Comparison theorems on resistance distances and Kirchhoff indices of the so-called S& T -isomer graphs are established. Then these results are applied to compare Kirchhoff indices of hexagonal chains, showing that the straight chain is the unique chain with maximum Kirchhoff index, whereas the minimum Kirchhoff index is achieved only when the hexagonal chain is an ‘‘all-kink’’ chain. © 2014 Els...

The fundamental relationship between matrices over the rational numbers and a newly defined type of graph, a Kirchhoff graph, is discussed. For a given matrix, a Kirchhoff graph for that matrix represents the orthogonal complementarity of the null and row spaces of the matrix. A number of basic results are proven, and then a relatively complicated Kirchhoff graph is constructed for a matrix tha...

The wind integrated multi-energy systems (MES) have gained significant momentum in recent years on account of their self-sufficiency and attractive clean attributes. This study puts forward a bi-level multi-follower optimization framework to the tactical response MES wholesale electricity market (WEM) natural gas (NGM) as price setter. At upper level, endeavors minimize overall operational cost...

PURPOSE The aim of this study was to radiographically and clinically compare the effect of extracellular matrix (ECM) membranes on dimensional alterations following a ridge preservation procedure. METHODS One of 2 different ECM membranes was applied during a ridge preservation procedure. A widely used ECM membrane (WEM; Bio-Gide, Geistlich Biomaterials, Wolhusen, Switzerland) was applied in t...

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interele...

The acoustic backscatter from pressure release prolate spheroids and a three-dimensional representation of a fish swimbladder (Chilean jack mackerel, Trachurus symmetricus murphyi) was calculated using four target strength models (Kirchhoff-approximation, Kirchhoff-ray-mode, finite element solution of the Helmholtz equation, and prolate-spheroid-modal-series). Smoothly varying errors were found...