Diffraction of sound pulses by a rigid cylinder in an inhomogeneous medium

We consider the problem of scattering of two-dimensional sound pulses by a rigid circular cylinder embedded in a cylindrically stratified inhomogeneous medium. The line source is parallel to the axis of the cylinder. It is assumed that the velocity of soundc is given byc ^?1=pr ^q, wherep andq are real constants andp>0. The method of dual integral transformation developed by Friedlander is used. The solution in terms of pulse propagation modes gives the diffracted pulse and the method of steepest descents yields the geometrical acoustic field.     

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     

Temperature Dependent Raman Spectroscopic Study of the Fe Doped La0.67Sr0.33MnO3 Prepared Using Ball Milling Method

Physics of the Solid State - Polycrystalline samples of La0.67Sr0.33Mn0.65Fe0.35O3 (LSMFO) were synthesized using the standard ball mill method with different calcination temperatures ranging from...     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Rankin–Cohen brackets on Jacobi forms and the adjoint of some linear maps

Given a fixed Jacobi cusp form, we consider a family of linear maps between the spaces of Jacobi cusp forms using the Rankin–Cohen brackets, and then we compute the adjoint maps of these linear maps with respect to the Petersson scalar product. The Fourier coefficients of the Jacobi cusp forms constructed using this method involve special values of certain Dirichlet series associated to Jacobi cusp forms. This is a generalization of the work due to Kohnen (Math Z, 207:657–660, 1991) and Herrero (Ramanujan J,  10.1007/s11139-013-9536-5, 2014) in case of elliptic modular forms to the case of Jacobi cusp forms which is also considered earlier by Sakata (Proc Japan Acad Ser A, Math Sci 74, 1998) for a special case.     

On subgroups and factor groups of GL(n, q) acting on spreads with the same characteristic

Let π^l_∞ be an affine translation plane of order q^r with GF(q) in its kern. Suppose G is a subgroup of the translation complement of π^l_∞ which leaves invariant a set Δ of q + 1 slopes and acts transitively on l_∞?Δ. We study the situation when G≌SL(n, q) or PSL(n, q).We show that if G|Δ = identity, then π^l_∞ is a Hall plane, a Lorimer-Rahilly plane (LR-16) or a Johnson-Walker plane (JW-16). Moreover, if n?3, then G fixes Δ elementwise and π^l_∞ is LR-16 or JW-16.     

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.     

The Ubiquity of the Orders of Fractional Semifields of Even Characteristic

To each non-square integer \(2^{2N+1}\ge 2^5\) there correspond semifields \(D\) of order of \(2^{2N+1}\) that contain \(\text{ GF}(4)\) . Hence there exist affine planes for each non-square order \(2^{2N+1}\ge 2^{5}\) that contain subaffine planes of order \(2^2\) . Moreover, there also exists semifields \(D_1\) and \(D_2\) , with \(|D_1|= |D_2| =|D|\) such that \(D_1\) is commutative and \(D_2\) is non-commutative but neither \(D_1\) nor \(D_2\) contains \(\text{ GF}(4)\) .     

One-pot thioetherification of aryl halides with thiourea and benzyl bromide in water catalyzed by Cu-grafted furfural imine-functionalized mesoporous SBA-15

Surface functionalization of SBA-15 followed by its reaction with Cu(OAc)(2) has been carried out to develop a new Cu-grafted functionalized mesoporous material, which catalyzes one-pot three component coupling of different aryl halides with thiourea and benzyl bromide in aqueous medium to produce aryl thioethers in very good yields (80-88%).     

An ab initio study of ground state, electronic and thermodynamical properties of GaP and Ga2P

In the present paper, we report an ab initio calculation of the ground state, electronic and thermodynamical properties like constant volume lattice specific heat, vibrational energy, internal energy, and entropy for GaP and Ga₂P is presented. These properties are obtained after calculating the phonon spectrum over the entire Brillouin zone. The calculations were performed using the ABINIT program package, which is based on density functional theory (DFT) method and the use of pseudopotentials and plane wave expansion. Difference in the ground state properties such as electronic structure and thermodynamical properties are discussed. The thermodynamical properties follow the expected trend. There is a good agreement between present theoretical and limited available experimental data in the case of ground state such as lattice constant and bulk modulus and electronic properties. With the increase of Ga atoms in the unit cell the semiconducting nature of Ga₂P turns to metallic. There is a noticeable difference in the thermodynamical properties in the case of both gallium compounds.