Twisted homology for the mirabolic nilradical

The notion of derivatives for smooth representations of GL(n, ? _p ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In [AGS] derivatives of all orders were defined for smooth admissible Fréchet representations (of moderate growth).A key ingredient of this definition is the functor of twisted coinvariants with respect to the nilradical of the mirabolic subgroup. In this paper we prove exactness of this functor and compute it on a certain class of representations. This implies exactness of the highest derivative functor, and allows to compute highest derivatives of all monomial representations.In [AGS] these results are applied to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations.     

Upper and lower bounds of buckling loads

Upper and lower bounds of buckling load for a nonuniform elastic column under conservative loading are considered. Compatible admissible moment and displacement functions are expressed in terms of a compatible coordinate system. The generalized Timoshenko Quotient and the modified Schreyer and Shih formula are the proposed upper and lower bounds. Both bounds when iterated converge to the exact buckling load. The method described here is simple and convenient and applies to all self-adjoint problems without exception.     

Comparing the enantioselective power of steric and electrostatic effects in transition-metal-catalyzed asymmetric synthesis

The current approach to improve and tune the enantioselective performances of transition-metal catalysts for asymmetric synthesis is mostly focused to modifications of the steric properties of the ancillary ligands of the active metal. Nevertheless, it is also known that electrostatic effects can have a remarkable role to promote selectivity in asymmetric synthesis. Using the Rh-catalyzed asymmetric 1,4-addition of phenylboronic acid to 2-cyclohexenone leading to chiral 3-phenylcyclohexanone as an example, we could show that high enantioselectivity can be indeed achieved using catalysts essentially based either on steric or electrostatic effects as the main source of enantioselective induction. In this contribution we suggest that the analysis of the surface of interaction between the catalyst and the substrate could be a useful tool to quantify the power of steric and electrostatic effects of catalysts.     

C2-symmetric chiral disulfoxide ligands in rhodium-catalyzed 1,4-addition: from ligand synthesis to the enantioselection pathway

A family of chiral C(2)-symmetric disulfoxide ligands possessing biaryl atropisomeric backbones has been synthesized by using the Andersen methodology. Complete characterization includes X-ray crystallographic studies of all ligands and some of their rhodium complexes. Their synthesis, optical purity, electronic properties, and catalytic behavior in the prototypical rhodium-catalyzed 1,4-addition of phenylboronic acid to 2-cyclohexen-1-one are presented through an in depth study of this ligand class. Density functional theory calculations on the step of the catalytic cycle that determines the enantioselectivity are presented and reinforce the first hypothetical explanations for the high levels of asymmetric induction observed.     

Liquid chromatographic/electrospray ionization mass spectrometric identification of the oxidation end‐products of trans‐resveratrol in aqueous solutions

trans‐Resveratrol (3,5,4′‐trihydroxystilbene) is a natural polyphenolic compound that exhibits antioxidant properties. Our study aimed at studying the HO ^. ‐induced oxidation of resveratrol (100 µmol.L^?1) in aerated aqueous solutions. Gamma radiolysis of water was used to generate HO ^. /O free radicals (I = 10 Gy.min^?1, dose = 400 Gy). Oxidation products were identified by direct infusion mass spectrometry and high‐performance liquid chromatography/mass spectrometry. For each product, structural elucidation was based on simple mass spectra, fragmentation spectra and deuterium/hydrogen exchange spectra; the comparison with mass spectra of synthetic products provided valuable information allowing the complete identification of the oxidation products. Four products resulting from the direct attack of HO ^. radicals towards resveratrol were identified respectively as piceatannol (trans‐3,5,3′,4′‐tetrahydroxystilbene), 3,5‐dihydroxybenzoic acid, 3,5‐dihydroxybenzaldehyde and 4‐hydroxybenzaldehyde. Copyright © 2010 John Wiley & Sons, Ltd.     

A Rare Cyclic Dimolybdenum Triad with Three Weakly Interacting Unpaired Electrons

Oxidation of α-[Mo₂(cis-DAniF)₂]₃(μ-F)₆ with an excess of FeCp₂BF₄ produces the triply oxidized species {β-[Mo₂(cis-DAniF)₂]₃(μ-F)₆}(BF₄)₃. During the oxidation process, the conformation in the α triangular species changes from an arrangement in which two dimetal units are parallel and the third one essentially orthogonal to a structure in which all three dimetal units are parallel. Furthermore, upon removal of three electrons, the Mo–Mo distances increase by about 0.05–0.06 Å and the Mo–F bond distances decrease by 0.04 Å. The structural data, as well as EPR, are consistent with an electronically localized system and a decrease in bond order from 4 to 3.5 for each dimetal unit.     

