Laguerre geometry of surfaces in R is given in the book of Blaschke [1], and have been studied by E.Musso and L.Nicolodi [5], [6], [7], B. Palmer [8] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in Rn. For any umbilical free hypersurface x : M → Rn with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invarian...

The Generalized Pólya Urn (GPU) is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential estimation-adjusted urn model (a nonhomogeneous GPU) which has a wide spectrum of applications. Because the proposed urn model depends on sequential estimations of unknown...

I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of consideri...

I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of consideri...

We consider a randomized urn model with objects of finitely many colors. The replacement matrices are random, and conditionally independent the color chosen given past. Further, conditional expectations close to an almost surely irreducible matrix. obtain sure $L^1$ convergence configuration vector, proportion vector count vector. show that first moment is sufficient for i.i.d.\ past choices. T...

The URN WG has defined a syntax for Uniform Resource Names (URNs) [RFC2141], as well as some proposed mechanisms for their resolution and use in Internet applications ([RFCXXXX], [RFCYYYY]). The whole rests on the concept of individual "namespaces" within the URN structure. Apart from proof-of-concept namespaces, the use of existing identifiers in URNs has been discussed ([RFC2288]), and this d...

There are three processes associated to a generalized Pólya urn model. First, the process that represents the proportion of balls of each type in the urn. As in each step a ball is drawn from the urn, its type is noted, and it is placed back in the urn, the second process represents the proportion of balls of each type that have been drawn from the urn. As the replacement policy consists in app...

Following the model of Bondesson, Nilsson, and Wikstrand, we consider randomly filled urns, where the probability of falling into urn i is the geometric probability (1− q)qi−1. Assuming n independent random entries, and a fixed parameter k, the interest is in the following parameters: Let T be the smallest index, such that urn T is non-empty, but the following k are empty, then: XT = number of ...

In this paper, I present a solution to the Doomsday argument based on a third type of solution, by contrast to on the one hand, the Carter-Leslie view and on the other hand, the Eckhardt et al. analysis. I begin by strengthening both competing models by highlighting some variations of their ancestors models, which renders them less vulnerable to some objections. I describe then a third line of ...