Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...

Edge detection and edge enhancement techniques play an essential role in interpreting potential field data. This paper describes the application of various edge detection techniques to gravity data in order to delineate the edges of subsurface structures. The edge detection methods comprise analytic signal, total horizontal derivative (THDR), theta angle, tilt angle, hyperbolic of tilt angle (H...

Purpose: To describe a case series of young adult patients with isolated chronic proximal biceps tendinitis refractory to conservative care found to have anatomic long head biceps tendon (LHBT) origin variations who underwent arthroscopic-assisted subpectoral biceps tenodesis. Methods: Patients were included in this retrospective case series if they met all the following criteria: 1) had ...

A 77-year old woman who underwent hybrid aortic arch repair using a Gore-TAG (Gore-Associates, Flagstaff, AZ, USA) endograft (Fig. 1A) complained of chest pain 5 months after operation. Blood cultures revealed Serratia marcescens. Computed tomography (CT) demonstrated dislocation of the endograft with formation of a pseudoaneurysm (Fig. 1B). Ascending aorta replacement with re-debranching was e...

Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...

one of the generalizations of the wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. the reliability wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. closed expressions are derived for t...

although host species generally face increased risk of brood parasitism in fragmented temperate landscapes and forest edge, little information exists to assess such risks in tropical birds. we studied how cuculidae species populations, host species population, and micro-environmental variables changed along an edge-to-interior gradient in peninsular malaysia. bird observations and environmental...

We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo batch size under which convergence is guaranteed: both increasing batch size and constant batch size are considered. We also derive non-asymptotic bounds for ...

Growth of an ultrathin lead oxide layer causes massive changes in the shape of lead crystallites. The dynamics of this process was investigated with time-lapsed scanning tunneling microscopy. Pure lead crystallites proved extremely resistant to oxidation. Once nucleated by surface impurities, monolayer films of lead oxide grew readily on lead (111) microfacets in an autocatalytic process. The a...

In the current case series we describe two cases of longitudinal stent deformation in ostial lesions treated with a new generation zotarolimus eluting stent and review current literature on longitudinal stent deformation. Historically not a common occurrence, longitudinal deformation occurred mainly in Promus Element everolimus eluting stents, which had only two rather than the commonly used 3 ...