On inner and outer radii in Minkowski spaces

On Lorentz–Minkowski geometry in real inner product spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Uller Spaces to Have Smallest Possible Inner Radii

If fR n g 1 n=1 is a sequence of hyperbolic Riemann surfaces such that for any r > 0 a hyperbolic ball of radius r embeds isometrically into R n for all n suuciently large, then as n ! 1 the inner radii of the associated Teichm uller spaces i(T(R n)) ! 2. A straightforward consequence of this is that if a Riemann surface R contains arbitrarily large hyperbolic balls then i(T(R)) = 2. Let ? be a...

Outer and Inner Confidence Intervals Based on Extreme Order Statistics in a Proportional Hazard Model

Let Mi and Mi be the maximum and minimum of the ith sample from k independent sample with different sample sizes, respectively. Suppose that the survival distribution function of the ith sample is F ̄i = F ̄αi, where αi is known and positive constant. It is shown that how various exact non-parametric inferential proce- ′ dures can be developed on the basis of Mi’s and Mi ’s for distribution ...

On Mean Outer Radii of Random Polytopes

In this paper we introduce a new sequence of quantities for random polytopes. Let KN = conv{X1, . . . ,XN} be a random polytope generated by independent random vectors uniformly distributed in an isotropic convex body K of R. We prove that the so-called k-th mean outer radius R̃k(KN ) has order max{ √ k, √ logN}LK with high probability if n ≤ N ≤ e √ . We also show that this is also the right or...