The Tate Conjecture for Generic Abelian Varieties

Let A V be a Kuga fibre variety of Mumford's Hodge type, definedover a finitely generated subfield of C, and let be the genericpoint of V. We show that any element of which is invariant under , for some finite extension E of k(), is fixed bythe semisimple part of the Hodge group of A. If A V satisfiesthe H₂-condition, then the Hodge and Tate conjectures are equivalentfor A, and the Mumford–Tate conjecture is true.     

Modeling the free radical polymerization of acrylates

Acrylates have gained importance because of their ease of conversion to high‐molecular‐weight polymers and their broad industrial use. Methyl methacrylate (MMA) is a well‐known monomer for free radical polymerization, but its α‐methyl substituent restricts the chemical modification of the monomer and therefore the properties of the resulting polymer. The presence of a heteroatom in the methyl group is known to increase the polymerizability of MMA. Methyl α‐hydroxymethylacrylate (MHMA), methyl α‐methoxymethylacrylate (MC₁MA), methyl α‐acetoxymethylacrylate (MAcMA) show even better conversions to high‐molecular‐weight polymers than MMA. In contrast, the polymerization rate is known to decrease as the methyl group is replaced by ethyl in ethyl α‐hydroxymethylacrylate (EHMA) and t‐butyl in t‐butyl α‐hydroxymethylacrylate (TBHMA). In this study, quantum mechanical tools (B3LYP/6‐31G*) have been used in order to understand the mechanistic behavior of the free radical polymerization reactions of acrylates. The polymerization rates of MMA, MHMA, MC₁MA, MAcMA, EHMA, TBHMA, MC₁AN (α‐methoxymethyl acrylonitrile), and MC₁AA (α‐methoxymethyl acrylic acid) have been evaluated and rationalized. Simple monomers such as allyl alcohol (AA) and allyl chloride (AC) have also been modeled for comparative purposes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Overtone spectroscopy of C-H ethyl stretches of 1-butyne

Room-temperature photoacoustic (PA) spectra and jet-cooled action spectra of the first to third overtone regions of the ethyl C-H stretches in vapor phase 1-butyne, CH3CH2C[Triple Bond]C-H, were measured. Both the PA and action spectra exhibit a complex multiple peak structure being better resolved and more pronounced in the latter, due to inhomogeneous structure reduction. The observed manifolds were analyzed in terms of a simplified joint local-/normal-mode (LM/NM) model accounting for two types of C-H stretches (methyl and methylene) and for Fermi resonances between stretches and deformations. The retrieved parameters, used for calculation of the eigenstates, come from the best-fit parameters based on the diagonalization of the vibrational Hamiltonian in the LM/NM basis. The parameters were obtained by comparing the eigenvalues and the sum of the squares of the expansion coefficients of the eigenvectors of the C-H stretches of methyl and methylene to the action spectra peak positions and intensities, respectively. This approximate model vibrational Hamiltonian is proposed to explain most observed spectral features, corresponding to C-H stretch bands and to combinations of C-H stretches and deformations, indicating the importance of the Fermi resonance. The model was also applied to calculate the dynamics of the C-H stretching modes resulting from coupling with the deformations, implying rapid initial state decay on subpicosecond time scale. Decays of several picoseconds were found for complete transfer of probability from the initially prepared state of methylene and methyl to the counterpart LM states.     

Evidence for new bands in the 3nu1 and 4nu1 regions of propyne

Vibrationally mediated photodissociation and room-temperature photoacoustic (PA) spectroscopy have been used for obtaining action (monitoring the yield of H photofragments) and absorption spectra of the second (3nu(1)) and third (4nu(1)) C-H acetylenic stretches overtone regions in propyne. The band contours appearing in these regions seem mostly regular even though they are perturbed, as expressed by the origin shifts in different K components, splitting of the K structure, and splitting due to resonances between neighboring states. Symmetric rotor simulations of the band contours of the PA and action spectra allowed extraction of the molecular parameters and rough estimates for the homogeneous broadening arising from energy flow to the bath vibrational states. We particularly benefited from the reduced congestion in the jet-cooled action spectra and their simulations, which enabled observation of yet unknown features in the vicinity of the 3nu(1) and 4nu(1) states. Particularly, the emergence of the new state in the 3nu(1) region was confirmed by the action spectra monitored at several differing jet temperatures, suggesting that it is a dark state in IR vibrational excitation that becomes brighter in UV excitation to the upper electronic state. The monitored and Gaussian-fitted Doppler profiles point to the release of H photofragments with low average translational energies, attributed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.     

