The radical of a vertex operator algebra associated to a module

The radical of a vertex operator algebra associated to a module is defined and computed.Comment: Latex 14 pages. This is part of the original paper with a new titl

Cleft Extensions and Quotients of Twisted Quantum Doubles

Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\Bbbk^G_\omega\#_c\,\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\rightarrow \overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\Bbbk^G_\omega\#_c\, \Bbbk F\rightarrow \Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{F}$. Our construction is particularly natural when $F=G$ acts on $G$ by conjugation, and $\Bbbk^G_\omega\#_c \Bbbk G$ is a twisted quantum double $D^{\omega}(G)$. In this case, we give necessary and sufficient conditions that Rep($\Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{G}$) is a modular tensor category.Comment: LaTex; 14 page

Bose-Einstein Condensates in Superlattices

We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice substructure as well as ultrasubharmonic resonances that result from interactions of both substructures of the superlattice. In each case, we determine the resulting system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding wavefunctions by direct simulations of the GP equation, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns

Mass spectrometric analysis of small negative ions (e/m < 100) produced by Trichel pulse negative corona discharge fed by ozonised air

Mass spectrometric analysis of small negative ions (e/m < 100) produced by DC negative corona discharge in ozonised wet air both in flow and flow-stopped regimes was conducted at pressure of 30 kPa. The point-to-plain electrode system has been used. The yield of individual ions is strongly affected by trace concentrations of ozone in both regimes. Ozone concentration greater than 25 ppm is sufficient to completely suppress the appearance of O2- and a NO2- ion as well as theirs clusters in the mass spectra. The temporal increase in concentration of NO3- ions and NO3-.(H2O)n (n = 1, 2) hydrated clusters was observed in flow-stopped regime accompanied by reduction in yield of CO3- ion and its water clusters CO3-.(H2O)n (n = 1, 2), which otherwise are the dominant ions in flowing wet air free of ozone. In contrast the addition of ozone into the flow of wet air resulted in evident increase in abundance of the clusters CO3-.(H2O)n (n = 1, 2). This is an evidence of an active role of nitrous oxide produced in flow-stopped regime in sufficient amount. The measured electrical conductivity of drift region confirmed the role of additional dissociative attachment of electrons by ozone molecules as well as a formation of clusters of lower mobility with increasing ozone concentration in the discharge gap

Band-collision gel electrophoresis.

Electrophoretic mobility shift assays are widely used in gel electrophoresis to study binding interactions between different molecular species loaded into the same well. However, shift assays can access only a subset of reaction possibilities that could be otherwise seen if separate bands of reagent species might instead be collisionally reacted. Here, we adapt gel electrophoresis by fabricating two or more wells in the same lane, loading these wells with different reagent species, and applying an electric field, thereby producing collisional reactions between propagating pulse-like bands of these species, which we image optically. For certain pairs of anionic and cationic dyes, propagating bands pass through each other unperturbed; yet, for other pairs, we observe complexing and precipitation reactions, indicating strong attractive interactions. We generalize this band-collision gel electrophoresis (BCGE) approach to other reaction types, including acid-base, ligand exchange, and redox, as well as to colloidal species in passivated large-pore gels