the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

In this paper, the two-stage procedure is considered for autoregressive parameters estimation in the p-order autoregressive model ( AR(p)). The point estimation and fixed-size confidence ellipsoids construction are investigated which are based on least-squares estimators. Performance criteria are shown including asymptotically risk efficient, asymptotically efficient, and asymptotically consist...

In this paper, we show that good structured codes over non-Abelian groups do exist. Specifically, we construct codes over the smallest non-Abelian group D6 and show that the performance of these codes is superior to the performance of Abelian group codes of the same alphabet size. This promises the possibility of using non-Abelian codes for multi-terminal settings where the structure of the cod...

We find soliton solutions in five-dimensional gauged supergravity, where a circle degenerates smoothly in the core of the geometry. In the family of solutions we consider, we find no completely smooth supersymmetric solutions, but we find discrete families of non-supersymmetric solitons. We discuss the relation to previous studies of the asymptotically flat case. We also consider gauged supergr...

Hawking radiation remains a crucial theoretical prediction of semi-classical gravity and is considered one the critical tests for model quantum gravity. However, Hawking’s original derivation used field theory on fixed background. Efforts have been made to include space–time fluctuations arising from quantization dynamical degrees freedom itself study effects particles. Using analysis, we scala...