the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...

This paper deals with the scattering problem by an inhomogeneous object embedded in a chiral medium. A combined Hilbert space and integral equation method is employed to prove the existence and uniqueness of the solutions to the scattering problem. It is shown that the classical Silver-M uller radiation condition remains valid in chiral media.

Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is ...

The harmonic wavelet transform is employed to analyze various kinds of nonstationary signals common in aseismic design. The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are p...

the electronic absorption spectral line shape of a diatomic molecule with harmonic potential curves is calculated using the time correlation function formalism. both the equilibrium shift and the frequency shift of the two linking electronic states ate taken into account. the spectrum is also calculated using the cumulated expansion which is related to the correlation function of the time-depen...

We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population k is greater than a first threshold m1 ≥ 1. If, furthermore, k is greater than a second threshold m2 ≥ m1, the normalized mean inverse population is at most 1/(k −m2). We express m1 and...