In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...

the purpose of this study is to compare the results of different probabilistic methods such as the perturbation method, stochastic finite element method (sfem) and monte carlo method. these methods were used to study the convergence of direct approach for slope stability analysis and are developed for a linear soil behavior. in this study, two dimensional random fields are used and both the fir...

A family of ideal MHD equilibria is considered introducing the concept of a driving parameter / the increase of which beyond a certain threshold Ao drives the plasma from a linearly stable to an unstable state. Using reductive perturbation theory, the nonlinear ideal MHD equations of motion are expanded in the neighbourhood of Ao with respect to a small parameter e. An appropriate scaling for t...

This technical note discusses convergence conditions of a generalized variant of primal-dual interior point methods. The generalization arises due to the permitted case of having a non-uniform complementarity perturbation vector, which is equivalent to having different barrier parameters for each constraint instead of a global barrier parameter. Widely used prediction-correction methods and rec...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

The first enantioselective organocatalytic reductive amination reaction has been accomplished. The development of a new chiral phosphoric acid catalyst has provided a convenient strategy for the enantioselective construction of protected primary amines and provided a highly stereoselective method for the reductive amination of heterocyclic amines. A diverse spectrum of ketone and amine substrat...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

We study a boundary perturbation problem for a one dimensional Schrödinger equation in which the potential has a regular singularity near the perturbed end point. We give the asymptotic behaviour of the eigenvalues under the perturbation. This problem arose out of the author’s studies of singular elliptic operators in higher dimensions and we illustrate this point with an example. The class of ...

We consider the diiusion problem for the standard map by examining the distribution functions both in the angle and the action. For small perturbations the diiusion occurs only in the presence of an external noise of small amplitude and it is well described by a local isochronous approximation which allows to compute analytically the diiusion coeecient. The angle diiusion is very fast since the...