Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.     

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A reversed phase high performance liquid chromatography approach in determining total red blood cell concentrations of 6-thioguanine, 6-mercaptopurine, methylthioguanine, and methylmercaptopurine in a patient receiving thiopurine therapy

A reversed phase high performance liquid chromatographic procedure was developed to quantify 6-thioguanine, 6-mercaptopurine, methylthioguanine, and methylmercaptopurine in red blood cells. The free base of each thiopurine was liberated from the respective nucleoside and nucleotide moiety by acid hydrolysis, which allowed for a determination of the total thiopurine present. 6-Thioguanine and 6-mercaptopurine were analyzed on an octadecylsilane column using methanol + 20 mM sodium phosphate (15:85), pH 7.5, containing 0.07% tetrabutylammonium chloride. Detection was by potassium permanganate oxidation and fluorescence detection at 290 nm excitation and 400 nm emission. Methylmercaptopurine and methylthioguanine were analyzed on a cyanopropylsilane column using methanol + 40 mM sodium phosphate (18:82), pH 2.7, and then ultraviolet absorption at 314 nm and 290 nm, respectively. The method was used to quantify the four primary thiopurines present in red blood cells of an acute lymphoblastic leukemia patient. The procedure may be a therapeutic monitoring technique that quantifies the cytotoxic drug burden in patients receiving azathioprine or 6-mercaptopurine therapy.     

Splitless on-line coupling of capillary high-performance liquid chromatography,capillary electrochromatography and pressurized capillary electrochromatography with nuclear magnetic resonance spectroscopy

A mixture of unsaturated fatty acid methyl esters was separated with a new splitless capillary set-up. With the employed apparatus configuration different capillary separation techniques such as capillary high-performance liquid chromatography (cHPLC), capillary electrochromatography (CEC) and pressurized capillary electrochromatography (pCEC) could be applied. The detection and identification of the sample compounds were accomplished by hyphenating these capillary separation techniques with nuclear magnetic resonance (NMR) spectroscopy using a novel configuration of the detection capillary set-up. Using modified electrokinetically driven separation techniques, the electric field was applied solely across the separation column. With this improved interface for capillary liquid chromatography-NMR on-line coupling, the stereochemical assignment of the cis and trans configuration of unsaturated fatty acids could be easily accomplished. Finally, the results of cHPLC-NMR, CEC-NMR and pCEC-NMR coupling experiments were compared.Dedicated to Professor Günter Häfelinger on the occasion of his 65th birthday     

A maximum likelihood estimator to distinguish single molecules by their fluorescence decays

We have developed a maximum likelihood estimator to distinguish between similar molecules at the single molecule level based upon fluorescence decay measurements. Time resolved fluorescence measurements for single Rhodamine 6G and tetramethylrhodamine isothiocyanate molecules in fluid flow are derived from time-correlated single photon counting. A maximum likelihood estimator is developed and applied to data from a mixture of molecules. Single molecules are identified and distinguished by their fluorescence time decays. Comparison is made between identification error rates and theoretical predictions. To our knowledge, this is the first reported example of single molecule identification by fluorescence decay in a mixture.     

Practical Considerations for Selection of Representative Elementary Volumes for Fluid Permeability in Fibrous Porous Media

We investigate the lower bound of the area of a square-shaped representative elementary volume (REV) for the permeability tensor for transverse Stokes flow through randomly packed, parallel, and monodisperse cylinders. The investigation is significant to flow models using small calculation regions for fibrous porous media, such as modeling defect formation during directional solidification in the mushy zone of dendritic alloys. Using 90 ensembles of 1,000 domains, where each ensemble comprises domains with the same number and size of cylinders, we develop correlations between the permeability tensor invariants and macroscopic features of the domain. We find that for ensembles of domains with fewer than 200 cylinders, the eigenvectors of the permeability tensors exhibit preferential alignment with the domain axes, demonstrating that the estimated permeability is significantly affected by the periodic boundary conditions for these cases. Our results also suggest that the anisotropy of the permeability tensor may not be insignificant even for large sampling volumes. These results provide a practical lower bound for the calculation volumes used in permeability simulations in fibrous porous media, and also suggest that modelers should consider using an anisotropic tensor for small calculation volumes if phenomena such as channeling are important.