We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on σ-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show that, if the principal symbol class of such an elliptic operator on the boundary of a manifold X has a suitable extension to K1(TX), then its index is zero. This con...

The main result of this paper is a version of the Atiyah-Singer index theorem for Dirac-type operators on (noncompact) complete Riemannian manifolds. The statement of the theorem involves a novel "cohomology" theory for such manifolds. This theory, called exotic cohomology, depends on the structure at infinity of a space; more precisely, it depends on the way that large bounded sets fit togethe...

Combiner and Stacked Generalization are two very similar meta-learning methods that combine predictions of multiple classiiers to improve accuracy of any single classiier. Both methods form a meta-level classiier from meta-data that are predictions of multiple classiiers on the same data items. The diierence between these two approaches lies in the way meta-data is formed. In this paper, we com...

Conventionally, diplexers are designed by connecting two filters of different frequencies using a transmission T-line junction which acts as distribution network serving the individual filters. Here, novel diplexer has been proposed and to utilize directly coupled resonator network. The is square open-loop resonators same resonant frequency 1.95 GHz. Coupling achieved ?/4 line couple them. This...

Here Index(D) is the Fredholm index of the Dirac operator acting on smooth sections of the spinor bundle S over an even dimensional compact Riemannian spin manifold M , e−tD 2 is the solution operator for the heat equation ∂s ∂t+D s = 0 for D, and Trs is the supertrace. The goal of this essay is to explicitly compute the righthand side in terms of local information on M , thereby proving the At...

The Maslov index is used to compute the spectra of different boundary value problems for Schrödinger operators on compact manifolds. The main result is a spectral decomposition formula for a manifold M divided into components Ω1 and Ω2 by a separating hypersurface Σ. A homotopy argument relates the spectrum of a second-order elliptic operator on M to its Dirichlet and Neumann spectra on Ω1 and ...

This paper concerns an index theory for Z-actions induced by a homeomorphism of a compact space. We give a definition of a genus for uniform spaces and prove that the genus for compact spaces is an index. To this end we show a Z-version of the Borsuk-Ulam theorem and the existence of a continuous equivariant extension for these Z-actions.