1. Domains with a distinguished boundary surface. Functions of the extended class. The real and imaginary parts of a function of « complex variables are harmonic functions of 2n real variables. Using Green's theorem one can transform Dirichlet integrals over a 2mdimensional domain, say D, into integrals over the (2n — ̂ -dimensional boundary of D. Using this procedure (and exploiting some furthe...

In geodesy and geophysics, spherical-harmonic techniques are popular for modelling to7 pography and potential fields with ever-increasing spatial resolution. For ultra-high degree spherical 8 harmonic modelling, i.e. degree 10000 or more, classical algorithms need to be extended to avoid 9 underor overflow problems associated with the computation of Associated Legendre Functions 10 (ALFs). In t...

microgrid presents an efficient and novel solution for integrating many new energy generating resources with traditional distribution networks. having an appropriate protective scheme is a fundamental challenge in achieving microgrid plans. it is proven that traditional protective plans are not efficient for protecting microgrid, since the network is dynamic and the level of fault current chang...

We demonstrate that phase-matched frequency upconversion of ultrafast laser light can be extended to shorter wavelengths by using longer driving laser wavelengths. Experimentally, we show that the phase-matching cutoff for harmonic generation in argon increases from 45 to 100 eV when the driving laser wavelength is increased from 0.8 to 1.3 microm. Phase matching is also obtained at higher pres...

The non-overlapping domain decomposition method is an efficient approach for solving time harmonic scattering wave problems. It is used here to reduce large size systems solution to that of several systems of small size and to construct efficient procedures to couple finite element and boundary element methods. The lack of a satisfactory treatment of the so-called cross-points, nodes being shar...

We report, for the first time, the generation of high-order harmonics in a spectral range between 200 eV and 1 keV with an unusual spectral property: only every 4(th) (4i + 1, i∈ℵ) harmonic line appears, whereas the usual high-harmonic spectra consist of every odd (2i + 1) harmonic. We attribute this unique property to the quantum path interference of two extended electron trajectories that exp...

Harmonic Resonance Mode Analysis (HRMA) is a technique developed to study harmonic resonance in a power system. Compared to conventional resonance analysis techniques, HRMA is a powerful method that can indicate the origin and the locations most affected by a given mode of resonance. The method has been shown to be effective for large scale resonance studies. However, very simplified models are...

Let p be a real number greater than one and let G be a connected graph of bounded degree. In this paper we introduce the p-harmonic boundary of G. We use this boundary to characterize the graphs G for which the constant functions are the only p-harmonic functions on G. It is shown that any continuous function on the p-harmonic boundary of G can be extended to a function that is p-harmonic on G....

In this paper, a frequency-domain-based transient electromagnetic model of grounding system in horizontally stratified multilayer medium is presented. The basis of the model is an improved version of the time-harmonic electromagnetic model of grounding system. Using the originally developed continuous numerical Fourier transform algorithm, the results obtained by the time-harmonic model are syn...