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...

A method for building a statistical shape model of sulci of the human brain cortex is described. The model includes sulcal fundi that are defined on a spherical map of the cortex. The sulcal fundi are first extracted in a semi-automatic way using an extension of the fast marching method. They are then transformed to curves on the unit sphere via a conformal mapping method that maps each cortica...

When performing Eulerian-Lagrangian simulations of particle-fluid flows collisions between the particles need to be accounted for. One of the methods used for this is the hard-sphere model. This model, however, does not take into account cohesive forces between the particles, and for this reason it is not able to simulate many aspects of real flows, such as the formation of agglomerates. There ...

Negative values of the Casimir entropy occur quite frequently at low temperatures in arrangements of metallic objects. The physical reason lies either in the dissipative nature of the metals as is the case for the plane-plane geometry or in the geometric form of the objects involved. Examples for the latter are the sphere-plane and the sphere-sphere geometry, where negative Casimir entropies ca...

We review here the Grassmann variety, Schubert cells, Schubert subvarieties and then Schubert cycles and how to compute their product. We then review vector bundles over the sphere, clutching functions and the universal bundle.

Characteristic polarization state theory is restudied for the symmetric coherent Sinclair scattering matrix case. First, the geometric relations of the characteristic polarization states on the Poincaré sphere are derived. Based on these relations, simple formulas are given for all of the characteristic polarization states of this Sinclair matrix in Stokes vector form. From the formulation, it ...