Let G 1 + G 2 , G 1 • G 2 and G 1 {G 2 } be the join, corona and cluster of graphs G 1 and G 2 , respectively. In this paper, Kirchhoff index formulae of these composite graphs are given.

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff–Love and Reissner– Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern [Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie. Arch. Rational Mech. Anal. 4, 145–152 (1959)] and is based on the two-energies principle of P...

In this paper, we derive a dispersion relation for sound waves in viscous and heat conducting fluids. particular (i.e. variation of speed with frequency) is shown to be second order magnitude, w.r.t. Knudsen numbers, as the Stokes [2] case, corresponding non-conductive fluid (Prandtl number P r = $\infty$). This formula completes classical attenuation called Stokes-Kirchhoff. We represent simpl...

Application of least-squares Kirchhoff migration (LSM) to synthetic reverse vertical seismic profile data (RVSP) demonstrates that LSM reduces the migration artifacts, improves the image resolution and produces a more accurate image than the standard migration, but cannot completely recover the model reflectivity for AVO analysis because of the limited data coverage. The influence of incomplete...

Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor (1 - nu2). A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff-Rayleigh theories...

Since the days of Kirchhoff, blackbody radiation has been considered to be a universal process, independent of the nature and shape of the emitter. Nonetheless, in promoting this concept, Kirchhoff did require, at the minimum, thermal equilibrium with an enclosure. Recently, the author stated (P.-M. Robitaille, IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267; P.-M. Robitaille, Progr. in Phys...

In this work we consider a multi-dimensional higher-order Kirchhoff-type wave equation, with Dirichlet boundary conditions. We establish a blow-up result for certain solutions with positive initial energy. c © 2006 Elsevier Ltd. All rights reserved.