The number of asymptotically de Sitter (non-singular) solutions of 5d dilatonic gravity with positive cosmological constant is found. These solutions are similar to the previously known asymptotically AdS spaces where dilaton may generate the singularity. Using these solutions the consistent c-function is proposed in the same way as in AdS/CFT. The consistency of RG flow gives further support f...

and Applied Analysis 3 Table 1: The operations for generalized differential transform method. Original function Transformed function f n, t g n, t h n, t F n, k G n, k H n, k f n, t αg n, t F n, k αG n, k f n, t ∂g n, t /∂t F n, k k 1 G n, k 1 f n, t g n, t h n, t F n, k ∑k r 0 G n, r H n, k − r f n, t ∂g n, t /∂t F n, k k m G n, k m f n, t g n s, t F n, k G n s, k To improve the accuracy and c...

and Applied Analysis 3 2.1. CNN Based on Aihara’s Model The dynamical equation of a chaotic neuron model with continuous functions described by 1 , x t 1 f ( A t − α t ∑ d 0 kg x t − d − θ ) , 2.1 where x t 1 is the output of the chaotic neuron at the discrete time t 1, which is an analogue value between 0 and 1; f is a continuous output function, such as logistic function f y 1/ 1 e−y/ε with t...

We define “tracial” analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and of approximate innerness. We prove the following four analogs of related “nontracial” results. • The crossed product of an infinite dimensional simple separable unital C*-algebra with tracial rank zero by an action of a finite group with the tra...

It is demonstrated how the hierarchy between the gauge coupling unification scale of minimal supersymmetry and the Planck (or string) scale, which resembles in order of magnitude a loop factor, can actually be explained as such in supergravity-coupled supersymmetry. A gauge and global singlet field acquires a linear potential term due to its one-loop supergravity interactions and slides to the ...

We show a method to effectively compute the Wedderburn decomposition and the primitive central idempotents of a semisimple finite group algebra of an abelian-by-supersolvable group G from certain pairs of subgroups of G. In this paper F = Fq denotes a finite field with q elements and G is a finite group of order n such that FG is semisimple, or equivalently (q, n) = 1. The group algebra FG is a...

We consider a manifold X obtained by a Kähler reduction of Cn, and we define its “hyperkähler analogue” M as a hyperkähler reduction of T ∗Cn ∼= Hn by the same group. In the case where the group is abelian and X is a smooth toric variety, M is a toric hyperkähler manifold, as defined in [BD], and further studied in [K1, K2] and [HS]. The manifold M carries a natural action of S1, induced by the...

We study the intrinsic heat equation governing the motion of plane curves. The normal velocity v of the motion is assumed to be a nonlinear function of the curvature and tangential angle of a plane curve Γ. By contrast to the usual approach, the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional α. Short time existence of a regular family of ...

A systematic study of turbulent Rayleigh-Bénard convection is carried out in two horizontal cylindrical cells of different lengths filled with water. Global heat transport and local temperature and velocity measurements are made over varying Rayleigh numbers Ra. The scaling behavior of the measured Nusselt number Nu(Ra) and the Reynolds number Re(Ra) associated with the large-scale circulation ...

We will prove a result concerning the inclusion of non-trivial invariant ideals inside nontrivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on C∗-algebras. The motivation of this study is our recent research on C-unique groups (or Fourier groups) in [10]. In fact, one in...