HERMITIAN VECTOR FIELDS AND SPECIAL PHASE FUNCTIONS

Triangle lattice Green functions for vector fields

All the identities and integral theorems of vector calculus are contained in the calculus of differential forms. The analogy between the exterior calculus of forms and the homology theory of a cell complex yields discrete lattice models for an array of interesting physical phenomena. These models, based on arbitrary combinations of coupled scalar and polar or axial vector field quantities, can ...

Hermitian Forms over Ordered ∗-fields

Let D be a division ring with an involution. Assuming that D admits Baer orderings, we can study the Witt group of hermitian froms over D by observing its image in the ring of continuous functions on the space of orderings. We are led to define a new class of rings which, when viewed in an abstract setting, provide a natural generalization of the spaces of orderings and real spectra studied in ...

Lattices from Hermitian function fields

We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices com...

Orderings, Valuations and Hermitian Forms over ∗-fields

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...