Holomorphic blocks in three dimensions

A Holomorphic Map in Infinite Dimensions

We prove, in great detail, holomorphy E ⊓ C (I ,Π ) → C (I ,Π ) of the map (x , y) 7→ x ◦ [ id , y ] where [ id , y ] : I ∋ t 7→ (t , y (t)) for a real compact interval I , and where Π is a complex Banach space and E is a certain locally convex space of continuous functions x : I× (υsΠ ) → υsΠ for which x (t , ·) is holomorphic for all t ∈ I . We also discuss aspects of the application of this ...

Krull Dimensions of Rings of Holomorphic Functions

We prove that the Krull dimension of the ring of holomorphic functions of a connected complex manifold is at least the cardinality of continuum if and only if it is > 0. Let R be a commutative ring. Recall that the Krull dimension dim(R) of R is the supremum of cardinalities lengths of chains of distinct proper prime ideals in R. Our main result is: Theorem 1. Let M be a connected complex manif...

Biology in three dimensions

Most things in biology spread out into three dimensions, and many biological web sites include three-dimensional images. But biologists want more than a look at something. They want to pick it up and look at it from all sides, which is where three-dimensional images that can be manipulated online really come into their own. One approach to such interactive images relies on VRML (virtual reality...

Collapsars in Three Dimensions

We present the results of 3-dimensional simulations of the direct collapse to a black hole of a rotating, 60M⊙, zero metallicity, population III star. Because the structure of this star (angular momentum, density and temperature profiles) is similar to many collapsar gamma-ray burst progenitors, these calculations have implications beyond the fate of population III stars. These simulations prov...

Supersymmetry in Three Dimensions