Symmetric, Hankel-symmetric, and Centrosymmetric Doubly Stochastic Matrices

We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their extreme points. We also determine a basis of the real vector spaces generated by permutation matrices with these special structures

Critical Behavior of Hadronic Fluctuations and the Effect of Final-State Randomization

The critical behaviors of quark-hadron phase transition are explored by use of the Ising model adapted for hadron production. Various measures involving the fluctuations of the produced hadrons in bins of various sizes are examined with the aim of quantifying the clustering properties that are universal features of all critical phenomena. Some of the measures involve wavelet analysis. Two of the measures are found to exhibit the canonical power-law behavior near the critical temperature. The effect of final-state randomization is studied by requiring the produced particles to take random walks in the transverse plane. It is demonstrated that for the measures considered the dependence on the randomization process is weak. Since temperature is not a directly measurable variable, the average hadronic density of a portion of each event is used as the control variable that is measurable. The event-to-event fluctuations are taken into account in the study of the dependence of the chosen measures on that control variable. Phenomenologically verifiable critical behaviors are found and are proposed for use as a signature of quark-hadron phase transition in relativistic heavy-ion collisions.Comment: 17 pages (Latex) + 24 figures (ps file), submitted to Phys. Rev.

On the dust tori in Palomar-Green quasars

The dust clouds in the torus of the quasar are irradiated by the central source, and the clouds at the inner radius of the torus re-radiate mostly in the near-infrared (NIR) wavebands. The ratio of the near-infrared luminosity to the bolometric luminosity L_NIR/L_bol can therefore reflect the torus geometry to some extent. We find a significant correlation between the ratio of the near-infrared luminosity to the bolometric luminosity L_NIR/L_bol and the central black hole mass M_bh for the Palomar-Green(PG) quasars, whereas no correlation is found between the Eddington ratio L_bol/L_Edd and the ratio L_NIR/L_bol. Similar correlations are found for the mid-infrared and far-infrared cases. It may imply that the torus geometry, i.e., the solid angle subtended by the dust torus as seen from the central source, does not evolve with the accretion rate. The correlation of the solid angle subtended by the torus with the central black hole mass M_bh implies that the formation of the dust torus is likely regulated by the central black hole mass. We find that the torus thickness H increases with quasar bolometric luminosities, which is different from the constant torus thickness H with luminosity assumed in the receding torus model. The mean covering factor of the dust clouds at the inner radius of the torus derived from the IR emission data is ~0.39 for PG quasars. The average relative thickness H/R of the tori in the PG quasars derived from the ratios of the infrared to bolometric luminosities is ~0.9. We suggest that the further IR observations on a larger quasar sample including more fainter quasars by the Spitzer Space Telescope will help understand the physics of the dust tori in quasars.Comment: The incorrect V-magnitude used for 1351+640 is fixed, the main conclusions are not changed, accepted for publication in Ap

Erraticity of Rapidity Gaps

The use of rapidity gaps is proposed as a measure of the spatial pattern of an event. When the event multiplicity is low, the gaps between neighboring particles carry far more information about an event than multiplicity spikes, which may occur very rarely. Two moments of the gap distrubiton are suggested for characterizing an event. The fluctuations of those moments from event to event are then quantified by an entropy-like measure, which serves to describe erraticity. We use ECOMB to simulate the exclusive rapidity distribution of each event, from which the erraticity measures are calculated. The dependences of those measures on the order of $q$ of the moments provide single-parameter characterizations of erraticity.Comment: 10 pages LaTeX + 5 figures p

On the masses of black-holes in radio-loud quasars

The central black-hole masses of a sample of radio-loud quasars are estimated by using the data of $H_{\beta}$ line-width and the optical continuum luminosity. The vast majority of the quasars in this sample have black-hole masses larger than $10^{8} M_{\odot}$, while a few quasars may contain relatively smaller black-holes. We found a significant anti-correlation between the radio-loudness and the central black-hole mass. It might imply that the jet formation is governed by the black-hole mass.Comment: 5 pages, two figures are added, accepted by MNRAS Letter

Achieving the Theoretical Depairing Current Limit in Superconducting Nanomesh Films

We show the theoretical depairing current limit can be achieved in a robust fashion in highly ordered superconductor nanomesh films having spatial periodicities smaller than both the superconducting coherence length and the magnetic penetration depth. For a niobium nanomesh film with 34 nm spatial periodicity, the experimental critical current density is enhanced by more than 17 times over the continuous film and is in good agreement with the depairing limit over the entire measured temperature range. The nanomesh superconductors are also less susceptible to thermal fluctuations when compared to nanowire superconductors. T_c values similar to the bulk film are achieved, and the nanomeshes are capable of retaining superconductivity to higher fields relative to the bulk. In addition, periodic oscillations in T_c are observed as a function of field, reflecting the highly ordered nanomesh structure

Inhomogeneous Boundary Value Problem for Hartree Type Equation

In this paper, we settle the problem for time-dependent Hartree equation with inhomogeneous boundary condition in a bounded Lipschitz domain in $\mathbb{R}^{N}$. A global existence result is derived.Comment: 10 page