Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models

There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit.Comment: 46 pages, no figure; LaTeX2e, amssymb, latexsym; typos correcte

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Continuous dependence estimates for nonlinear fractional convection-diffusion equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Levy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinearities and on the Levy measure of the diffusion term. Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary. Our results both cover, and extend to new equations, a large part of the known error estimates in the literature.Comment: In this version we have corrected Example 3.4 explaining the link with the results in [51,59

Laudatores Temporis Acti, or Why Cosmology is Alive and Well - A Reply to Disney

A recent criticism of cosmological methodology and achievements by Disney (2000) is assessed. Some historical and epistemological fallacies in the said article have been highlighted. It is shown that---both empirically and epistemologically---modern cosmology lies on sounder foundations than it is portrayed. A brief historical account demonstrates that this form of unsatisfaction with cosmology has had a long tradition, and rather meagre results in the course of the XX century.Comment: 11 pages, no figures; a criticism of astro-ph/0009020; Gen. Rel. Grav., accepted for publicatio

Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports

We demonstrate a new class of hollow-core Bragg fibers that are composed of concentric cylindrical silica rings separated by nanoscale support bridges. We theoretically predict and experimentally observe hollow-core confinement over an octave frequency range. The bandwidth of bandgap guiding in this new class of Bragg fibers exceeds that of other hollow-core fibers reported in the literature. With only three rings of silica cladding layers, these Bragg fibers achieve propagation loss of the order of 1 dB/m.Comment: 9 pages including 5 figure

Coarse-grained simulation of transmembrane peptides in the gel phase

We use Dissipative Particle Dynamics simulations, combined with parallel tempering and umbrella sampling, to investigate the potential of mean force between model transmembrane peptides in the various phases of a lipid bilayer, including the low-temperature gel phase. The observed oscillations in the effective interaction between peptides are consistent with the different structures of the surrounding lipid phases

Intergalactic HeII absorption towards QSO 1157+3143

We report the discovery of a further line of sight allowing detection of HeII Ly alpha absorption by the intergalactic medium. A HST/STIS survey of 32 bright z ~ 3 quasars selected from the Hamburg Quasar Surveys yielded one detection toward QSO 1157+3143 (z ~ 3, B ~ 17). A 10 orbit follow-up spectrum reveals a UV spectrum significantly supressed by two intervening Lyman limit systems at z=2.77 and 2.94, but with the continuum flux recovering sufficiently shortward of ~ 1700 A to allow study of the HeII absorption spectrum in the redshift range 2.75 < z < 2.97. The absorption is characterized by alternating voids and dense filament structures seen in both HeII and HI. Attempts to model the HeII opacity in terms of HI Ly alpha forest absorption are not successful in the voids, suggesting that HeII reionization is not complete between z=2.77 and 2.97 or that an optically thin Lyman limit system with z ~ 0.3 is responsible for the additional opacity.Comment: 6 pages, 4 figures, accepted by A&

Metal enrichment and evolution in four z > 6.5 quasar sightlines observed with JWST/NIRSpec

We present JWST/NIRSpec R$\approx$2700 spectra of four high-redshift quasars: VDES J0020-3653 (z = 6.860), DELS J0411-0907(z = 6.825), UHS J0439+1634 (z = 6.519) and ULAS J1342+0928 (z = 7.535). The exquisite data quality, signal-to-noise ratio of 50-200, and large $0.86\!~\mu{\rm m}\le \lambda \le 5.5\!~\mu{\rm m}$ spectral coverage allows us to identify between 13 and 17 intervening and proximate metal absorption line systems in each quasar spectrum, with a total number of 61 absorption-line systems detected at $2.42<z<7.48$ including the highest redshift intervening OI $\lambda$1302 and MgII systems at $z=7.37$ and $z=7.44$. We investigate the evolution of the metal enrichment in the epoch of reionization at $z>6$ and find: i) A continued increase of the low-ionization OI, CII, and SiII incidence, ii) Decreasing high-ionization CIV and SiIV incidence with a transition from predominantly high- to low-ionization at $z\approx6.0$, and iii) a constant MgII incidence across all redshifts. The observations support a change in the ionization state of the intergalactic medium in the EoR rather than a change in metallicity. The abundance ratio of [Si/O] in five $z>6$ absorption systems show enrichment signatures produced by low-mass Pop III pair instability supernovae, and possibly Pop III hypernovae. In the Gunn-Peterson troughs we detect transmission spikes where Ly$\alpha$ photons can escape. From 22 absorption systems at $z>5.7$, only a single low-ionization system out of 13 lies within 2000 km s$^{-1}$ from a spike, while four high-ionization systems out of nine lie within $\sim$2000 km s$^{-1}$ from a spike. This confirms that galaxies responsible for the heavy elements that are transported into the circumgalactic medium lie in predominantly in high-density, neutral environments, while lower density environments are ionized without being polluted by metals at $z\approx$ 6-7. [abridged]Comment: 50 pages including 30 pages of appendices. Submitted to A&

Возникновение и развитие еврейской прессы Крыма

В статье выделяются основные этапы процесса возникновения и развития еврейской прессы Крыма, вводится в научный оборот ряд еврейских изданий.У статті виділяються основні етапи процесу виникнення і розвитку єврейської преси Криму, вводиться в науковий обіг ряд єврейських видань.The article researches the Jewish Crimean mass-media

Emergence of Order in Textured Patterns

A characterization of textured patterns, referred to as the disorder function \bar\delta(\beta), is used to study properties of patterns generated in the Swift-Hohenberg equation (SHE). It is shown to be an intensive, configuration-independent measure. The evolution of random initial states under the SHE exhibits two stages of relaxation. The initial phase, where local striped domains emerge from a noisy background, is quantified by a power law decay \bar\delta(\beta) \sim t^{-{1/2} \beta}. Beyond a sharp transition a slower power law decay of \bar\delta(\beta), which corresponds to the coarsening of striped domains, is observed. The transition between the phases advances as the system is driven further from the onset of patterns, and suitable scaling of time and \bar\delta(\beta) leads to the collapse of distinct curves. The decay of $\bar\delta(\beta)$ during the initial phase remains unchanged when nonvariational terms are added to the underlying equations, suggesting the possibility of observing it in experimental systems. In contrast, the rate of relaxation during domain coarsening increases with the coefficient of the nonvariational term.Comment: 9 Pages, 8 Postscript Figures, 3 gif Figure