Measuring current and voltage harmonics has paramount importance for improving the power quality of distribution grids. However, achieved accuracy strongly depends on adopted instrument transformer. The present paper proposes an adaptive technique that enables effective compensation both filtering behavior harmonic distortion introduced by transformers, namely strongest nonlinear effect at low-...

We prove polynomial upper bounds on the growth of solutions to $2d$ cubic nonlinear Schrödinger equation where Laplacian is confined by harmonic potential. Due better bilinear effects, our improve those available for in periodic setting: rate a Sobolev norm order $s$ $t^{2(s-1)/3+\varepsilon}$, $s=2k$ and $k\geq 1$ integer. In appendix we provide direct proof, based integration parts, estimates...

Let $F$ be a real valued generalized biaxisymmetric potential (GBASP) in $L^{\beta}$ on $S_{R}$, the open sphere of radius $R$ about origin. In this paper we have obtained necessary and sufficient conditions rate decrease sequence best harmonic polynomial approximates to such that is harmonically continues as an entire function GBASP determine their $(p,q)$-order $(p,q)$-type with respect proxi...

We derive a formula for the number of pre-images under non-degenerate harmonic mapping $f$, using argument principle. This reveals connection between and caustics. Our results allow to deduce $f$ geometrically every non-caustic point. approximately locate points near Moreover, we apply our prove that $k = n, n+1, \ldots, n^2$ there exists polynomial degree $n$ with $k$ zeros.

A new very high-order finite volume method to solve the harmonic and the biharmonic operators for one-dimensional geometries is proposed. The main ingredient is the polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic ope...

The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground st...

enters many phenomenological and methodical considerations as a “next-to-solvable” model [1]. In fact, among all the real polynomial interactions, only the harmonic and sextic models can generate an arbitrary N–plet of bound state wavefunctions in an elementary form. All the similar models are often called quasi-exactly solvable (QES, cf. [2]). Unfortunately, the close parallel between the sext...

‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

Let $u$ be a harmonic function in $C^1$-Dini domain such that vanishes on an open set of the boundary. We show near every point set, can written uniquely as sum non-trivial homogeneous polynomial and error term higher degree (depending Dini parameter). In particular, this implies has unique tangent at point, convergence rate to estimated. also study relationship functions nearby points special ...

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as reproduction of second-degree polynomials, approximation order, conditions for convexity preservation. In particular, σ quasi-uniform grids with σ≤4, get quasi C3 that maintains properties initia...