Let φ be a holomorphic self-map of the open unit polydisk U in C and p, q > 0. In this paper, the generally weighted Bloch spaces B log(U ) are introduced, and the boundedness and compactness of composition operator Cφ from B p log(U ) to B log(U ) are investigated.

In this short note we provide computational evidence for the main result found in On the Bloch-Kato conjecture for elliptic modular forms of square-free level.

In this paper, we study composition operators Cφf = f ◦ φ, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

CHRISTOPHER J . BISHOP The little Bloch space, 130 , is the space of all holomorphic functions f on the unit disk such that lim1 z 1l (f'(z)j(1 Iz12) = 0. Finite Blaschke products are clearly in 130, but examples of infinite products in 80 are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others) . Stephenson has asked whether 130...

Underwater cameras are typically placed behind glass windows to protect them from the water. Spherical glass, a dome port, is well suited for high water pressures at great depth, allows large field of view, and avoids refraction if pinhole camera positioned exactly sphere's center. Adjusting real lens perfectly center challenging task, both in terms how actually guide centering process (e.g. vi...

I In her book, Philosophy in a New Key, Susanne Langer remarks that certain ideas burst upon the intellectual landscape with a tremendous force. They resolve so many fundamental problems at once that they seem also to promise that they will resolve all fundamental problems, clarify all obscure issues. Everyone snaps them up as the open sesame of some new positive science, the conceptual center-...

Abstract The abundance and distribution of solids inside the Hill sphere are central to our understanding giant planet dichotomy. Here, we present a 3D characterization dust density, mass flux, mean opacities in envelope subthermal superthermal-mass planets. We simulate dynamics multiple species global protoplanetary disk model accounting for feedback. find that meridional flows do not effectiv...

The possibility of volumetric phase recording based on photo-oxidation the side anthracene groups a new polymer with glass transition temperature ~338 K by oxygen that enters layer across boundary atmospheric medium, was established experimentally. Volumetric holographic gratings maximum diffraction efficiency 2.5–9.5% were recorded radiation from He–Ne laser (λ = 633 nm) in layers 5–20-μm thic...

Introduction: CSCs have been identified in prostate cancer (PCa), one of the most diagnosed malignancies in men over the world, for which radiation resistance is a major problem in the treatment of advanced stages. Cancer stem cells (CSCs) have the ability to self-renew and differentiate to give rise to heterogeneous phenotype of the tumor cells. It is believed that CSCs are ...