‎let $g=(v(g),e(g))$ be a simple connected graph with vertex set $v(g)$ and edge‎ ‎set $e(g)$‎. ‎the (first) edge-hyper wiener index of the graph $g$ is defined as‎: ‎$$ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),$$‎ ‎where $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

ABSTRACT- Paddy soils make up the largest anthropogenic wetlands on earth. Present study was performed to investigate and compare soil formation of paddy soils with long-term rice cultivation history with non-paddy soils and study the effect of waterlogging on soil pedogenesis. Soil samples were taken from paddy and non-paddy soils derived from the same calcareous parent materials. Some pedogen...

We develop an adaptive finite element method for island dynamics in epitaxial growth. We study a step-flow model, which consists of an adatom (adsorbed atom) diffusion equation on terraces of different height; thermodynamic boundary conditions on terrace boundaries including anisotropic line tension; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, t...

Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...

The occurrence of edge loading in hip joint replacement has been associated with many factors such as prosthetic design, component malposition and activities of daily living. The present study aimed to quantify the occurrence of edge loading/contact at the articulating surface and to evaluate the effect of cup angles and edge loading on the contact mechanics of a modular metal-on-polyethylene (...

Edge loading can negatively impact the biomechanics and long-term performance of hip replacements. Although edge loading has been widely investigated for hard-on-hard articulations, limited work has been conducted for hard-on-soft combinations. The aim of the present study was to investigate edge loading and its effect on the contact mechanics of a modular metal-on-polyethylene (MoP) total hip ...

In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...