This paper presents the results of a recent study about the following aspects relevant to tunneling in soft grounds:e) The domain of deformations due to tunneling in soft ground can be specified within a boundary of a parabolic shape. This boundary is defined by a parabolic formula as a function of a central angle which depends on the soil type i.e., either cohesive or cohesionless. This para...

‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎Also, the method is implemented to three‎ ‎numerical examples‎. ‎The results reveal‎ ‎that the technique is very effective and simple.

We report about results revolving around Kostka–Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup, which we call Liskova semigroup. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among ...

Concentrating collectors are also known as focusing collectors. A parabolic trough is a type of concentrating collector in which the energy from the sunlight is reflected and focused on the absorber tube. This paper focused on the performance of parabolic trough collector which has a ceramic-Metal coating on the absorber tube. A comparison of performance has made between with and without coatin...

The talk concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the require...

We consider the perturbation of parabolic operators of the form ∂t + P (x,D) by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseu...

in his book quranic studies, wansbrough presents two criteria of style and function for typification of old commentatorial texts before al-tabari. recognizing twelve commentatorial devices and borrowing some expressions from jewish commentatorial works, he divides old quranic commentaries into five categories of parabolic, juristic, textual, rhetorical, and analogical. based on literary analysi...

The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave–current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91...

In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain Ω× [0, T ] which is decomposed into an overlapping collection of cylindrical subregions of the form Ωl ×[0, T ], fo...

Background: Focusing with a 4π parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror’s fabrication process and might introdu...