VECTOR BUNDLES ON RIEMANN SURFACES
... The important thing for us is that Pn is compact. In the case of Cn the zero sets of polynomials give us (non-compact) complex manifolds. The equivalent of a polynomial in the setting of Pn is a homogeneous polynomial. Definition 2.10. Check that a polynomial f (z0 , . . . , zn ) is homogeneous if f ...
... The important thing for us is that Pn is compact. In the case of Cn the zero sets of polynomials give us (non-compact) complex manifolds. The equivalent of a polynomial in the setting of Pn is a homogeneous polynomial. Definition 2.10. Check that a polynomial f (z0 , . . . , zn ) is homogeneous if f ...
Spacetime algebra as a powerful tool for electromagnetism
... that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex ...
... that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex ...
ANNALS OF MATHEMATICS
... Let 0 O.2; 1/ be a Schottky group, and let † D H2 = 0 be the corresponding hyperbolic surface. Let C.†/ denote the space of unit length geodesic currents on †. The cohomology group H 1 .0 ; V/ parametrizes equivalence classes of affine deformations u of 0 acting on an irreducible representati ...
... Let 0 O.2; 1/ be a Schottky group, and let † D H2 = 0 be the corresponding hyperbolic surface. Let C.†/ denote the space of unit length geodesic currents on †. The cohomology group H 1 .0 ; V/ parametrizes equivalence classes of affine deformations u of 0 acting on an irreducible representati ...
Vector bundles and torsion free sheaves on degenerations of elliptic
... computations in Section 3.2. However, the way we prove this theorem, essentially uses ideas from representation theory and the technique of matrix problems [Bon92]. Using a similar approach, Theorem 2 was generalized by Burban and Drozd [BD04] to classify indecomposable complexes of the bounded (fro ...
... computations in Section 3.2. However, the way we prove this theorem, essentially uses ideas from representation theory and the technique of matrix problems [Bon92]. Using a similar approach, Theorem 2 was generalized by Burban and Drozd [BD04] to classify indecomposable complexes of the bounded (fro ...
Lecture 5: Polarization and Related Antenna Parameters
... 1. Introduction and Definition The polarization of the EM field describes the orientation of its vectors at a given point and how it varies with time. In other words, it describes the way the direction and magnitude of the field vectors (usually E) change in time. Polarization is associated with TEM ...
... 1. Introduction and Definition The polarization of the EM field describes the orientation of its vectors at a given point and how it varies with time. In other words, it describes the way the direction and magnitude of the field vectors (usually E) change in time. Polarization is associated with TEM ...
