The E8 {manifold has several natural framed link descriptions, and we give an e cient method (via \grapes") for showing that they are indeed the same 4{manifold. This leads to explicit handle pictures for the perturbation of singular bers in an elliptic surface to a collection of shtails. In the same vein, we show how the degeneration of a regular ber to a singular ber in an elliptic surface pr...

The E8 –manifold has several natural framed link descriptions, and we give an efficient method (via “grapes”) for showing that they are indeed the same 4–manifold. This leads to explicit handle pictures for the perturbation of singular fibers in an elliptic surface to a collection of fishtails. In the same vein, we show how the degeneration of a regular fiber to a singular fiber in an elliptic ...

The peristaltic flow of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel is investigated. The channel asymmetric is produced by choosing the peristaltic wave train on thewall of different amplitude and phase. The governing nonlinear partial differential equations for the Jeffrey fluid model are derived in Cartesian coordinates system. Analytic solutions f...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

The software SAFE has been developed at the State Statistical Institute Berlin-Brandenburg and has been in regular use there for several years now. It involves an algorithm that yields a controlled cell frequency perturbation. When a microdata set has been protected by this method, any table which can be computed on the basis of this microdata set will not contain any small cells, e.g. cells wi...

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...

Using an effective low-energy Hamiltonian derived from the first-principles electronic structure calculations for the narrow t2g bands of YTiO3, LaTiO3, YVO3, and LaVO3, we evaluate the contributions of the correlation energy (EC) to the stability of different magnetic structures, which can be realized in these distorted perovskite oxides. We consider two approximations for EC , which are based...

It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a choice of scales of independent variables in the reductive perturbation method. Recently a novel method based on the perturbative renormalization group theory has...