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In this note we establish existence of solutions of singular boundary value problem $-(p(x)y^{\prime }(x))^{\prime}=q(x)f(x,y,py')$ for $0< x\leq b$ and $y'(0)=0$, $\alpha_{1}y(b)+\beta_{1}p(b)y^{\prime}(b)=\gamma_{1}$ with $p(0)=0$ and $q(x)$ is integrable. Regions of multiple solutions have also been determined., Comment: 12 pages

Barrium fluoride (BaF2) thin films were prepared by electron beam evaporation technique at room temperature, on glass, Silicon and Aluminum substrates having thickness of 20 nm each. Its structural property and surface morphology were studied using glancing angle X-ray diffraction (GAXRD) and atomic force microscopy (AFM) respectively. It was found that grain size, average surface roughness and interface width changes with different substrates. Higuchi algorithm is applied for the fractal measure on AFM images.It was observed found that the fractal dimension varied from substrate to substrate.

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings in normal gauge for Lyra's manifold by applying the variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein's modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the expansion ($\theta$) in the model is proportional to the component $\sigma^{1}_{~1}$ of the shear tensor $\sigma^{j}_{i}$. This condition leads to $A = (BC)^{m}$, where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector $\beta$ behaves like cosmological term $\Lambda$ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. Some physical and geometric behaviour of these models are also discussed., Comment: 24 pages, 10 figures

We carry out a detailed investigation of neutral ($D^0$) and charged ($D^-$) impurity states of hydrogen-like donors in spherical semiconductor quantum dots. The investigation is carried out within the effective mass theory (EMT). We take recourse to local density approximation (LDA) and the Harbola-Sahni (HS) schemes for treating many-body effects. We experiment with a variety of confining potentials: square, harmonic and triangular. We observe that the donor level undergoes shallow to deep transition as the dot radius ($R$) is reduced. On further reduction of the dot radius it becomes shallow again. We term this non-monotonic behaviour \textbf{SHADES}. This suggests the possibility of carrier {\textbf{\textit{``freeze out''}}} for both $D^0$ and $D^-$. Further, our study of the optical gaps also reveals a {\textbf{SHADES}} transition., Comment: 19 pages, 8 figures, Revised Version

We present a study of anisotropy of transport and magnetic properties in La_{1-x}Ca_{x}MnO_{3} (x \approx 1/3) film prepared by pulsed-laser deposition onto a LaAlO_{3} sunstrate. We found a non-monotonic dependence of magnetoresistance (MR) on magnetic field H for both H perpendicular and parallel to the film plane but perpendicular to the current. This rather complex behavior of MR manifests itself at low temperatures, far below the Curie temperature. Two main sources of MR anisotropy have been considered in the explanantion of the results: (1) the existence of preferential directions of magnetization (due to strains stemming from the lattice film-substrate mismatch or other reasons); (2) dependence of resistance on the angle between current and the magnetization, which is inherent in ferromagnets., Comment: 11 pages, 12 EPS figures