Infinitely divisible probabilities on discrete linear groups

We investigate the structure of infinitely divisible probability measures on a discrete linear group. It is shown that for any such measure there is an infinitely divisible elementz in the centralizer of the support of the measure, such that the translate of the measure byz is embeddable over the subgroup generated by the support of the measure. Examples are given to show that this reult is best possible.     

Infinitely divisible probabilities on linearp-adic groups

In this paper we extend the work of Shah, on the structure of infinitely divisible probabilities onp-adic linear groups, to give a classification for all such probabilities.     

On the supports of absolutely continuous Gauss measures on connected Lie groups

The behaviour of the supports of an absolutely continuous Gauss semigroup on certain Lie groups is discussed. It is shown that on a connected nilpotent Lie group any absolutely continuous Gauss semigroup has full supports but on compact connected Lie groups which are not Abelian there exist absolutely continuous Gauss semigroups which do not have common supports.     

On the factor sets of measures and local tightness of convolution semigroups over Lie groups

It is shown that for a large class of Lie groups (called weakly algebraic groups) including all connected semisimple Lie groups the following holds: for any probability measure on the Lie group the set of all two-sided convolution factors is compact if and only if the centralizer of the support of inG is compact. This is applied to prove that for any connected Lie groupG, any homomorphism of any real directed (submonogeneous) semigroup into the topological semigroup of all probability measures onG is locally tight.     

Hydrogel‐Forming and Dissolving Microneedles for Enhanced Delivery of Photosensitizers and Precursors

We present “one‐step application” dissolving and hydrogel‐forming microneedle arrays (MN) for enhanced delivery of photosensitizers/precursors. MN (280 μm) prepared from 20% w/w poly(methylvinylether/maelic acid) and cross‐linked with glycerol by esterification to form hydrogels upon skin insertion, or allowed to dissolve rapidly in skin, were combined with patches containing 19 mg cm^?2 of 5‐aminolevulinic acid (ALA) or meso‐tetra (N‐methyl‐4‐pyridyl) porphine tetra tosylate (TMP) for drug delivery. Both MN types were mechanically robust, with compression forces of 20.0 N only causing height reductions of 14%. Application forces as low as 8.0 N per array allowed >95% of the MN in each array type to penetrate excised porcine skin, with the MN penetrating to approximately 220 μm. MN significantly enhanced transdermal delivery of ALA and TMP in vitro, with the hydrogel‐forming system comparable with the dissolving system for ALA delivery (approximately 3000 nmol cm^?2 over 6 h), but superior for delivery of the much larger TMP molecule (approximately 14 nmol cm^?2 over 24 h, compared to 0.15 nmol cm^?2). As this technology clearly has potential in enhanced photodynamic therapy of neoplastic skin lesions, we are currently planning animal studies, to be followed by preliminary human evaluations. GMP manufacturing scale‐up is ongoing.     

Ultra resolution chemical fingerprinting of dense non-aqueous phase liquids from manufactured gas plants by reversed phase comprehensive two-dimensional gas chromatography

Ultra resolution chemical fingerprinting of dense non-aqueous phase liquids (DNAPLs) from former manufactured gas plants (FMGPs) was investigated using comprehensive two-dimensional gas chromatography coupled with time of flight mass spectrometry (GC×GC TOFMS). Reversed phase GC×GC (i.e. a polar primary column coupled to a non-polar secondary column) was found to significantly improve the separation of polycyclic aromatic hydrocarbons (PAHs) and their alkylated homologues. Sample extraction and cleanup was performed simultaneously using accelerated solvent extraction (ASE), with recovery rates between 76% and 97%, allowing fast, efficient extraction with minimal solvent consumption. Principal component analysis (PCA) of the GC×GC data was performed in an attempt to differentiate between twelve DNAPLs based on their chemical composition. Correlations were discovered between DNAPL composition and historic manufacturing processes used at different FMGP sites. Traditional chemical fingerprinting methods generally follow a tiered approach with sample analysis on several different instruments. We propose ultra resolution chemical fingerprinting as a fast, accurate and precise method of obtaining more chemical information than traditional tiered approaches while using only a single analytical technique.