Divisors in residue classes, constructively

Let be integers satisfying , , , and let . Lenstra showed that the number of integer divisors of equivalent to is upper bounded by . We re-examine this problem, showing how to explicitly construct all such divisors, and incidentally improve this bound to .

     

Degenerations of the moduli spaces of vector bundles on curves II (generalized Gieseker moduli spaces)

LetX ₀ be a projective curve whose singularity is one ordinary double point. We construct a birational modelG(n, d) of the moduli spaceU(n, d) of stable torsion free sheaves in the case (n, d)= 1, such that G(n, d) has normal crossing singularities and behaves well under specialization i.e. if a smooth projective curve specializes toX ₀, then the moduli space of stable vector bundles of rankn and degreed onX specializes toG(n, d). This generalizes an earlier work of Gieseker in the rank two case.     

Mechanistic investigations on the oxidation of <Emphasis Type="SmallCaps">l</Emphasis>-valine by diperiodatocuprate(III) in aqueous alkaline medium: a kinetic model

The oxidation of l-valine (l-val) by diperiodatocuprate(III) (DPC) in aqueous alkaline medium at a constant ionic strength of 3.0 × 10⁻³ mol dm⁻³ was studied spectrophotometrically at 298 K and follows the rate law;

Oxidative degradation and deamination of atenolol by diperiodatocuprate(III) in aqueous alkaline medium: A mechanistic study

The kinetics of oxidation of atenolol (ATN) by diperiodatocuprate(III) (DPC) in aqueous alkaline medium at a constant ionic strength of 0.10 mol dm⁻³ was studied spectrophotometrically. The reaction between DPC and ATN in alkaline medium exhibits 1:2 stoichiometry (ATN:DPC). The reaction is of first order in [DPC] and has less than unit order in both [ATN] and [alkali]. However, the order in [ATN] and [alkali] changes from first order to zero order as their concentration increase. Intervention of free radicals was observed in the reaction. Increase in periodate concentration decreases the rate. The oxidation reaction in alkaline medium has been shown to proceed via a monoperiodatocuprate(III)–ATN complex, which decomposes slowly in a rate-determining step followed by other fast steps to give the products. The main oxidative products were identified by spot test, IR, NMR and LC–ESI-MS studies. The reaction constants involved in the different steps of the mechanism are calculated. The activation parameters with respect to slow step of the mechanism are computed and discussed, and thermodynamic quantities are also determined.     

Rhodotorula aurantiaca penicillin V acylase: Active site characterization and fluorometric studies

Penicillin V acylase (PVA), a member of newly evolved Ntn-hydrolase superfamily, is a pharmaceutically important enzyme to produce 6-aminopenicillanic acid. Active site characterization of recently purified monomeric PVA from Rhodotorula aurantiaca (Ra-PVA), the yeast source, showed the involvement of serine and tryptophan in the enzyme activity. Modification of the protein with serine and tryptophan specific reagents such as PMSF and NBS showed partial loss of PVA activity and substrate protection. Ra-PVA was found to be a multi-tryptophan protein exhibiting one tryptophan, in native and, four in its denatured condition. Various solute quenchers and substrate were used to probe the microenvironment of the putative reactive tryptophan through fluorescence quenching. The results obtained indicate that the tryptophan residues of Ra-PVA were largely buried in hydrophobic core of the protein matrix. Quenching of the fluorescence by acrylamide was collisional. Acrylamide was the most effective quencher amongst all the used quenchers, which quenched 71.6% of the total intrinsic fluorescence of the protein, at a very less final concentration of 0.1 M. Surface tryptophan residues were found to have predominantly more electropositively charged amino acids around them, however differentially accessible for ionic quenchers. Denaturation led to shift in λ_max from 336, in native state, to 357 nm and more exposed to the solvent, consequently increase in fluorescence quenching with all quenchers. This is an attempt towards the conformational studies of Ra-PVA.     

