In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mas...

We prove a combinatorial rule for complete decomposition, in terms of Langlands parameters, representations p-adic GLn that appear as parabolic induction from large family (ladder representations). Our obviates the need computation Kazhdan-Lusztig polynomials these cases, and settles conjecture posed by Lapid. These results are transferrable into various type A frameworks, such decomposition co...

In an axisymmetric CO2-N2-H2O gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. To obtain a maximal small signal gain, some authors have tested several families of curves for ?. To find the most general solution for ?, an application of Pontryagin’s principle led to the conjuncture that the optimal ? must consist o...

in an axisymmetric co2-n2-h2o gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. to obtain a maximal small signal gain, some authors have tested several families of curves for ?. to find the most general solution for ?, an application of pontryagin’s principle led to the conjuncture that the optimal ? must consist o...

Based on the fundamental combustible systems properties - distributed nonlinear energy sources and flow connection between environment elements an analysis of various combustion dust modes is presented. Depending ratio betweencharacteristic burning times (thermokinetic characteristics) heat transfer (scale characteristics), limiting are considered as self-ignition, diffusion auto-wave combustio...

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.

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...