From a monotonicity property, we derive several results characterizing positive harmonic functions in the unit ball in R and positive measures on the unit sphere Sn−1. Let Bn = {x ∈ Rn : |x| < 1}, n ≥ 2 be the unit ball in Rn and Sn−1 = ∂Bn be the unit sphere. From a monotonicity property, we derive several results characterizing positive harmonic functions in Bn and positive measures on Sn−1. ...

Both A-harmonic equations and p-harmonic geometry are rich subjects 1–5 . Many results on both topics have been derived, respectively, but there are very few papers relating both subjects. In this paper, we will connect these two subjects by extending several results from 1-Harmonic functions to A-Harmonic functions. We consider the following setting: a C1 function f : R → R is said to be A-har...

We use a few-cycle, carrier-envelope-phase (CEP) stabilized laser system to generate high-harmonic emission in argon, neon, and carbon dioxide. The high-harmonic spectra consist of discrete harmonic orders whose positions shift as a function of the CEP. Near the cutoff harmonic, the peaks are separated by two photon orders, and can correspond to either even or odd harmonics of the driving laser...

In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet's principles, is concurrently able to be expanded in Taylor's representation, over a particular interval of their do...

A continuous case of new density function called harmonic probability density function (HPDF) is structured using mathematical method. The mean and variance of this probability function is presented using both the definition and moment generating function. A discussion has started on many other connections that may exist between this new model and its applications in geometry, probability, and ...

Harmonic pollution of double fed induction generators (DFIGs) has become a vital concern for its undesirable effects on power quality issues of wind generation systems and grid-connected system, and the double pulse width modulation (PWM)converter is one of the main harmonic sources in DFIGs. Thus the harmonic analysis of the converter in DFIGs is a necessary step to evaluate their harmonic pol...

This paper presents a new method for evaluation and simulation of inrush current in various transformers using operational matrices and Hartley transform. Unlike most of the previous works, time and frequency domain calculations are conducted simultaneously. Mathematical equations are first represented to compute the inrush current based on reiteration and then Hartley transform is used to stud...

This paper describes a multi-pitch analysis method using specmurt analysis with iterative estimation of the quasioptimal common harmonic structure function. Specmurt analysis (Sagayama et al., 2004) is based upon the idea that superimposed harmonic structure pattern can be expressed as a convolution of two components, a fundamental frequency distribution and a ‘common harmonic structure’ functi...

Let L be a second order elliptic differential operator on a Riemannian manifold E with no zero order terms. We say that a function h is L-harmonic if Lh = 0. Every positive L-harmonic function has a unique representation

preprint numerics no. 2/2007 norwegian university of science and technology trondheim, norway The 'pseudo-harmonic' extension is an approximation to the common harmonic extension for extending a function over a domain based on its trace along the boundary of the domain. On a circle the two extension methods produce identical results. We present explicit formulas for the computation of distance ...