In this article, we suggested a novel design of polarization splitter based on coupler waveguide on InP substrate at 1.55mm wavelength. Photonic crystal structure is consisted of two dimensional (2D) air holes embedded in InP/InGaAsP material with an effective refractive index of 3.2634 which is arranged in a hexagonal lattice. The photonic band gap (PBG) of this structure is determined using t...

We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among graphs. (This is consequence general theorem proved L. Ham and M. Jackson, counterpart this for all in class well-known compactness theorem.) Also, to exemplify our method applicable various fields mathematics, we prove neither simple groups, nor ordered sets join-irre...

The paper describes a few ways in which the concept of a Coxeter group (in its most ubiquitous manifestation, the symmetric group) emerges in the theory of ordinary matroids: • Gale’s maximality principle which leads to the Bruhat order on the symmetric group; • Jordan–Hölder permutation which measures distance between two maximal chains in a semimodular lattice and which happens to be closely ...

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind-MacNeille completion of P. The latticeK(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closu...

The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the paper. In the second part the theorem is applied to show that interesting combinatorial sets related to a planar graph have lattice structure: Eulerian orientations, spanning trees and Schnyder woods. For the Schnyder w...

Shafer’s mathematical theory of evidence is one of the most remarkable attempts to introduce a complete generalized probability theory. One of its features is the central role of the notion of different level of knowledge of a given phenomenon, embodied into the idea of compatible frames of discernment . In this work we are going to analyze the algebraic basement of the concept of family of fra...