We study Dirac-harmonic maps from a Riemann surface to a sphere Sn. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.

In this paper we describe the extension of the Mathematica package HPL to treat harmonic polylogarithms of complex arguments. The harmonic polylogarithms have been introduced by Remiddi and Vermaseren [1] and have many applications in high energy particle physics.

this paper presents a new control methodology for active power filters that provide an adaptive online harmonic estimation with partial and selective harmonic reduction schemes, which has been implemented within an integrated controller. the proposed approach is to provide partial and selective reduction of those individual harmonics which exceed the recommended levels as set by regulatory bodi...

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms f : Ω onto −→ Ω∗ between bounded doubly connected domains such that ModΩ 6 ModΩ∗ there exists, unique up to conformal authomorphisms of Ω, an energy-minimal diffeomorphism. No boundary conditions are imposed on f . Although any energyminimal diffeomorphis...

A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell’s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are deriv...

this paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a least square support vector machine (lssvm). two wavelet selection criteria maximum energy to shannon entropy ratio and maximum relative wavelet energy are used and compared to select an appropriate wavelet for feature extraction. the fault diagnosis method co...

this paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a least square support vector machine (lssvm). two wavelet selection criteria maximum energy to shannon entropy ratio and maximum relative wavelet energy are used and compared to select an appropriate wavelet for feature extraction. the fault diagnosis method co...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...