in this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $m$-hyponormal operator‎. ‎we show that every analytic extension of a $n$th roots of $m$-hyponormal operator is subscalar of order $2k+2n$‎. ‎as a consequence‎, ‎we get that if the spectrum of such operator $t$ has a nonempty interior in $mathbb{c}$‎, ‎then $t$ has a nontrivial invariant subspace‎. ‎finally‎, ‎w...

Using reasonableness, we examine the U.S. Catholic bishops’ opposition to provisions of the Affordable Care Act of 2010. Weaving contributions from theology, philosophy, and jurisprudence, we emphasize the reasonable importance of mental health therapy for women within a relevant Catholic/Christian dialogue, particularly in the wake of the U.S. Supreme Court’s decision on healthcare. We princip...

The public profile of the Roman Catholic bishops of the United States results not simply from their own interventions in political life, but from the broad array of actions and actors within “public Catholicism” broadly conceived. This article assesses the contemporary profile of the American bishops from this broad angle, particularly in light of new dynamics under the papacy of Francis I. It ...

Baker (2019), Barany and Kaenmaki (2019) independently showed that there exist iterated function systems without exact overlaps are super-exponentially close cylinders at all small levels. We adapt the method of obtain further examples this type. prove for any algebraic number \(\beta\ge 2\) real numbers \(s, t\) such system \(\left \{\frac{x}{\beta}, \frac{x+1}{\beta}, \frac{x+s}{\beta}, \fr...

These sets were introduced in the domain of quasicrystallography, see e.g. [2]. It is not difficult to see that Z−β =Z when β ∈Z, and that Z−β = {0} when β < 1+ √ 5 2 . For β ≥ 1+ √ 5 2 , Ambrož et al. [1] showed that Z−β can be described by the fixed point of an anti-morphism on a possibly infinite alphabet. They also calculated explicitely the set of distances between consecutive (−β )-intege...

Pope Francis is very concerned to transform the Church through synodality. He has chosen synod of bishops as main tool for this reform. This paper shows how functioning Synod Bishops, which pope profoundly transformed, puts project a synodal into effect. From point view, process 2018 on youth an example synodality transforming Church. By taking steps step by step, practice deeply and paves way ...