The Equivalence Principle is a key element in the development of General Relativity. In one its formulations, states that reference frame at rest uniform gravitational field equivalent to uniformly accelerated motion absence any gravitation field. We analyze spacetime surrounding non-rotating spherically symmetric charged body, known as Reissner–Nordström geometry, and exhibit coordinate transf...

The nature of the singularity at the origin of the solution of Dirac's equation in Reissner-Nordström geometry is different from that in flat space. Here, both independent solutions are regular at the origin, and both give a convergent normalization integral. The choice between the two solutions is made by requiring that the variational integral, from which the differential equation can be deri...

An analysis is presented for a recently proposed nite element method for the Reissner{ Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual \locking problem" by interpolating the shear stress into a rotated ...

We present a new Neumann–Neumann-type preconditioner of large scale linear systems arising from plate and shell problems. The advantage of the new method is a smaller coarse space than those of earlier methods of the authors; this improves parallel scalability. A new abstract framework for Neumann–Neumann preconditioners is used to prove almost optimal convergence properties of the method. The ...

The aim of the present paper is, to employ the Hybrid Stress Boundary Element Method for the computation of acoustic scattering and radiation in innnite domains. The introduced method is based on multi-eld variational principles and leads to symmetric matrices. Starting from Hellinger-Reissner's principle in the frequency domain a two-eld hybrid principle for acoustics is developed allowing for...

In this paper we prove a generalized version of the Ekeland variational principle, which is a common generalization of Zhong variational principle and Borwein Preiss Variational principle. Therefore in a particular case, from this variational principle we get a Zhong type variational principle, and a Borwein-Preiss variational principle. As a consequence, we obtain a Caristi type fixed point th...

We consider the plate bending problem in the framework of the Reissner-Mindlin theory. For a clamped plate, the problem can be written in variational form as follows. Find (θ, w) ∈ (H 0 (Ω)) ×H 0 (Ω) : ∫ Ω Cε(θ) : ε(η) + μ t−2 ∫ Ω (∇w − θ) · (∇v − η) = ∫