We prove that a Jordan curve in the 2-sphere is a quasicircle if and only if the closure of its orbit under the action of the conformal group contains only points and Jordan curves.

The Albian- Cenomanian (Kazhdumi Formation) sediments from northeast of Shiraz, Zagros Basin, represents a carbonate sedimentary succession and contain diverse gastropods and bivalves. Detailed studies on 80 samples of invertebrate macrofauna on two stratigraphic sections led to recognized 2 species and 5 genera of gastropods and 7 species and 13 genera of bivalves assemblages. The abscence of ...

Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...

In this work we introduce generalized projective geometries which are a natural generalization of projective geometries over a field or ring K but also of other important geometries such as Grassmannian, Lagrangian or conformal geometry (see [3]). We also introduce the corresponding generalized polar geometries and associate to such a geometry a symmetric space over K. In the finite-dimensional...

We develop a cohomology theory for Jordan triples, including the infinite dimensional ones, by means of the cohomology of TKK Lie algebras. This enables us to apply Lie cohomological results to the setting of Jordan triples.

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors Fi from finitely generated kE-modules of constant Jordan type to vector bundles over projective space Pr−1. The fibers of the functors Fi encode complete information about the Jordan type of the module. We prove that given any vector bundle F of rank s on Pr−1, there is a kE-module M...

The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this report we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed one-dimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for finding the shortest poly...

The chemical composition of groundwater in the Jordan Valley, along the section between the Sea of Galilee and the Dead Sea, is investigated in order to evaluate the origin of the groundwater resources and, in particular, to elucidate the role of deep brines on the chemical composition of the regional groundwater resources in the Jordan Valley. Samples were collected from shallow groundwater in...

If F is an algebraically closed field, any element in M n (F) is similar to a sum of a diagonal matrix and a nilpotent matrix whose non-zero entries are all 1, just above the diagonal. Something similar is true for elements of an arbitrary affine algebraic group as well as its Lie algebra. That's what this essay will attempt to explain. I begin with a very elementary account of what happens for...