The small quantum group as a quantum double

We prove that the quantum double of the quasi-Hopf algebra of dimension attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. Math. J. 5 (2) (2005) 371–378] to a simple complex Lie algebra and a primitive root of unity q of order n² is equivalent to Lusztig's small quantum group (under some conditions on n). We also give a conceptual construction of using the notion of de-equivariantization of tensor categories.     

Response times in gated M/G/1 queues: The processor-sharing case

A class of single server queues with Poisson arrivals and a gated server is considered. Whenever the server becomes idle the gate separating it from the waiting line opens, admitting all the waiting customers into service, and then closes again. The batch admitted into service may be served according to some arbitrary scheme. The equilibrium waiting time distribution is provided for the subclass of conservative schemes with arbitrary service times and the processor-sharing case is treated in some detail to produce the equilibrium time-in-service and response time distributions, conditional on the length of required service. The LIFO and random order of service schemes and the case of compound Poisson arrivals are treated briefly as examples of the effectiveness of the proposed method of analysis. All distributions are provided in terms of their Laplace transforms except for the case of exponential service times where the L.T. of the waiting time distribution is inverted. The first two moments of the equilibrium waiting and response times are provided for most treated cases and in the exponential service times case the batch size distribution is also presented.     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

Dynamic of the Fluorescence of the Complex Zn++/Bis-N-Carbazolyl-Distyrylbenzene

The discrimination between similar concentrations of the different metal ions is one of the important roles of fluorescent sensors. Here we present the study of the fluorescence dynamic of the chromophore bis-N-carbazolyl-distyrylbenzene (BCDSB) in acetonitrile/water (mmol/L), doped with metal ions such as K+; Ca++; Mg++; Zn++(10 micromol/L). BCDSB has the fluorescence with lambda(max) at 448 nm by excitation at lambda(exc) = 378 nm, lifetime 1.089 ns: quantum yield of the fluorescence is 0.68. With continuation of irradiation fluorescence quenching has been registered for all investigated metal ions. However, in the presence of Zn++ oscillation of the intensity was observed. The energy activation of the oscillation as much as 15 kcal/mol was estimated. We believe, that the specificity of the complex Zn++/BCDSB, is in an asymmetrical structure, formed via binding sites of Zn++ with the electron-enriched binding sites of the BCDSB, excited in n(pi)* state. This asymmetrical complex structure can cause the photoinduced structural fluctuation in the complex coordination.