In this paper a novel method based on evolutionary algorithms is presented to estimate the Harmonic components. In general, the optimization of the Harmonic Estimation process is a multi-component problem, in which evaluation of the phase and Harmonic frequency is the nonlinear part of the problem and is solved based on the mathematical and evolutionary methods; while Estimation of amplitude of the Harmonic component is a linear issue that is performed by combining the least squares method with the aforementioned approaches. In this paper, firstly, the optimal Estimation of integer Harmonic components has been introduced based on the improved shuffled frog leaping algorithm (ISFLA) in the presence of two types of noise. The obtained results present the lower error of the proposed method than to IGHS, FBF PSO, GA and FFT methods. Thereafter, the effectiveness of the presented algorithm in optimal Estimation of frequency, phase, and amplitude of the integer and non-integer Harmonics are investigated. The optimization of the Estimation of various Harmonic components under different conditions using ISFLA leads to an improvement in the assessment of power quality in power systems especially in the distribution networks, considering a lot of the nonlinear loads and Harmonic resources connected to the network.

Financial Mathematics is the application of mathematical methods to financeial problems. It is shown that Harmonic Univalent Functions play important roles in Financial Mathematics. This paper introduced and established a subclass of Harmonic univalent functions involving the argument of complex-value functions of the form f = h + 𝑔 . Additionally, this study investigates some properties of this subclass such as necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.

Surface nuclear magnetic resonance (surface-NMR) method is a well-known tool for determining the water-bearing layers and subsurface resistivity structure. Harmonic interference is an inevitable interference in surface-NMR measurements. Accurate Estimation of Harmonic interference parameters (i. e., fundamental frequency, phase and amplitude) leads to better retrieval of power-line Harmonics and consequently, more effective suppression of Harmonics from surface-NMR recordings. To that end, two algorithms are addressed for isolation and then subtraction of Harmonic interfering noise based on modeling of power-line Harmonics by a modified version of Nyman-Gaiser Estimation (NGE) and residual signal power (RSP) technique. Then, the results derived from the proposed algorithms are analyzed and compared through the modeling of some synthetic signals embedded in simulated noise and real recordings obtained from multichannel surface-NMR measurements. The numerical experiments on simulated and real surface-NMR signals show that the application of the proposed procedures results in significant decline of the level of the standard deviation of imaginary part of the detected signal and consequently, relatively accurate recovery of the Harmonic signal components with an accompanying enhancement in Estimation of the surface-NMR signal parameters.