An exercise concerning the selfdual cusp forms on GL(3)

Using L-functions and various known results, we provide a proof of the following Let F be a number field and II a cuspidal automorphic form on GL(3)/F which is selfdual. Then, up to replacing II by a quadratic twist, it can be realized as the adjoint of a cusp form π on GL(2)/F, with π unramified at any prime where II is. We also investigate the properties of π when II is regular and algebraic.     

Study on the ferromagnetism in Co and N doped ZnO thin films

Present investigation reports the structural, optical and magnetic properties of co-doping of Co and N ions in ZnO samples, prepared by two distinct methods. In the first method, samples are synthesized by Sol–gel technique in which the Co and N are co-doped simultaneously during the growth process itself. In the second case, N ions are implanted in the Co doped ZnO thin films grown by Pulsed Laser Deposition (PLD). Structural studies showed that the nitrogen implantation on Co doped ZnO samples developed compressive stress in the films. X-ray photoelectron spectroscopy confirmed the doping of Co and N in ZnO matrix. In the Resonant Raman scattering multiple LO phonons up to fifth order are observed in the (Co, N) co-doped ZnO. Photoluminescence spectra showed that there is reduction in the bandgap due to the presence of Co in the lattice and also the presence of Zn vacancies in the films. All samples showed ferromagnetic behavior at room temperature. The magnetic moment observed in the implanted films is found to be varied with the different dosages of the implanted N ions. First principle calculations have been carried out to study the possible magnetic interaction in the co-doped system. Present study shows that the ferromagnetic interaction is due to the hybridization between N 2p and Co 3d states in the (Co, N) co-doped ZnO and is very sensitive to the geometrical configurations of dopants and the vacancy in the ZnO host lattice.     

Synthesis of GaN phase by ion implantation

GaN phase is synthesized using systemic implantation of nitrogen ions of multiple energies (290, 130 and 50 keV) into Zn-doped GaAs (1 0 0) at room temperature and subsequent annealing at 850 °C for 30 min in Ar + H₂ atmosphere. The implanted doses of nitrogen ions are 5 × 10¹⁶ and 1 × 10¹⁷ ions-cm⁻². Glancing angle X-ray diffraction studies show that hexagonal phase of GaN were formed. The photoluminescence studies show the emission from the band edge as well as from point defects.     

Covariant and consistent anomalies in two dimensions in path-integral formulation

We give a definition of a one-parameter family of regularized chiral currents in a chiral non-Abelian gauge theory in two dimensions in path-integral formulation. We show that covariant and consistent currents are obtained from this family by selecting two specific values of the free parameter, and thus our regularization interpolates between these two. Our procedure uses chiral bases constructed from eigenfunctions of thesame operator for defining _L and . Definition of integration measure and regularization is done in terms of thesame Hermitian operator . Covariant and consistent currents (and indeed the entire family) are classically conserved. Difference with previous works are explained, in particular, that anomaly in a general basis does differ from the Jacobian contribution.     

Mössbauer study of ferromagnetic metallic glasses irradiated by swift heavy ions at temperatures 100 and 300 K

The effect of swift heavy ion irradiation on ferromagnetic metallic glasses Fe₄₀Ni₃₈Mo₄B₁₈ and Fe₇₈Si₉B₁₃ has been studied. The ion beams used are 100 MeV ¹²⁷I and 180 MeV ¹⁹⁷Au. The specimens were irradiated at fluences ranging from 3 × 10¹² to 1.5 × 10¹⁴ ions/cm². The irradiations have been carried out at temperatures 100 and 300 K. The magnetic moments are sensitive towards the irradiation conditions such as irradiation temperature and stopping power of incident ion beam. The irradiation-induced effects have been monitored, by using Mössbauer spectroscopy. The modifications in magnetic anisotropy and hyperfine magnetic field distributions, as an effect of different irradiation temperature as well as different stopping power have been discussed. After irradiation, all the samples remain amorphous and magnetic anisotropy considerably changes from its original in-plane direction. The results show enhancement in magnetic anisotropy in the specimen irradiated at 100 K, as compared to that of irradiated at 300 K. It is expected that at low temperature, the stresses produced in the material would remain un-annealed, compared to the samples irradiated at room temperature and therefore, the modification in magnetic anisotropy would be enhanced. A distribution of hyperfine magnetic field, of the samples irradiated at low temperature, show a small but distinct peak at ～?11 Tesla, indicating Fe-B pairing.     

Effects of 50 MeV Si ion irradiation on nonlinear optical benzimidazole single crystals

The 50 MeV Si⁷⁺ ion irradiation induced modifications on structural, dielectric, optical and mechanical properties of Vertical Bridgman grown benzimidazole (BMZ) crystals were studied. The high resolution X‐ray diffraction studies show the quality of as grown BMZ and irradiated BMZ crystals. The dielectric constant and dielectric loss as a function of frequency and temperature was studied in detail. The ion induced mechanical behaviour of both as grown BMZ and irradiated BMZ crystals has been explained with the indentation effects using Vickers microhardness tester. UV‐VIS. studies reveal the decrease in bandgap values and defects on irradiation. The above results are discussed in detail. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On bilinear Hardy inequality and corresponding geometric mean inequality

Ricerche di Matematica - The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case $$1< q, p_1, p_2<\infty $$ with...