We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of vertices when the considered network has some symmetries which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster’s n-th Formula.

Mit der Erstellung eines Web-basierten Lernkurses entstehen vielfache Fragen zu den erwarteten Nutzenden und deren Verhalten bei der Durchführung des Kurses. Bisher geben wenige Studien begrenzt Auskunft darüber, wie und von wem Web-basierte Lernkurse genutzt werden. Dieser Beitrag versucht auf Basis des Nutzungsverhaltens eines frei verfügbaren Web-basierten Kurses aufschlussreiche Aussagen zu...

In this paper we illustrate the use of the Beckmann-Kirchhoff model for analysing rough surface reflectance. The Beckmann-Kirchhoff model is a physical model that describes the reflectance of light from rough surfaces. The parameter of the model is the surface slope, or ratio of the surface roughness to the correlation length. We show how this parameter may be estimated using pairs of surface i...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, closed-form formulae for the Kirchhoff index and resistance distances of the Cayley graphs ov...

Method of Moments (MOM) combining with the Kirchhoff Approximation(KA) for analysis of the problem of optical wave scattering by a stack of two one-dimensional Gaussian rough interfaces is solved. The scattered field from the upper interface is solved by MOM and the transmitted field from the lower one is expressed from the Kirchhoff approximation where the multiple scattering phenomenon is neg...

The aim of this paper is to develop new Coherent Interferometry (CINT) algorithms to correct the effect of an unknown cluttered sound speed (random fluctuations around a known constant) on photoacoustic images. By back-propagating the correlations between the pre-processed pressure measurements, we show that we are able to provide statistically stable photo-acoustic images. The pre-processing i...

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow fie ld are modeled with the aid of Spalart-Alimaras one-equation turbulence modeL Appropriate acoustic and outflow boundary conditions were implemented to ...

Missing single nucleotide polymorphisms (SNPs) are quite common in genetic association studies. Subjects with missing SNPs are often discarded in analyses, which may seriously undermine the inference of SNP-disease association. In this article, we develop two haplotype-based imputation approaches and one tree-based imputation approach for association studies. The emphasis is to evaluate the imp...

WE DERIVE FIELD EQUATIONS for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order sheardeformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Ki...

We analyze in detail directivity enhancement in imaging with small arrays of closely spaced sensors, in homogeneous media. Imaging is done with Kirchhoff or travel time migration of the array data after applying an inverse filter that increases the resolution of the image. In general, the construction of such a filter requires invasive measurements on a control array in the vicinity of the obje...