By means of ab-initio calculations on the basis of the FPLAPW method, we compared the energy loss near edge structure (ELNES) of carbon K edges in crystalline phenanthrene and its isomer, anthracene. In these two organic compounds, different non-equivalent carbon atoms can result in distinct K edge spectra due to the different carbon-carbon bond lengths, as a characteristic behavior of the mole...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

The Tree Decomposition Conjecture by Bárat and Thomassen states that for every tree T there exists a natural number k(T ) such that the following holds: If G is a k(T )-edge-connected simple graph with size divisible by the size of T , then G can be edge-decomposed into subgraphs isomorphic to T . The results on modulo k-orientations by Thomassen show that the Tree Decomposition Conjecture hold...

Edge detection remains a crucial stage in numerous image processing applications. Thus, an edge detection technique needs to be assessed before use it in a computer vision task. As dissimilarity evaluations depend strongly of a ground truth edge map, an inaccurate datum in terms of localization could advantage inaccurate precise edge detectors or/and favor inappropriate a dissimilarity evaluati...

Classic convexity can be extended to graphs in a natural way by considering shortest paths, also called geodesics: a set S of vertices of a graph is convex if it contains all the vertices lying in some geodesic with endpoints in S and the convex hull of a set S of vertices is the minimum convex set containing S. Farber and Jamison [9] characterized the graphs such that every convex set is the c...

A Hamilton cycle in a graph Γ is a cycle passing through every vertex of Γ. A Hamiltonian decomposition of Γ is a partition of its edge set into disjoint Hamilton cycles. One of the oldest results in graph theory is Walecki’s theorem from the 19th century, showing that a complete graph Kn on an odd number of vertices n has a Hamiltonian decomposition. This result was recently greatly extended b...

The network reliability analysis based on Binary Decision Diagram (BDD) consists of three steps: edge ordering, BDD generation and BDD evaluation. The BDD generation process using edge expansion technique should recursively decompose the network and construct the edge expansion subnet in a top-down manner. There is large number of useless or redundant subnets generated in this decomposition, wh...

We consider a network design problem in which flow bifurcations are allowed. The demand data are assumed to be uncertain, and the uncertainties of demands are expressed by an uncertainty set. The goal is to install facilities on the edges at minimum cost. The solution should be able to deliver any of the demand requirements defined in the uncertainty set. We propose an exact solution algorithm ...

A novel approach of edge detection is proposed that utilizes a bidimensional empirical mode decomposition (BEMD) method as the primary tool. For this purpose, a recently developed fast and adaptive BEMD (FABEMD) is used to decompose the given image into several bidimensional intrinsic mode functions (BIMFs). In FABEMD, order statistics filters (OSFs) are employed to get the upper and lower enve...