Adjacent Crossings Do Matter

Adjacent Crossings Do Matter

In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) be the smallest number of independent odd pairs in a drawing of G. We construct a graph G with iocr(G) < ocr(G), answering a question by Széke...

Distribution of the spacing between two adjacent avoided crossings.

We consider the frequency at which avoided crossings appear in an energy-level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings is investigated. Using a random matrix model, we find that the distribution of these spacings is well fitted by a power-law distribution for small spacings. ...

Simple Waves Do Not Avoid Eigenvalue Crossings

General one-parameter families of matrices avoid eigenvalue crossings. It is shown that the matrices associated with the simple waves of nonlinear systems of conservation laws do not obey this rule: a subset of simple waves with nonzero measure has crossing eigenvalues. © 2009 Wiley Periodicals, Inc.

Dark Chocolate and Metabolic Syndrome; Do Polyphenols All that Matter?

Do Workers\' Remittances Matter for the Egyptian Economy?

Workers’ remittances constitute one of the most important sources of external finance for many developing countries. Although it shows a decreasing trend in recent years, Egypt after 1970s with her regular and massive labor migration to abroad has been still one of the gainer countries on remittances across the world. Empirical studies that implemented for various countries reveal workers’ ...