Open-closed field algebras

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a \C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few references are adde

SED-inferred properties and morphology of Lyman-break galaxies at z∼1z\sim 1 in the CDF-S

After carefully cross-identifying a previously discovered GALEX-selected Lyman Break Galaxy (LBG) candidates one-to-one with their optical counterparts in the field of the CDF-S, we re-estimate their photometric redshifts using multi-wavelength data from UV, optical to NIR. We refine a new updated sample of 383 LBGs at 0.7\la z \la 1.4. Most LBGs are classified as starburst and irregular types. Ages spread from several Myr to 1.5Gyr. Their dust-corrected star formation rates (SFRs) and stellar masses ($M_*$) are from 4\my to 220\my and from 2.3\times 10^8 \msun to 4 \times 10^{11} \msun. The rest-frame FUV luminosity function of LBGs are presented. LBGs of irregular types mainly distribute along the "main sequence" of star forming galaxies while most LBGs of starburst types locate in the starburst region. A "downsizing" effect is clearly found and LBGs distribute in the "blue" cloud. HST images in F606W ($V$ band) and F850LP ($z$ band) are taken from the GEMS and GOODS-S surveys. SExtractor and GALFIT are applied to get their morphological parameters. A morphological sample of 142 LBGs with reliable results of \sersic and sizes in both bands is defined. We find that LBGs at $z\sim 1$ are dominated by disk-like galaxies. Correlations between photometric and morphological properties of LBGs are investigated. Strong correlations between their half-light radii and $M_*$, i.e., size-stellar mass relations, are found in both bands. Physical connections between correlations and the "downsizing" effect are discussed.Comment: 26 pages, 30 figures, 6 tables, accepted by MNRA

Gamma-Ray Burst Afterglows from Realistic Fireballs

A GRB afterglow has been commonly thought to be due to continuous deceleration of a postburst fireball. Many analytical models have made simplifications for deceleration dynamics of the fireball and its radiation property, although they are successful at explaining the overall features of the observed afterglows. We here propose a model for a GRB afterglow in which the evolution of a postburst fireball is in an intermediate case between the adiabatic and highly radiative expansion. In our model, the afterglow is both due to the contribution of the adiabatic electrons behind the external blastwave of the fireball and due to the contribution of the radiative electrons. In addition, this model can describe evolution of the fireball from the extremely relativistic phase to the non-relativistic phase. Our calculations show that the fireball will go to the adiabatic expansion phase after about a day if the accelerated electrons are assumed to occupy the total internal energy. In all cases considered, the fireball will go to the mildly relativistic phase about $10^4$ seconds later, and to the non-relativistic phase after several days. These results imply that the relativistic adiabatic model cannot describe the deceleration dynamics of the several-days-later fireball. The comparison of the calculated light curves with the observed results at late times may imply the presence of impulsive events or energy injection with much longer durations.Comment: 18 pages, 10 figures, plain latex file, submitted to Ap

Theory and Calibration of Swap Market Models

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework, and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.Swap Market Model, Cap, Swaption, Calibration, Graph Theory