Necessary Condition for a Region to Be Divided into Spatially Contiguous, Homogeneous Subregions

A necessary condition for a Shearlet system to be a frame via admissibility

    Necessary conditions for  shearlet  and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.

A Necessary Condition for Weyl-Heisenberg Frames

A necessary condition for multiple objective fractional programming

In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

A Necessary and Sufficient Condition for Graph Matching to be equivalent to Clique Search

This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are threefold: first, the condition is general enough to cover a broad range of practical graph matching problems; second, a proof to establish equivalence between gr...

A necessary and sufficient eigenvector condition for a connected graph to be bipartite

We give a necessary and sufficient condition for a graph to be bipartite in terms of an eigenvector corresponding to the largest eigenvalue of the adjacency matrix of the graph.