Let X be an irreducible smooth projective curve defined over complex numbers, S = {p1, p2, . . . , pn} ⊂ X a finite set of closed points and N ≥ 2 a fixed integer. For any pair (r, d) ∈ N × 1 N Z, there exists a parabolic vector bundle Rr,d,∗ on X , with parabolic structure over S and all parabolic weights in 1 N Z, that has the following property: Take any parabolic vector bundle E∗ of rank r ...

Two difference approximations to the solution of a pseudo-parabolic problem are constructed and shown by means of stability analysis to converge in the "discrete" £2 norm. A relation between parabolic and pseudo-parabolic difference schemes is discussed, and the stability of difference approximations to backward time parabolic and pseudo-parabolic problems is also considered.

We report the first observation of accelerating parabolic beams. These accelerating parabolic beams are similar to the Airy beams because they exhibit the unusual ability to remain diffraction-free while having a quadratic transverse shift during propagation. The amplitude and phase masks required to generate these beams are encoded onto a single liquid crystal display. Experimental results agr...

let $f$ be a locally univalent function on the unit disk $u$. we consider the normalized extensions of $f$ to the euclidean unit ball $b^nsubseteqmathbb{c}^n$ given by$$phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in b^n$ and$$psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$in which $betain[0,1]$, $f(z_1)neq 0$ and $...

in the present work the effect of cu-water nanofluid, as heat transfer fluid, on the performance of a parabolic solar collector was studied numerically. the temperature field, thermal efficiency, mean-outlet temperatures have been evaluated and compared for the conventional parabolic collectors and nanofluid based collectors. further, the effect of various parameters such as fluid velocity, vol...

With the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. Many site-specific methods have been proposed for modeling indoor radio channels. Among these methods, the ray tracing algorithm and the finite-difference time domain (FDTD) method are the most popular ones. The ray tracing approach ...

it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

with the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. many site-specific methods have been proposed for modeling indoor radio channels. among these methods, the ray tracing algorithm and the finite-difference time domain (fdtd) method are the most popular ones. the ray tracing approach ...