If each four spheres in a set of five unit spheres in R have nonempty intersection, then all five spheres have nonempty intersection. This result is proved using Grace’s theorem: the circumsphere of a tetrahedron encloses none of its escribed spheres. This paper provides self-contained proofs of these results; including Schläfli’s double six theorem and modified version of Lie’s line-sphere tra...

In this paper, the boundedness and compactness of weighted composition operators from analytic Morrey spaces into Bloch-type spaces and little Bloch-type spaces are studied.

This paper was written as a part of [8] and is intended primarily to provide the definitions and results concerning motives over simplicial schemes, which are used in the proof of the Bloch-Kato conjecture.

Let g be a holomorphic map of B, where B is the unit ball of C. Let 0 < p < +∞,−n − 1 < q < +∞, q > −1 and α > 0. This paper gives some necessary and sufficient conditions for the Extended Cesáro Operators induced by g to be bounded or compact between generalized Besov space B(p, q) and αBloch space B.

We discuss the relationship between different notions of “integrality” in motivic cohomology/K-theory which arise in the Beilinson and Bloch-Kato conjectures, and prove their equivalence in some cases for products of curves, as well as obtaining a general result, first proved by Jannsen (unpublished), reducing their equivalence to standard conjectures in arithmetic algebraic geometry.

This research paper addresses secularization from both political and religious perspectives. One of its manifestations in the political sphere is that of globalization that can lead to alienation within society; and in the United Kingdom this is exemplified by Brexit. Within the religious sphere secularization is usually couched in oppositional terms. This paper reclaims the original use ...

We give a new proof of Ohta’s Λ-adic Eichler-Shimura isomorphism using p-adic Hodge theory and the results of Bloch-Kato and Hyodo on p-adic étale cohomology.

A description of the closure in the Bloch norm of the Bloch functions that are in a Hardy space is given. The result uses the classical estimates for the Lusin area function. §

New criteria for the boundedness and the compactness of the generalized weighted composition operators from mixed norm spaces into Blochtype spaces are given in this paper.