In 1993 two novel distance-based topological indices were put forward. In the case of acyclic molecular graphs both are equal to the Wiener index, but both differ from it if the graphs contain cycles. One index is defined (Mohar, B.; Babić, D.; Trinajstić, N. J. Chem. Inf. Comput. Sci. 1993, 33, 153-154) in terms of eigenvalues of the Laplacian matrix, whereas the other is conceived (Klein, D. ...

Pre-stack Kirchhoff time migration (PKTM) is one of the most widely used migration algorithms in seismic imaging area. However, PKTM takes considerable time due to its high computational cost, which greatly affects the working efficiency of oil industry. Due to its high fault tolerance and scalability, Hadoop has become the most popular platform for big data processing. To overcome the shortcom...

The investigation of hydrodynamic models with partially penetrable obstacles has been initiated by the recent progress in the development of free flow turbines [l] for the purpose of estimating their efficiency limit [2]. In the previous paper [3], an explicitly solvable analog of the Kirchhoff cavitation flow was obtained. As in the classical situation, the main deficiency of the Kirchhoff mod...

Free-surface multiples can be considered to be signal and migrated by the crosscorrelogram migration method (Schuster and Rickett, 2000; Sheng, 2000). By merging the Kirchhoff and crosscorrelogram migration images, the true reflectors can be reinforced and the artifacts can be attenuated. For simple flat layered models direct multiplication of the Kirchhoff and crosscorrelogram migration images...

This paper is the second in a series of two in which we care about the asymptotics of the three-dimensional displacement field in thin elastic plates as the thickness tends to zero. In Part I we have investigated four types of lateral boundary conditions when the transverse component is clamped. In this Part II we study four other types of lateral conditions when the transverse component is fre...

The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld's rigorous theory of half-plane diffraction and Maxwell's equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld's theory in most of the positive near zone, except at sub-wavelength distance...

We analyze the resolution and statistical fluctuations of images when the ambient medium is random and scattering can be modeled primarily by wavefront distortion. We compare the coherent interferometric imaging method to the widely used Kirchhoff migration and show how the latter loses statistical stability at an exponential rate with the distance of propagation. In Kirchhoff migration we form...

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.