Russer, "Two, three, and four-dimensional electromagnetics using differential forms
," Turkish Journal of Electrical Engineering and Computer Sciences, Vol.
Our objective is to determine the structure of its graded quotient [gr.sup.m] [k.sub.q,n] := [U.sup.m] [k.sub.q,n] /[U.sup.m+1] [k.sub.q,n] in terms of differential forms
of the residue field of K under the assumption that K contains a primitive [p.sup.n] -th root of unity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (Thm.
on Wasserstein space and infinite-dimensional Hamiltonian systems.
He describes local and global duality in the special case of irreducible algebraic varieties of an algebraically closed base field k in terms of differential forms
and their residues.
In Section 2 we give a brief exposition of the basic notions from the time scale calculus and an overview of the algebraic framework of differential forms
on a homogeneous time scale.
thus provide precise assignment rules, according to their degree, for the localization of the degree-of-freedom (DoF) of the lattice field theory: a p-form is always assigned to a p-cell.
Among the topics are functions on Riemann surfaces, complex differential forms
, uniformization, and the Riemann-Roch theorem.
This book is an introduction to the fundamentals of differential geometry that covers manifolds, flows, Lie groups and their actions, invariant theory, differential forms
and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.
It also addresses background on differential geometry and differential forms
and applications in several classical problems in differential geometry, as well as the nonhomogeneous case via moving frames on Riemannian manifolds.
Fortunately, these difficulties can be overcome by using a differential forms
Superconnections, Thom classes and equivariant differential forms
. Topology, 1986, 25, 85-110.
The author covers smooth manifolds and vector bundles, vector fields and differential equations, tensors, differential forms
, the integration of manifolds, metric and symplectic structures, and a wide variety of other related subjects.