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...

The potential function of Lippincott and Schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. The parameters originally introduced to the potential function by Lippincott and Schroeder have been determined from the structural parameters such as 0.. .Odistance 0-H bond distance, H.. .O distance and HOO angle. Thevalidity of harmonic oscillator appr...

For x x1, x2, . . . , xn ∈ 0, 1 n and r ∈ {1, 2, . . . , n}, the symmetric function Fn x, r is defined as Fn x, r Fn x1, x2, . . . , xn; r ∑ 1≤i1<i2 ···<ir≤n ∏r j 1 1 xij / 1−xij , where i1, i2, . . . , in are positive integers. In this paper, the Schur convexity, Schur multiplicative convexity, and Schur harmonic convexity of Fn x, r are discussed. As consequences, several inequalities are est...

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

let denote the unit circle in the complex plane. given a function , one uses t usual (harmonic) poisson kernel for the unit disk to define the poisson integral of , namely . here we consider the biharmonic poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . we then consider the dilations for and . the ...

This paper proposes an improved control method based on modified Delta-Sigma Modulator (DSM) to enhance transient response and improve harmonic contents of buck DC-DC converter. The main advantages of the proposed method are improving the output voltage frequency spectrum, correction of the output voltage harmonic contents and sideband harmonics, reduction of switching noise peaks at the output...