Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra

The Fock space of $m+p$ bosonic and $n+q$ fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra $gl_{m+p|n+q}$. Its tensor powers decompose into direct sums of infinite dimensional irreducible highest weight $gl_{m+p|n+q}$-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irreducible $gl_{m+p|n+q}$-modules arising in this way.Comment: 25 Pages, LaTeX forma

Appearance of the canine meninges in subtraction magnetic resonance images

The canine meninges are not visible as discrete structures in noncontrast magnetic resonance (MR) images, and are incompletely visualized in T1‐weighted, postgadolinium images, reportedly appearing as short, thin curvilinear segments with minimal enhancement. Subtraction imaging facilitates detection of enhancement of tissues, hence may increase the conspicuity of meninges. The aim of the present study was to describe qualitatively the appearance of canine meninges in subtraction MR images obtained using a dynamic technique. Images were reviewed of 10 consecutive dogs that had dynamic pre‐ and postgadolinium T1W imaging of the brain that was interpreted as normal, and had normal cerebrospinal fluid. Image‐anatomic correlation was facilitated by dissection and histologic examination of two canine cadavers. Meningeal enhancement was relatively inconspicuous in postgadolinium T1‐weighted images, but was clearly visible in subtraction images of all dogs. Enhancement was visible as faint, small‐rounded foci compatible with vessels seen end on within the sulci, a series of larger rounded foci compatible with vessels of variable caliber on the dorsal aspect of the cerebral cortex, and a continuous thin zone of moderate enhancement around the brain. Superimposition of color‐encoded subtraction images on pregadolinium T1‐ and T2‐weighted images facilitated localization of the origin of enhancement, which appeared to be predominantly dural, with relatively few leptomeningeal structures visible. Dynamic subtraction MR imaging should be considered for inclusion in clinical brain MR protocols because of the possibility that its use may increase sensitivity for lesions affecting the meninges

Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions

Speciation without chromatography: Part I. Determination of tributyltin in aqueous samples by chloride generation, headspace solid-phase microextraction and inductively coupled plasma time of flight mass spectrometry

An analytical procedure was developed for the determination of tributyltin in aqueous samples. The relatively high volatility of the organometal halide species confers suitability for their headspace sampling from the vapour phase above natural waters or leached solid samples. Tributyltin was collected from the sample headspace above various chloride-containing matrices, including HCl, sodium chloride solution and sea-water, by passive sampling using a polydimethylsiloxane/divinylbenzene (PDMS/DVB)-coated solid-phase microextraction (SPME) fiber. Inductively coupled plasma time-of-flight mass spectrometry (ICP-TOFMS) was used for detection following thermal desorption of analytes from the fiber. A detection limit of 5.8 pg ml–1(as tin) was realized in aqueous samples. Method validation was achieved using NRCC PACS-2 (Sediment) certified reference material, for which reasonable agreement between certified and measured values for tributyltin content was obtained