Topological persistence methods provide a robust framework for analyzing large point cloud datasets topologically, and have been applied with great success towards homology computations on simplicial complexes. In this paper, we apply the persistence algorithm towards calculating a set of invariants related to the cup product structure on the cohomology ring for a space. These invariants expres...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

Motivated by the construction of Steenrod cup-i products in singular cochain algebra a space and non-commutative differential forms, we define category binomial cup-one graded algebras over integers prime fields positive characteristic. The Hirsch identities bind cup-product, product, package that further enhance with ring structure arising from integer-valued rational polynomials. This allows ...

Let M M be a negatively curved compact Riemannian manifold with (possibly empty) convex boundary. Every closed differential alttext="2"...

Economic challenges for small size IC design and manufacturing require: reduced die size without adding layers or other costs, bonding with Cu wire instead of Au wire, and maintained or improved reliability. Die size shrinking involves extensive use of circuit under pad (CUP) or bond over active circuitry (BOAC) on IC’s having at least two levels of metal. CUP however, introduces more potential...