Abstract In this short note, we reformulate the task of calculating pair correlation statistics a Kronecker sequence as lattice point counting problem. This can be done analogously to based approach which was used (re-)prove famous three gap property for sequences. We show that recently developed techniques then applied derive certain class sequences have $$\beta $$ <mml:math xmlns:mml="http://...

Cubic Pisot units with finite beta expansion property are classified (Theorem 3). The results of [6] and [3] are well combined to complete its proof. Further, it is noted that the above finiteness property is equivalent to an important problem of fractal tiling generated by Pisot numbers. 1991 Mathematics Subject Classification: 11K26,11A63,11Q15,28A80

We analyse dynamical properties of the negative beta transformation, which has been studied recently by Ito and Sadahiro. Contrary to the classical beta transformation, the density of the absolutely continuous invariant measure of the negative beta transformation may be zero on certain intervals. By investigating this property in detail, we prove that the (−β)-transformation is exact for all β ...

Social Network Analysis (SNA) has shed light on cultures where the influence of patronage, preferment, and reciprocal obligations are traditionally important. We argue here that episcopal appointments, culture, governance within Catholic Church ideal topics for SNA interrogation. This paper presents preliminary findings, using original network data Bishops’ Conference England Wales United State...

A number of spacetime fields in string theory—notably the metric, dilaton, bulk (bosonic and type 0) closed string tachyon, and bosonic open string tachyon—have the property that, whenever the spacetime field configuration factorizes in an appropriate sense, the matter sector of the world-sheet theory factorizes into a tensor product of two decoupled theories. Since the beta functions for such ...

The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the flow between these sectors. In most functions, expansion Hubble considered and sometimes it argued that, as a local property, inclusion may influence overall dynamics. This starting point present article where we consider very simple cosmic scenario vacuum cold matter...

The third phase of the Council Trent (1562–63) witnessed a crisis erupt over whether bishops resided in, and ruled, their dioceses de iure divino (by divine right) or by papal authority. Cosimo I de’ Medici, Duke Florence, cooperated with instructions from Pope Sixtus IV to send Tuscan Trent, vote as bloc for Episcopal residency This position strengthened primacy weakened bishops’ claims autono...

We prove that many of beta, beta prime, gamma, inverse gamma, Student tand ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, many of ultraspherical and Student t-distributions have free divisibility indicator 1.

[The discussions between Joseph Ratzinger and Walter Kasper on the relationship between the universal Church and the local/ particular churches touch on one of today’s major theological and pastoral issues. If the universal Church is ontologically and temporally prior to the local church, then how is the local church fully Church, and how are bishops truly vicars of Christ and not simply delega...

Abstract This paper studies the pricing of risk associated with location assets. The local real estate market is measured by ‘local beta’, which combines systematic property markets and allocation strategy firms. empirical results confirm a higher equity return for firm exposure to most volatile markets, particularly REITs are more geographically concentrated. For highly diversified assets, ris...