We will drop the compactness hypothesis on G in the results of §6, doing this in such a way that problems can be reduced to the compact case. This involves the notions of reductive Lie groups and algebras and Cartan involutions. Let © be a Lie algebra. A subalgebra S c © is called a reductive subaU gebra if the representation ad%\® of ίΐ on © is fully reducible. © is called reductive if it is a...

The Zakharov-Kuznetsov equation governs the behaviour of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic eld. We consider the more realistic situation in which the electrons are non-isothermal. With an appropriate modiied form of the electron number density proposed by Schamel (1973), we show that the reduct...

We will prove that any weakly-split spherical Tits system (B,N) inG = G(k) (G a reductive or a pseudo-reductive k-group) satisfying some natural conditions is “standard”. In particular, if G is anisotropic over k, then such a Tits system is trivial, i.e., B = G.

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

This paper presents a mixed perturbation Monte-Carlo method for static and reliability analysis of structural systems with a mixture of random and interval parameters/loadings. Using a combination of the Taylor expansion, matrix perturbation theory and random interval moment method, the expressions for the mean value and standard deviation of random interval structural responses are developed. ...

Perturbation theory is the standard method to study quantum field theories in the small coupling regime. However, the interplay of the perturbative expansion and the thermodynamic limit remains controversial. In particular, arguments were put forward that the infinite volume limit of perturbative coefficients does not give the correct infinite volume asymptotic perturbation expansion of asympto...

Perturbation theory is the standard method to study quantum field theories in the small coupling regime. However, the interplay of perturbative expansion and the thermodynamic limit remains controversial. In particular, arguments were put forward that the infinite volume limit of perturbative coefficients does not give the correct infinite volume asymptotic perturbation expansion of asymptotica...

A singularly perturbed linear convection-diffusion problem for heat transfer in two dimensions with a parabolic boundary layer is solved numerically. The numerical method consists of a special piecewise uniform mesh condensing in a neighbourhood of the parabolic layer and a standard finite difference operator satisfying a discrete maximum principle. The numerical computations demonstrate numeri...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

The modeling of traffic dynamics under intelligent transportation system (for short, ITS) is an important and interesting topic in flow theory. In this paper, a novel lattice hydrodynamic model presented to describe dynamic features with consideration multi-anticipative average flux effect ITS environment. corresponding stability condition obtained by using the linear analysis analytical result...