Ultrafast and high-throughput mass spectrometric assay for therapeutic drug monitoring of antiretroviral drugs in pediatric HIV-1 infection applying dried blood spots

Kaletra® (Abott Laboratories) is a co-formulated medication used in the treatment of HIV-1-infected children, and it contains the two antiretroviral protease inhibitor drugs lopinavir and ritonavir. We validated two new ultrafast and high-throughput mass spectrometric assays to be used for therapeutic drug monitoring of lopinavir and ritonavir concentrations in whole blood and in plasma from HIV-1-infected children. Whole blood was blotted onto dried blood spot (DBS) collecting cards, and plasma was collected simultaneously. DBS collecting cards were extracted by an acetonitrile/water mixture while plasma samples were deproteinized with acetone. Drug concentrations were determined by matrix-assisted laser desorption/ionization-triple quadrupole tandem mass spectrometry (MALDI-QqQ-MS/MS). The application of DBS made it possible to measure lopinavir and ritonavir in whole blood in therapeutically relevant concentrations. The MALDI-QqQ-MS/MS plasma assay was successfully cross-validated with a commonly used high-performance liquid chromatography (HPLC)–ultraviolet (UV) assay for the therapeutic drug monitoring (TDM) of HIV-1-infected patients, and it showed comparable performance characteristics. Observed DBS concentrations showed as well, a good correlation between plasma concentrations obtained by MALDI-QqQ-MS/MS and those obtained by the HPLC-UV assay. Application of DBS for TDM proved to be a good alternative to the normally used plasma screening. Moreover, collection of DBS requires small amounts of whole blood which can be easily performed especially in (very) young children where collection of large whole blood amounts is often not possible. DBS is perfectly suited for TDM of HIV-1-infected children; but nevertheless, DBS can also easily be applied for TDM of patients in areas with limited or no laboratory facilities.     

A complete Raman mapping of phase transitions in Si under indentation

Crystalline Si substrates are studied for pressure‐induced phase transformation under indentation at room temperature (RT) using a Berkovich tip. Raman spectroscopy, as a nondestructive tool, is used for the identification of the transformed phases. Raman lines as well as area mapping are used for locating the phases in the indented region. Calculation of pressure contours in the indented region is used for understanding the phase distribution. We report here a comprehensive study of all the phases of Si, reported so far, leading to possible understanding of material properties useful for possible electromechanical applications. As a major finding, distribution of the amorphous phase in the indented region deviates from the conventional wisdom of being in the central region alone. We present phase mapping results for both Si(100) and Si(111) substrates. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliability and reproducibility of perfusion MRI in cognitively normal subjects

Arterial spin labeling (ASL) magnetic resonance imaging (MRI) is becoming a popular method for measuring perfusion due to its ability of generating perfusion maps noninvasively. This allows for frequent repeat scanning, which is especially useful for follow-up studies. However, limited information is available regarding the reliability and reproducibility of ASL perfusion measurements. Here, the reliability and reproducibility of pulsed ASL was investigated in an elderly population to determine the variation in perfusion among cognitively normal individuals in different brain structures. Intraclass correlation coefficients (ICC) and within-subject variation coefficients (wsCV) were used to estimate reliability and reproducibility over a period of 1 year. Twelve cognitively normal subjects (75.5±5.3 years old, six male and six female) were scanned four times (at 0, 3, 6 and 12 months). No significant difference in cerebral blood flow (CBF) was found over this period. CBF values ranged from 46 to 53 ml/100 g per minute in the medial frontal gyrus (MFG) and from 40 to 44 ml/100 g per minute over all gray matter regions in the superior part of the brain. Data obtained from the first two scans were processed by two readers and showed high reliability (ICC >0.97) and reproducibility (wsCV <6%). However, over the total period of 1 year, reliability reduced to a moderate level (ICC=0.63–0.74) with wsCVs of gray matter, left MFG, right MFG of 13.5%, 12.3%, and 15.4%, respectively. In conclusion, measurement of CBF with pulsed ASL provided good agreement between inter-raters. A moderate level of reliability was obtained over a 1-year period, which was attributed to variance in slice positioning and coregistration. As such pulsed ASL has the potential to be used for CBF comparison in longitudinal studies.     

In vivo C magnetic resonance spectroscopy of a human brain tumor after application of C-1-enriched glucose

Objectives

As a unique tool to assess metabolic fluxes noninvasively, ¹³C magnetic resonance spectroscopy (MRS) could help to characterize and understand malignancy in human tumors. However, its low sensitivity has hampered applications in patients. The aim of this study was to demonstrate that with sensitivity-optimized localized ¹³C MRS and intravenous infusion of [1-¹³C]glucose under euglycemia, it is possible to assess the dynamic conversion of glucose into its metabolic products in vivo in human glioma tissue.

Materials and Methods

Measurements were done at 3 T with a broadband single RF channel and a quadrature ¹³C surface coil inserted in a ¹H volume coil. A ¹H/¹³C polarization transfer sequence was applied, modified for localized acquisition, alternatively in two (50 ml) voxels, one encompassing the tumor and the other normal brain tissue.

Results

After about 20 min of [1-¹³C]glucose infusion, a [3-¹³C]lactate signal appeared among several resonances of metabolic products of glucose in MR spectra of the tumor voxel. The resonance of [3-¹³C]lactate was absent in MR spectra from contralateral tissue. In addition, the intensity of [1-¹³C]glucose signals in the tumor area was about 50% higher than that in normal tissue, likely reflecting more glucose in extracellular space due to a defective blood–brain barrier. The signal intensity for metabolites produced in or via the tricarboxylic acid (TCA) cycle was lower in the tumor than in the contralateral area, albeit that the ratios of isotopomer signals were comparable.

Conclusion

With an improved ¹³C MRS approach, the uptake of glucose and its conversion into metabolites such as lactate can be monitored noninvasively in vivo in human brain tumors. This opens the way to assessing metabolic activity in human tumor tissue.