The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

Understanding Internal Capital Markets and Corporate Policies

This study looks inside a large retail-banking group to understand how corporate politics affect internal capital allocation. The group consists of a headquarters organization and about 150 member banks which own the headquarters. Our data is from the firm’s managerial accounting system and covers all cash flows, internal capital transfers, and investments at the local member bank level. We first show that a member bank’s investment (net loan growth) is generally not fully independent from its own cash flow (net deposit growth). Then we show that such constraints are not apparent at more influential member banks, where influence is measured by the divergence of voting rights from ownership rights. The more influential banks are allocated more funds from the headquarters, but also show more restraints in investments when experiencing large deposit inflows. Influence matters more among member banks requiring more information exchanges with the headquarters as a result of more volatile funding requests. Influence also matters more for small business loans, which contain more soft information, than for standardized residential mortgage loans. These results suggest that corporate politics can be used to address allocation inefficiencies resulting from information asymmetries between the headquarters and divisions (member banks in our case).internal capital markets;capital markets;retail banking;corporate politics

Heavy Pentaquarks

We construct the spin-flavor wave functions of the possible heavy pentaquarks containing an anti-charm or anti-bottom quark using various clustered quark models. Then we estimate the masses and magnetic moments of the $J^P={1\over 2}^+$ or ${3\over 2}^+$ heavy pentaquarks. We emphasize the difference in the predictions of these models. Future experimental searches at BESIII, CLEOc, BELLE, and LEP may find these interesting states

Pentaquark Magnetic Moments In Different Models

We calculate the magnetic moments of the pentaquark states from different models and compare our results with predictions of other groups.Comment: 17 pages, no figur

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

Magnetic Moments of JP=3/2+J^P={3/2}^+ Pentaquarks

If the $J^P$ of $\Theta_5^+$ and $\Xi_5^{--}$ pentaquarks is really found to be ${1\over 2}^+$ by future experiments, they will be accompanied by $J^P={3\over 2}^+$ partners in some models. It is reasonable to expect that these $J^P={3\over 2}^+$ states will also be discovered in the near future with the current intensive experimental and theoretical efforts. We estimate $J^P={3/2}^+$ pentaquark magnetic moments using different models.Comment: 13 page

Structure and substrate selectivity of the 750-kDa α6β6 holoenzyme of geranyl-CoA carboxylase.

Geranyl-CoA carboxylase (GCC) is essential for the growth of Pseudomonas organisms with geranic acid as the sole carbon source. GCC has the same domain organization and shares strong sequence conservation with the related biotin-dependent carboxylases 3-methylcrotonyl-CoA carboxylase (MCC) and propionyl-CoA carboxylase (PCC). Here we report the crystal structure of the 750-kDa α6β6 holoenzyme of GCC, which is similar to MCC but strikingly different from PCC. The structures provide evidence in support of two distinct lineages of biotin-dependent acyl-CoA carboxylases, one carboxylating the α carbon of a saturated organic acid and the other carboxylating the γ carbon of an α-β unsaturated acid. Structural differences in the active site region of GCC and MCC explain their distinct substrate preferences. Especially, a glycine residue in GCC is replaced by phenylalanine in MCC, which blocks access by the larger geranyl-CoA substrate. Mutation of this residue in the two enzymes can change their substrate preferences

An Efficient Cloud Market Mechanism for Computing Jobs with Soft Deadlines

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