We construct center-stable and center-unstable manifolds, as well as stable and unstable manifolds, for the nonlinear Klein–Gordon equation with a focusing energy subcritical nonlinearity, associated with a family of solitary waves which is generated from any radial stationary solution by the action of all Lorentz transforms and spatial translations. The construction is based on the graph trans...

This paper presents low cycle fatigue (LCF) life prediction of a coated and uncoated exhaust manifolds. First Solidworks software was used to model the exhaust manifolds. A thermal barrier coating system was applied on the tubes c of the exhaust manifolds, consists of two-layer systems: a ceramic top coat (TC), made of yttria stabilized zirconia (YSZ), ZrO2-8%Y2O3 and also a metallic bond coat ...

We show that certain mechanical systems, including a geodesic flow in any dimension plus a quasi-periodic perturbation by a potential, have orbits of unbounded energy. The assumptions we make in the case of geodesic flows are: a) The metric and the external perturbation are smooth enough. b) The geodesic flow has a hyperbolic periodic orbit such that its stable and unstable manifolds have a tra...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

The geodesic orbit property is useful and interesting in Riemannian geometry. It implies homogeneity has important classes of manifolds as special cases. Those include weakly symmetric naturally reductive manifolds. corresponding results for indefinite metric are much more delicate than signature, but the last few years structural were proved Lorentz Here, we carry out a major step analysis nil...

Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...