional measures of a mineral province, for example, fractal dimension or more generally multi-fractal measures, is it possible to infer, even with small increase in probability, where the unknown (preferably large) deposits might be located

Hadronic B Decays to Charmed Baryons

We study exclusive B decays to final states containing a charmed baryon within the pole model framework. Since the strong coupling for $\Lambda_b\bar B N$ is larger than that for $\Sigma_b \bar BN$, the two-body charmful decay $B^-\to\Sigma_c^0\bar p$ has a rate larger than $\bar B^0\to\Lambda_c^+\bar p$ as the former proceeds via the $\Lambda_b$ pole while the latter via the $\Sigma_b$ pole. By the same token, the three-body decay $\bar B^0\to\Sigma_c^{++}\bar p\pi^-$ receives less baryon-pole contribution than $B^-\to\Lambda_c^+\bar p\pi^-$. However, because the important charmed-meson pole diagrams contribute constructively to the former and destructively to the latter, $\Sigma_c^{++}\bar p\pi^-$ has a rate slightly larger than $\Lambda_c^+\bar p\pi^-$. It is found that one quarter of the $B^-\to \Lambda_c^+\bar p\pi^-$ rate comes from the resonant contributions. We discuss the decays $\bar B^0\to\Sigma_c^0\bar p\pi^+$ and $B^-\to\Sigma_c^0\bar p\pi^0$ and stress that they are not color suppressed even though they can only proceed via an internal W emission.Comment: 25 pages, 6 figure

Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE

Inversion For Permeability From Stoneley Wave Velocity And Attenuation

The in situ permeability of a formation is obtained by the inversion of Stoneley wave phase velocity and attenuation, which are evaluated by applying the Extended Prony's method to the array sonic logging data. The Maximum Likelihood inversion is used together with logarithmic parameterization of the permeabilities. Formation shear wave velocity is also inverted for. This process is tested on both synthetic and field data. Logarithmic parameterization contributes to rapid convergence of the algorithm. Permeabilities estimated from field data are in good agreement with core measurements.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu

Fourth-Order Finite Difference Acoustic Logs In A Transversely Isotropic Formation

In this paper we present a finite difference scheme for seismic wave propagation in a fluid-filled borehole in a transversely isotropic formation. The first-order hyperbolic differential equations are approximated explicitly on a staggered grid using an algorithm that is fourth-order accurate in space and second-order accurate in time. The grid dispersion and grid anisotropy are analyzed. Grid dispersion and anisotropy are well suppressed by a grid size of 10 points per wavelength. The stability condition is also obtained from the dispersion analysis. This finite difference scheme is implemented on the nCUBE2 parallel computer with a grid decomposition algorithm. The finite difference synthetic waveforms are compared with those generated using the discrete wavenumber method. They are in good agreement. The damping layers effectively absorbed the boundary reflections. Four vertically heterogeneous borehole models: a horizontal layered formation, a borehole with a radius change, a semi-infinite borehole, and a semi-infinite borehole with a layer, are studied using the finite difference method. Snapshots from the finite difference results provide pictures of the radiating wavefields.Massachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu