Serre’s modularity conjecture (II)

This paper is the first part of a work which proves Serre’s modularity conjecture. We first prove the cases p 1 2p\not=2 and odd conductor, and p=2 and weight 2, see Theorem 1.2, modulo Theorems 4.1 and 5.1. Theorems 4.1 and 5.1 are proven in the second part, see Khare and Wintenberger (Invent. Math., doi:, 2009). We then reduce the general case to a modularity statement for 2-adic lifts of modular mod 2 representations. This statement is now a theorem of Kisin (Invent. Math., doi:, 2009).     

On the curious structural phases in Al-deficient (Al62Cu23Cr15) and Al-rich (Al68Cu17Cr15) quasicrystalline alloys

In the present work investigations on the effect of stoichiometric variations on the Occurrence and stabilization of quasicrystalline (qc) and related phases have been carried out. Based on the explorations of several Al-deficient and Al-rich versions of the ideal nominal composition i.e. Al₆₅Cu₂₀Cr₁₅, it has been found that the alloy compositions corresponding to Al₆₂Cu₂₃Cr₁₅ (Al-deficient) and Al₆₈Cu₁₇Cr₁₅ (Al-rich) exhibit several structural subtleties. The Al-deficient alloy, has been found to exhibit crystalline bcc and fcc phases with a = 8.90 Å and a = 17.98 Å respectively. In addition to these phases, a new crystalline bcc variant (a = 15.42 Å) originating from the bcc (a = 8.90 Å) phase has been found. Also a curious superstructure of the fcc (a = 17.98 Å) has been observed. The Al-rich alloy typified by Al₆₈Cu₁₇Cr₁₅, on the other hand, does not exhibit any structural variants, instead it shows nearly pure i-phase.     

A note on restriction maps in the cohomology¶of S-arithmetic groups

We prove injectivity results for restriction maps in the cohomology of S-arithmetic groups: the results proved are valid for cohomology with both characteristic 0 and characteristic p coefficients. Received: 12 March 1999 / Revised version: 10 July 2000     

Harmonic generation in superconducting Bi(Pb)SrCaCuO thick films

We present a detailed study of harmonic generation in Bi(Pb)SrCaCuO superconducting thick film prepared by screen printing technique. A comparative study of amplitude of harmonics of two films of different J_c have been carried out. The variation of amplitudes of the harmonics are studied as a function of magnitude of ac and dc field. The temperature dependence of amplitude of third harmonic (V³) is studied with increasing amplitude as well as frequency of ac field. These results are analyzed in the frame work of critical state model. V₃ -T curve also indicates the presence of two phases in Bi(Pb)SrCaCuO film.     

A non-mixing technique for enhancement of the tuning range of Rhodamine 6G using Rhodamine B

An optical scheme for extension of spectral tuning range of Rhodamine 6G by Rhodamine B is reported. The dye solutions are kept separately in a specially designed coupled resonator. The tuning range of Rhodamine 6G dye laser is extended from 564–609 to 564–645 nm.     

ϒ′ (10.01) resonance parameters

On the basis of some exactly solvable models we suggest that the Rayleigh-Schrödinger perturbation series for the energy eigenvalue may have nothing to do with the corresponding exact value in case the vacuum expectation value of the system changes discontinuously, i.e. the system undergoes first-order phase transition.     

Mass Spectrometry in the Structural Studies of Oligosaccharides

Abstract

On the basis of the reported low-resolution electron impact (EI) mass spectral decomposition patterns of a few underivatlsed simple disaccnarides^1-3 and the results of a high-resolution electron impact mass spectrum of a model disaccharide β-methyl pachybioside,⁴ a common fragmentation pathway of such compounds could be worked out. Using the derived standard decomposition pathways, structure of a novel tetrasaccharide, orthenthose, has been elucidated as oleandrose tetrasaccharide.     

One-step purification and characterization of an alkaline protease from haloalkaliphilic Bacillus sp

An alkaline protease producer haloalkaliphilic bacteria (isolate Vel) was isolated from west coast of India. It was related to Bacillus pseudofirmus on the basis of 16S r RNA gene sequencing, lipid profile and other biochemical properties. The protease secreted by this bacteria was purified 10-fold with 82% yield by a single step method on Phenyl Sepharose 6 Fast Flow column. The apparent molecular mass based on the sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS-PAGE) was estimated to be 29 000 Da. The Km and Vmax towards caseinolytic activity were found to be 2 mg ml(-1) and 289.8 microg min(-1), respectively. The enzyme was active over the pH range of 8.5-12.0, the optimum being 10-11.0. The purified enzyme when kept at 45 degrees C and 50 degrees C for 40 min retained 92% and 85% protease activity, respectively. Effect of NaCl concentration on protease activity showed that the enzyme was slightly inhibited with high concentration of salt. The proteolytic activity was inhibited by PMSF, suggesting that the enzyme may belong to serine type protease. Interestingly, the activity was slightly enhanced with SDS (0.1%) and Triton X-100 (0.1%) but remained unaffected by Tween 80 (0.1%). The activity was affected by metal ions to varying extent. While Mn2+, Zn2+ and Mg2+ had no significant effect on protease activity, the enzyme was activated with Ca2+ (1 mM) and Cu2+ (5 mM). The stability of the enzyme in the presence of detergent components and surfactants is particularly attractive for its application in detergent industries.     

Large-scale muLC-MS/MS for silver- and Coomassie blue-stained polyacrylamide gels

2-DE combined with LC-MS/MS has become a routine, reliable protein separation and identification technology for proteome analysis. The demand for large-scale protein identifications after 2-DE separation requires a sensitive and high-throughput LC-MS/MS method. In this report, a simple, splitless, fully automated capillary LC-MS/MS system was described for the large-scale identification of proteins from gels stained with either silver or CBB. The gel samples were digested and peptides were extracted using an in-gel digestion workstation. The peptides were automatically introduced into a capillary column by an autosampler connected to an HPLC pump. A nanoLC pump was then used to deliver the gradient and elute the peptides from the capillary column directly into an LCQ IT mass spectrometer. Neither a peptide trapping setting nor a flow split is needed in this simple setup. The collected MS/MS spectra were then automatically searched by SEQUEST, and filtered and organized by DTASelect. Hundreds of silver-stained or CBB-stained Shewanella oneidensis, Geobacter sulfurreducens, and Geobacter metallireducens proteins separated by denaturing or nondenaturing 2-DE were digested and routinely analyzed using this fully automated muLC-MS/MS system. High peptide hits and sequence coverage were achieved for most CBB-stained gel spots. About 75% of the spots were found to contain multiple proteins. Although silver staining is not commonly thought to be optimal for MS analysis, protein identifications were successfully obtained from silver-stained 2-DE spots detected using methods with and without formaldehyde for protein fixation.     

A crosslinked preparation ofE. coli β-D-galactosidase

β-D-Galactosidase fromE. Coli was crosslinked using glutaraldehyde and two bisimidoesters. With glutaraldehyde and dimethyl adipimidate (DMA), it is possible to obtain preparations having higher activity than the native enzyme. Glutaraldehyde and DMA gave preparations showing enhanced thermal stability. The preparation crosslinked with DMA, when used for continuous hydrolysis of lactose in milk, was found to be significantly better than the native enzyme.