A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Hyperfine magnetic fields at sp-sites in Co2YZ Heusler alloys

The systematics of hyperfine magnetic fields at sp impurities on the Z-sites in Co based Heusler alloys are investigated. New TDPAC measurements of Cd hyperfine fields are reported.     

Translation planes of large dimension admitting nonsolvable groups

In this article, the question is considered whether there exist finite translation planes with arbitrarily small kernels admitting nonsolvable collineation groups. For any integerN, it is shown that there exist translation planes of dimension >N and orderq ³ admittingGL(2,q) as a collineation group.     

Transversal-Free Translation Nets

Translation planes of order q ² containing non-Desarguesian Baer subplanes are used to construct transversal-free translation nets with very small deficiencies. Also, a generalization of the ideas of Bruen shows that any non-Desarguesian spread in PG(3, q) produces a transversal-free net of small deficiency.     

Isospin symmetry violation, meson production and η-nucleus interaction studies

We have studied isospin symmetry violation in nuclear reactions by measuring simultaneously the cross-section of the following two reactionsp +d →³H π⁺ andp +d →³He π⁰. The experiment was perfomed at the cooler synchrotron accelerator COSY, Jülich at several beam energies close to the correspondingη production threshold. We also have ongoing programmes onη-nucleus final-state interaction studies viap+⁶ Li →⁷ Be +η reactions, high resolution search for dibaryonic resonances and lambda-proton final state interaction studies. The experimental details and results obtained so far are presented here     

ENSTAR detector forη- mesic studies

We have initiated a search for a new type of nuclear matter, theη-mesic nucleus, using beams from the multi-GeV hadron facility, COSY at Juelich, Germany. A large acceptance scintillator detector, ENSTAR has been designed and built at BARC, Mumbai and fully assembled and tested at COSY. A test run for calibration and evaluation has been completed. In this contribution we present the design and technical details of the ENSTAR detector and how it will be used to detect protons and pions (the decay products ofη-mesic bound state). The detector is made of plastic scintillators arranged in three concentric cylindrical layers. The readout of the detectors is by means of optical fibres. The layers are used to generate ΔE –E spectra for particle identification and total energy information of stopped particles. The granularity of the detector allows for position (θ and ?ø determination making the event reconstruction kinematically complete     

Concise syntheses of the cruciferous phytoalexins brassilexin, sinalexin, wasalexins, and analogues: expanding the scope of the vilsmeier formylation

Efficient syntheses of the phytoalexins brassilexin, sinalexin, and analogues are demonstrated through the application of the Vilsmeier formylation to indoline-2-thiones followed by a new aqueous ammonia workup procedure. Similarly, a very concise two-pot synthesis of the phytoalexins wasalexins using sequential formylation-amination of indolin-2-ones is described. Remarkably, this novel aqueous ammonia workup allows the sequential one-pot formylation-amination, expanding substantially the scope of the Vilsmeier formylation of both indoline-2-thiones and indolin-2-ones. The examination of the formylation-amination reaction and optimization of conditions, as well as the syntheses and antifungal activities of several brassilexin analogues, are reported.     

Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights

A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weightedL _p convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weightsW ²:=e ^–2Q , by first proving a bound for the difference of the orthonormal polynomials of degreen+1 andn–1 of the weightW ². Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least forp>1. Moreover, our necessary conditions apply whenQ(x)=|x|, >1 while our sufficient conditions apply at least for =2,4,6,....Communicated by Vilmos Totik.