Theoretical Expectations for Rare and Forbidden Tau Decays

Given the experimental evidence for $\nu_\mu - \nu_\tau$ oscillations, the existence of lepton flavor violation in $\tau$ decays is a theoretical certainty. In this brief review, I consider the connection between models of neutrino mass and the expected observability of some $\tau$ decays.Comment: Talk at TAU 02 (Santa Cruz, CA

Plato's Fire and the Neutrino Mass Matrix

With the accumulation of many years of solar and atmospheric neutrino oscillation data, the approximate form of the 3 X 3 neutrino mixing matrix is now known. The theoretical challenge is to understand where this mixing matrix comes from. Recently, a remarkable fact was discovered that for a specific pattern of the neutrino mass matrix at a high scale, any flavor-changing radiative correction will automatically lead to the desired mixing matrix. It was also discovered that the required specific pattern at the high scale can be maintained by the non-Abelian discrete symmetry A_4 which is also the symmetry group of the regular tetrahedron, one of five perfect geometric solids known to Plato who associated it with the element ``fire''. I discuss this recent development and add to it a new and very simple mechanism for the implementation of the flavor-changing radiative correction.Comment: 12 pages, to appear as a Brief Review in MPL

Neutrino, Lepton, and Quark Masses in Supersymmetry

The recently proposed model of neutrino mass with no new physics beyond the TeV energy scale is shown to admit a natural and realistic supersymmetric realization, when combined with another recently proposed model of quark masses in the context of a softly broken U(1) symmetry. Four Higgs doublets are required, but two must have masses at the TeV scale. New characteristic experimental predictions of this synthesis are discussed.Comment: 7 pages, no figur

Discovery of Newly Formed Broad Absorption Lines in a Radio-Loud Quasar

We report a serendipitous discovery of broad absorption lines that were newly formed in the spectrum of the high-redshift, luminous radio-loud quasar TEX 1726 + 344, in a time interval of only 12 years. This is the first quasar showing a transition from narrow absorption lines to broad absorption lines. It also becomes one of the few radio-loud broad absorption line quasars. The gas cloud responsible for these broad absorption lines is derived to have parameters coinciding with those of the remnant of a tidally disrupted star.Comment: 6 pages, 1 figure, accepted for publication as a Letter in Mon. Not. R. Astron. So

A catalog of Kazarian galaxies

The entire Kazarian galaxies (KG) catalog is presented which combines extensive new measurements of their optical parameters with a literature and database search. The measurements were made using images extracted from the STScI Digitized Sky Survey (DSS) of Jpg(blue), Fpg(red) and Ipg(NIR) band photographic sky survey plates obtained by the Palomar and UK Schmidt telescopes. We provide accurate coordinates, morphological type, spectral and activity classes, blue apparent diameters, axial ratios, position angles, red, blue and NIR apparent magnitudes, as well as counts of neighboring objects in a circle of radius 50 kpc from centers of KG. Special attention was paid to the individual descriptions of the galaxies in the original Kazarian lists, which clarified many cases of misidentifications of the objects, particularly among interacting systems. The total number of individual Kazarian objects in the database is now 706. We also include the redshifts which are now available for 404 galaxies and the 2MASS infrared magnitudes for 598 KG. The database also includes extensive notes, which summarize information about the membership of KG in different systems of galaxies, and about revised activity classes and redshifts. An atlas of several interesting subclasses of KG is also presented.Comment: 15 pages, 5 figures, 1 table, Accepted in Astrophysics, Vol. 53, No. 1, 2010 (English translation of Astrofizika

Phase Transitions for Belousov-Zhabotinsky Reactions

The main objective of this article is to study the dynamic phase transitions associated with the spatial-temporal oscillations of the BZ reactions, given by Field, Koros and Noyes, also referred as the Oregonator. Two criteria are derived to determine 1) existence of either multiple equilibria or spatiotemporal oscillations, and 2) the types of transitions. These criteria gives a complete characterization of the dynamic transitions of the BZ systems from the homogeneous states. The analysis is carried out using a dynamic transition theory developed recently by the authors, which has been successfully applied to a number of problems in science

Extending Hamiltonian Operators to Get Bi-Hamiltonian Coupled KdV Systems

An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of lower order, new local bi-Hamiltonian coupled KdV systems are proposed. As a consequence of bi-Hamiltonian structure, they all possess infinitely many symmetries and infinitely many conserved densities.Comment: 13 pages, late

Calculating excited states of molecular aggregates by the renormalized excitonic method

In this paper, we apply the recently developed ab initio renormalized excitonic method (REM) to the excitation energy calculations of various molecular aggregates, through the extension of REM to the time-dependent density functional theory (TDDFT). Tested molecular aggregate systems include one-dimensional hydrogen-bonded water chains, ring crystals with $\pi$-$\pi$ stacking or van-der Waals interactions and the general aqueous systems with polar and non-polar solutes. The basis set factor as well as the effect of the exchange-correlation functionals are also investigated. The results indicate that the REM-TDDFT method with suitable basis set and exchange-correlation functionals can give good descriptions of excitation energies and excitation area for lowest electronic excitations in the molecular aggregate systems with economic computational costs. It's shown that the deviations of REM-TDDFT excitation energies from those by standard TDDFT are much less than 0.1 eV and the computational time can be reduced by one order

Phase Transitions for the Brusselator Model

Dynamic phase transitions of the Brusselator model is carefully analyzed, leading to a rigorous characterization of the types and structure of the phase transitions of the model from basic homogeneous states. The study is based on the dynamic transition theory developed recently by the authors