Showing papers on "Distribution (differential geometry) published in 1982"

On a Structure Defined by a Tensor Field f of Type (1,1) Satisfying f3+f = 0.

Abstract: Publisher Summary A necessary and sufficient condition for an n-dimensional manifold to admit a tensor field f ≠ O of type (1,1) and of rank r such that f 3 +f = O is that r is even: r =2m and the group of tangent bundle of the manifold be reduced to the group U(m) × O(n-2m). A symmetric affine connexion Γ h ji in the original manifold is introduced, the thing that is always possible. For example, we have only to introduce a Riemannian metric in the manifold and denote by Γ h ji the connexion given by the Levi-Civita parallelism. The tensor does not depend on a special choice of symmetric affine connexion involved and the covariant differentiation can be replaced by partial differentiation. When the distribution L is integrable and the almost complex structure induced on the integral manifold by the f- structure is also integrable say that the f -structure is partially integrable.

Analysis of mixed mode microwave distribution manifolds

Abstract: The 28-GHz microwave distribution manifold used in the ELMO Bumpy Torus-Scale (EBT-S) experiments consists of a toroidal metallic cavity, whose dimensions are much greater than a wavelength, fed by a source of microwave power. Equalization of the mixed mode power distribution ot the 24 cavities of EBT-S is accomplished by empirically adjusting the coupling irises which are equally spaced around the manifold. The performance of the manifold to date has been very good, yet no analytical models exist for optimizing manifold transmission efficiency or for scaling this technology to the EBT-P manifold design. The present report develops a general model for mixed mode microwave distribution manifolds based on isotropic plane wave sources of varying amplitudes that are distributed toroidally around the manifold. The calculated manifold transmission efficiency for the most recent EBT-S coupling iris modification is 90%. This agrees with the average measured transmission efficiency. Also, the model predicts the coupling iris areas required to balance the distribution of microwave power while maximizing transmission efficiency, and losses in waveguide feeds connecting the irises to the cavities of EBT are calculated using an approach similar to the calculation of mainfold losses. The model will be used to evaluate EBT-P manifold designs.