Arithmetic coding as a non-linear dynamical system

In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon’s entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.     

Synthesis and antimicrobial activity of novel 2‐(aryl)‐3‐[5‐(2‐oxo‐2H‐3‐chromenyl)‐1,3‐oxazol‐2‐yl]‐1,3‐thiazolan‐4‐ones

A series of novel 2‐(aryl)‐3‐[5‐(2‐oxo‐2H‐3‐chromenyl)‐1,3‐oxazol‐2‐yl]‐1,3‐thiazolan‐4‐ones 4a , 4b , 4c , 4e , 4f , 4g , 4h , 4i , 4j have been synthesized and assayed for their antibacterial activity against Gram‐positive bacteria viz. Bacillus subtilis (ATCC 6633), Staphylococcus aureus (ATCC 6538p), Micrococcus luteus (IFC 12708), and Gram‐negative bacteria viz. Proteus vulgaris (ATCC 3851), Salmonella typhimurium (ATCC 14028), Escherichia coli (ATCC 25922), and also antifungal activity against Candida albicans (ATCC 10231), Aspergillus fumigatus (HIC 6094), Trichophyton rubrum (IFO 9185), and Trichophyton mentagrophytes (IFO 40996). Among the screened compounds, 4d , 4e , 4f , 4g , and 4j exhibited potent inhibitory activity compared with the standard drug at the tested concentrations. The results reveal that, the presence of difluorophenyl in 4f and pipernyl ring in 4j at 2‐position of thiazolidine‐4‐one ring show significant inhibitory activity. The other compounds also showed appreciable activity against the test bacteria and fungi and emerged as potential molecules for further development. J. Heterocyclic Chem., 2011.     

Detecting cortical lesions in multiple sclerosis at 7 T using white matter signal attenuation

Cortical lesions have recently been a focus of multiple sclerosis (MS) MR research. In this study, we present a white matter signal attenuating sequence optimized for cortical lesion detection at 7 T. The feasibility of white matter attenuation (WHAT) for cortical lesion detection was determined by scanning eight patients (four relapsing/remitting MS, four secondary progressive MS) at 7 T. WHAT showed excellent gray matter-white matter contrast, and cortical lesions were hyperintense to the surrounding cortical gray matter, The sequence was then optimized for cortical lesion detection by determining the set of sequence parameters that produced the best gray matter-cortical lesion contrast in a 10-min scan. Despite the B1 inhomogeneities common at ultra-high field strengths, WHAT with an adiabatic inversion pulse showed good cortical lesion detection and would be a valuable component of clinical MS imaging protocols.     

Studies on outer-sphere electron transfer reactions of surfactant–cobalt(III) complexes with iron(II) in liposome (dipalmitoylphosphotidylcholine) vesicles

The effect of unilamellar vesicles of dipalmitoylphosphotidylcholine (DPPC), both below and above the phase transfer region, on the second-order rate constants for outer-sphere electron transfer between Fe²⁺ and the surfactant?Ccobalt(III) complexes, cis-[Co(en)₂(C₁₂H₂₅NH₂)₂]³⁺ and cis-[Co(trien)(C₁₂H₂₅NH₂)₂]³⁺ (en?=?ethylenediamine, trien?=?triethylenetetramine, C₁₂H₂₅NH₂?=?dodecylamine) was studied by UV?CVis absorption spectroscopy. Below the phase transition temperature of DPPC, the rate decreased with increasing concentration of DPPC, while above the phase transition temperature the rate increased with increasing concentration of DPPC. It is concluded that below the phase transition temperature, there is an accumulation of surfactant?Ccobalt(III) complexes at the interior of the vesicle membrane through hydrophobic effects, and above the phase transition temperature the surfactant?Ccobalt(III) complex is released from the interior to the exterior surface of the vesicle. Through isokinetic plots, we have established that the mechanism of the reaction does not alter during the phase transition of DPPC.