Counting Humps in Motzkin paths

In this paper we study the number of humps (peaks) in Dyck, Motzkin and Schr\"{o}der paths. Recently A. Regev noticed that the number of peaks in all Dyck paths of order $n$ is one half of the number of super Dyck paths of order $n$. He also computed the number of humps in Motzkin paths and found a similar relation, and asked for bijective proofs. We give a bijection and prove these results. Using this bijection we also give a new proof that the number of Dyck paths of order $n$ with $k$ peaks is the Narayana number. By double counting super Schr\"{o}der paths, we also get an identity involving products of binomial coefficients.Comment: 8 pages, 2 Figure

Two photon couplings of the lightest isoscalars from BELLE data

Amplitude Analysis of two photon production of $\pi\pi$ and ${\overline K}K$, using S-matrix constraints and fitting all available data, including the latest precision results from Belle, yields a single partial wave solution up to 1.4 GeV. The two photon couplings of the $\sigma/f_0(500)$, $f_0(980)$ and $f_2(1270)$ are determined from the residues of the resonance poles.Comment: 11 pages, 3 figures, extended for detail

Supernova pencil beam survey

Type Ia supernovae (SNe Ia) can be calibrated to be good standard candles at cosmological distances. We propose a supernova pencil beam survey that could yield between dozens to hundreds of SNe Ia in redshift bins of 0.1 up to $z=1.5$, which would compliment space based SN searches, and enable the proper consideration of the systematic uncertainties of SNe Ia as standard candles, in particular, luminosity evolution and gravitational lensing. We simulate SNe Ia luminosities by adding weak lensing noise (using empirical fitting formulae) and scatter in SN Ia absolute magnitudes to standard candles placed at random redshifts. We show that flux-averaging is powerful in reducing the combined noise due to gravitational lensing and scatter in SN Ia absolute magnitudes. The SN number count is not sensitive to matter distribution in the universe; it can be used to test models of cosmology or to measure the SN rate. The SN pencil beam survey can yield a wealth of data which should enable accurate determination of the cosmological parameters and the SN rate, and provide valuable information on the formation and evolution of galaxies. The SN pencil beam survey can be accomplished on a dedicated 4 meter telescope with a square degree field of view. This telescope can be used to conduct other important observational projects compatible with the SN pencil beam survey, such as QSOs, Kuiper belt objects, and in particular, weak lensing measurements of field galaxies, and the search for gamma-ray burst afterglows.Comment: Final version, to appear in ApJ, 531, #2 (March 10, 2000). 22 pages including 5 figures. Improved presentatio

Can Universe Experience Many Cycles with Different Vacua ?

Recently, the notion that the number of vacua is enormous has received increased attentions, which may be regarded as a possible anthropical explanation to incredible small cosmological constant. Further, a dynamical mechanisms to implement this possibility is required. We show in an operable model of cyclic universe that the universe can experience many cycles with different vacua, which is a generic behavior independent of the details of the model. This might provide a distinct dynamical approach to an anthropically favorable vacuum.Comment: RevTex, 10 pages, 4 eps figures, accepted by PRD(R), new title and changes in the text to match publicatio

Magnetically Regulated Star Formation in Turbulent Clouds

We investigate numerically the combined effects of supersonic turbulence, strong magnetic fields and ambipolar diffusion on cloud evolution leading to star formation. We find that, in clouds that are initially magnetically subcritical, supersonic turbulence can speed up star formation, through enhanced ambipolar diffusion in shocks. The speedup overcomes a major objection to the standard scenario of low-mass star formation involving ambipolar diffusion, since the diffusion time scale at the average density of a molecular cloud is typically longer than the cloud life time. At the same time, the strong magnetic field can prevent the large-scale supersonic turbulence from converting most of the cloud mass into stars in one (short) turbulence crossing time, and thus alleviate the high efficiency problem associated with the turbulence-controlled picture for low-mass star formation. We propose that relatively rapid but inefficient star formation results from supersonic collisions of somewhat subcritical gas in strongly magnetized, turbulent clouds. The salient features of this shock-accelerated, ambipolar diffusion-regulated scenario are demonstrated with numerical experiments.Comment: 10 pages, 3 figures, accepted for publication in ApJ

Racial and Ethnic Disparities in the Use of Drug Therapy

The purpose of this research is to explain the variation in the utilization of drug therapy for the medical conditions of depression, high cholesterol, and hypertension between Hispanics, non-Hispanic blacks, and non-Hispanics whites using Oaxaca-type decomposition analysis based on logit estimates. We find that almost the entire share of the utilization differences in drug therapy between blacks and whites can be explained by the differences in the coefficients of observable characteristics, while the sources of the utilization difference between the whites and Hispanics are split between the differences in the observable characteristics and the coefficient estimates. This result implies that strategies to improve racial and ethnic disparities need to be tailored to each group by focusing on the specific factors that are attributed to causing the disparity.high cholesterol, depression, drug therapy, racial and ethnic disparities, hypertension, Oaxaca decomposition

Wind-Interaction Models for the Early Afterglows of Gamma-Ray Bursts: The Case of GRB 021004

Wind-interaction models for gamma-ray burst afterglows predict that the optical emission from the reverse shock drops below that from the forward shock within 100s of seconds of the burst. The typical frequency $\nu_m$ of the synchrotron emission from the forward shock passes through the optical band typically on a timescale of minutes to hours. Before the passage of $\nu_m$, the optical flux evolves as $t^{-1/4}$ and after the passage, the decay steepens to $t^{-(3p-2)/4}$, where $p$ is the exponent for the assumed power-law energy distribution of nonthermal electrons and is typically $\sim 2$. The steepening in the slope of temporal decay should be readily identifiable in the early afterglow light curves. We propose that such a steepening was observed in the R-band light curve of GRB 021004 around day 0.1. Available data at several radio frequencies are consistent with this interpretation, as are the X-ray observations around day~1. The early evolution of GRB 021004 contrasts with that of GRB 990123, which can be described by emission from interaction with a constant density medium.Comment: 16 pages, 1 figure, submitted to ApJ