Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V (D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u, v ∈ N there is no monochromatic direc...

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. We call the digraph D an m-coloured digraph if each arc of D is coloured by an element of {1, 2, . . . , m} where m ≥ 1. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if there is no monochromatic path...

Monochromatic aberrations that exist in the human eye will cause differences in the appearance of the point-spread function (PSF) depending on whether there is positive or negative defocus. We establish whether it is possible to use these differences in the PSF to distinguish the direction of defocus. The monochromatic aberrations of eight subjects were measured with a Hartmann-Shack wave-front...

For an edge-colored graph G , we call edge–cut M of monochromatic if the edges are colored with same color. The is called monochromatically disconnected any two distinct vertices separated by a edge–cut. connected disconnection number denoted m d ( ) maximum colors that needed in order to make disconnected. We show almost all graphs have numbers equal 1. also obtain Nordhaus–Gaddum-type results...

We have developed a software package for reconstruction of quasi-monochromatic images from a multiple monochromatic x-ray imager for inertial confinement fusion implosions. The instrument consists of a pinhole array, a multi-layer Bragg mirror, and a image detector. The pinhole array projects hundreds of images onto the detector after reflection off the multi-layer Bragg mirror, which introduce...

The development of technology to measure and correct the eye's higher-order aberrations, i.e., those beyond defocus and astigmatism, raises the issue of how much visual benefit can be obtained by providing such correction. We demonstrate improvements in contrast sensitivity and visual acuity in white light and in monochromatic light when adaptive optics corrects the eye's higher-order monochrom...