Synthesis and Antimycobacterial Activity of New 2-Hydroxy- N -(3-oxo-1-thia-4-azaspiro[4.4]non-4-yl)/(3-oxo-1-thia-4-azaspiro[4.5]dec-4-yl)-2,2-diphenylacetamide Derivatives

2-Hydroxy-2,2-diphenylacetohydrazide (2), cyclic ketones, and mercaptoalkanoic acids were converted into 2-hydroxy-N-(3-oxo-1-thia-4-azaspiro[4.4]non/[4.5]dec-4-yl)-2,2-diphenylacetamide derivatives (3, 4) in a one pot procedure. Compounds 3 and 4 were tested for in vitro antimycobacterial activity against M. tuberculosis H37Rv. The compounds were found to provide 0–86% inhibition of mycobacterial growth in the primary screen conducted at 6.25 μg/cm³.     

Determining the vibrational pattern via overtone cold spectra: C-H methyl stretches of propyne

Vibrationally mediated photodissociation and photoacoustic (PA) spectroscopy were employed for studying the intramolecular dynamics of propyne initially excited to the first through fourth overtone of methyl C-H stretching modes. Room-temperature PA and jet-cooled action spectra, monitoring the absorption of the parent and the yield of the ensuing H photofragments, respectively, were obtained. The PA spectra exhibit mainly broad features, while the action spectra, due to inhomogeneous structure reduction, expose multiple peaks of recognizable shapes in the differing overtone manifolds. Symmetric rotor simulations of the band contours of the action spectra allowed retrieving of band origins and linewidths. The linewidths of the bands in each manifold enabled estimates for energy redistribution times out of the corresponding states to the bath states, the times ranging from 18+/-6 ps for two quanta of C-H excitation to subpicosecond for five quanta. The data were also analyzed in terms of a normal-mode model and a joint local-/normal-mode model. These models enabled determination of harmonic frequencies, anharmonicities, and interaction parameters reproducing the observed data in all monitored regions and provided spectral assignments. The measured Doppler profiles were well fitted by Gaussians with widths suggesting low average translational energies for the released H photofragments. These low energies and their similarities to those for dissociation of propyne isotopomers preexcited to acetylenic C-H stretches were ascribed to an indirect dissociation process occurring after internal conversion to the ground electronic state and isomerization to allene.     

HPLC estimation of iothalamate to measure glomerular filtration rate in humans

Glomerular filtration rate (GFR) is usually determined by estimation of iothalamate (IOT) clearance. We have developed and validated an accurate and robust method for the analysis of IOT in human plasma and urine. The mobile phase consisted of methanol and 50 mM sodium phosphate (10:90; v/v). Flow rate was 1.2 mL/min on a C18 reverse phase column, Synergi-hydro (250 × 4.6 mm) 4 µm 80 Å, with an ultraviolet detector set to 254 nm. Acetonitrile was used for the deproteination and extraction of IOT from human plasma and urine. Precision and accuracy were within 15% for IOT in both plasma and urine. The recoveries of IOT in urine and plasma ranged between 93.14% and 114.74 and 96.04–118.38%, respectively. The linear range for urine and plasma assays were 25–1500 and 1–150 µg/mL respectively. The lower limits of detection were 0.5 µg/mL for both urine and plasma, with no interference from plasma and urine matices. This method has been fully validated according to FDA guidelines and the new HPLC assay has been applied to a new formulation of IOT (Conray? 43), to calculate GFR in healthy volunteers. The new method is simple, less expensive and it would be instrumental in future clinical and pharmacokinetic studies of iothalamate in kidney patients.     

Syntheses and crystal structures of mixed-ligand copper(II)–imidazole–carboxylate complexes

The syntheses, characterization, and crystal structures of the reaction products of Cu²⁺ with imidazole (Himz) and different aromatic carboxylates, viz.: [Cu(Himz)₂(cinn)₂(H₂O)] (1), [Cu(Himz)₂(paba)₂] (2) and [Cu(Himz)₂(clba)₂] (3) (cinn^– = C₉H₇O₂^–, paba^– = C₇H₆NO₂^–, clba^– = C₇H₄ClO₂^–) are described and studied by spectroscopic (UV–visible, FTIR) measurements. Single-crystal X-ray diffraction analyses indicate that each complex is monomeric. The metal ion in 1 adopts square-pyramidal coordination geometry arising from two imidazole nitrogens, two cinnamate oxygens, and an apical aqua. The metal ions of 2 and 3, however, assume a square planar configuration, which is realized by coordination of two nitrogens of two imidazoles and two oxygens; in both complexes, the imidazole moieties are trans to each other. TGA results indicate that upon heating, these complexes lose their carboxylate anions first, followed by removal of the imidazole molecules.