‎Let $G$ be a finite group‎. ‎An element $gin G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $G$‎, ‎$chi(g)neq 0$‎. ‎The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}$‎. ‎Let ${rm nv}(G)$ be the set‎ ‎of all non-vanishi...

We investigate the classical stability of the higher-dimensional Schwarzschild black holes against linear perturbations, in the framework of a gauge-invariant formalism for gravitational perturbations of maximally symmetric black holes, recently developed by the authors. The perturbations are classified into the tensor, vector, and scalar-type modes according to their tensorial behaviour on the...

In this paper, a specific solution to the second-order cosmological perturbation theory is given. Perturbations are performed around any FLRW spacetime filled with dust and positive constant. particular, possibly non-vanishing spatial curvature. The adopted symmetry condition allows us simplify equations, leaving great deal of freedom choose density distribution. result, we get relatively simpl...

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflatio...

We study the Gaussian semiclassical soliton ensemble, a collection of multisoliton solutions of the focusing nonlinear Schrödinger equation. The ensemble is generated by adding a particular asymptotically vanishing sequence of perturbations to Gaussian initial data. Recent results [Lee, Lyng, & Vankova (2012)] suggest that, remarkably, these perturbations—interlaced as they are with the integra...

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as...

Zirconia-nickel functionally graded materials were obtained by powder metallurgy technique. The microstructure, residual stress, fracture toughness and Vickers hardness were investigated. Mixed-mode fracture response of YSZ /Ni functionally graded materials was examined utilizing the three point bending test and finite element method (Cosmos/M 2.7). The results show that the stress intensity fac...

We present a new quasidilaton theory of Poincare invariant massive gravity, based on the recently proposed framework of matter coupling that makes it possible for the kinetic energy of the quasidilaton scalar to couple to both physical and fiducial metrics simultaneously. We find a scaling-type exact solution that expresses a self-accelerating de Sitter universe, and then analyze linear perturb...

In these lecture notes I review the theory of the non–linear evolution of cosmological perturbations in a self–gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian approximation, where the basic properties of the Zel’dovich, frozen–flow and adhesion algorithms are introduced. An exact general relativistic formalism is then pre...