Min–Max formulas for nonlocal elliptic operators on Euclidean Space

Minmax Tree Cover in the Euclidean Space

Let G = (V,E) be an edge-weighted graph, and let w(H) denote the sum of the weights of the edges in a subgraph H of G. Given a positive integer k, the balanced tree partitioning problem requires to cover all vertices in V by a set T of k trees of the graph so that the ratio α of maxT∈T w(T ) to w(T ∗)/k is minimized, where T ∗ denotes a minimum spanning tree of G. The problem has been used as a...

Homological index formulas for elliptic operators over C*-algebras

We prove index formulas for elliptic operators acting between spaces of sections of C∗-vector bundles on a closed manifold. The formulas involve Karoubi’s Chern character from K-theory of a C∗algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theory for coverings and to flat foliated bundles, and prove an index theorem for C∗-dynamical systems associat...

Anomalies of Dirac Type Operators on Euclidean Space

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Effective Nonlocal Euclidean Gravity

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newton’s constant between regions of space with vanishing or nonvani...