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...

A bstract We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. provide geometric understanding that unifies various recently discovered as part an SO(4 , 2) group. Of these, subset are exact static sector and give rise to ladder responsible for vanishing Love numbers. In Kerr case, we compare different approximations in literature, focus imple...

We consider small perturbations of the Zakharov-Shabat nonlinear Schrr odinger equation on 0; ] with vanishing or periodic boundary conditions; we prove a Nekhoroshev type result for solutions starting in the neighbourhood (in the H 1 topology) of the majority of small amplitude nite dimensional invariant tori of the linearized system. More precisely we will prove that along the considered solu...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

Abstract In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For holes, focus on static perturbations, which the (exact) have group structure SO(1,3). The generators consist three spatial rotations, conformal Killing vectors obeying special melodic condition. perturbation solutions form unitary (principal series) re...

Tour into the picture (TIP) proposed by Horry et al.[1] is a method for generating a sequence of walk-through images from a single reference picture (or image). By navigating a 3D scene model constructed from the picture, TIP produced convincing 3D effects. Assuming that the picture has one vanishing point, they proposed the scene modeling scheme called spidery mesh. However, this scheme has to...

This article reviews eight proposed strategies for solving the Symbol Grounding Problem (SGP), which was given its classic formulation in Harnad (1990). After a concise introduction, we provide an analysis of the requirement that must be satisfied by any hypothesis seeking to solve the SGP, the zero semantical commitment condition. We then use it to assess the eight strategies, which are organi...

After the fuzziness in Europe that surrounded the implementation of the excessive deficit procedure foreseen by the Stability and Growth Pact (SGP), the European Union had to restore the credibility of the weakened fiscal rule. On March 2005, the 25 members amended the SGP. The constraint was to keep alive the Treaty of Amsterdam, which instituted the SGP. Indeed, an attempt to make major chang...