In this paper, we introduce higher-order harmonic numbers and derive their relevant properties and generating functions by using an umbral-type method. We discuss the link with recent works on the subject, and show that the combinations of umbral and...
The main aim of this paper is to define and investigate a new class of symmetric beta type distributions with the help of the symmetric Bernstein-type basis functions. We give symmetry property of these distributions and the Bernstein-type basis func...
In this article, the up and down harmonically convex fuzzy-number-valued mapping which is a novel kind of harmonically convex fuzzy-number-valued mapping is introduced. In addition, it is highlighted that the new idea of up and down harmonically conv...
In this paper,
Utilizing non-overlap windings has emerged as a favourable choice for minimizing electrical machine manufacturing costs, among other benefits. Nevertheless, it is widely acknowledged that these windings exhibit a notable level of harmonic contents in...
By employing the coefficient extraction method, a class of binomial series involving harmonic numbers will be reviewed through three hypergeometric
A very recent article delved into and expanded the four parametric linear Euler sums, revealing that two well-established subjects—Euler sums and series involving the zeta functions—display particular correlations. In this study, we prese...
Harmonic numbers appear, for example, in many expressions involving Riemann zeta functions. Here, among other things, we introduce and study discrete versions of those numbers, namely the discrete harmonic numbers. The aim of this paper is twofold. T...
In this paper, inspired by recent works, we define q-analogs of
In this paper, we express
We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued mapping as our main goal in this work. With the help of up and down harmonically fuzzy-number convexity and the fuzzy fractional integral operator, we also show...
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are immediate con...
In this study, two-dimensional numerical simulation was carried out for an oscillatory flow between parallel flat plates having a suddenly expanded section. Governing equations were discretized with the second-order accuracy by a finite volume method...
In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirl...
We address the second-harmonic generation process in a quantum frame. Starting with a perturbative approach, we show that it is possible to achieve a number of analytic results, ranging from the up-conversion probability to the statistical properties...
Power inverters are extensively employed in a wide range of applications such as VSD, PV, UPS, and Vehicle-to-Grid systems. Different control topologies are used in power electronic inverters. Of these, PWM and MLVSIs are implemented to minimize the...
We study inverse-binomial double series involving ordinary and alternating harmonic numbers. Using iterated integrals associated with admissible 3-posets, we establish twenty-four explicit evaluations in terms of multiple zeta values and alternating...
We present some addition theorems for spin-weighted spherical harmonics, generalizing previous results for scalar (spin-zero) spherical harmonics. These addition theorems involve sums over the azimuthal quantum number of products of two spin-weighted...
This paper studies the electromechanical characteristics of synchronous generators under dynamic stator interturn short circuit (DSISC). First, the air gap magnetic flux density (MFD) of the generator under normal and DSISC fault was obtained. Then,...
Novel methods of coherent short-wavelength sources generation require thorough analysis for their further amendments and practical implementations. In this work, we report on the quasi-phase matching (QPM) of high-order harmonics generation during th...
We report on the theoretical/numerical investigation of simultaneous second- and third-harmonic generation from a single wavelength input in quasi-phase-matched crystals. The presented technique consists of a quadratic crystal with two first-order qu...
The application of seed morphology to descriptive systematics requires methods for shape analysis and quantification. The complexity of lateral and dorsal views of seeds of Silene species is investigated here by the application of the Elliptic Fourie...
Integrating the general expression of the generalized harmonic wavelet (GHW)-based spectral representation method (SRM) and the idea of stochastic harmonic function (SHF), a novel stochastic generalized harmonic wavelet (SGHW) method for fully nonsta...
Expanding the number of photovoltaic (PV) systems integrated into a grid raises many concerns regarding protection, system safety, and power quality. In order to monitor the effects of the current harmonics generated by PV systems, this paper present...
Free-electron lasers (FELs) can produce radiation in the short wavelength range extending from the extreme ultraviolet (XUV) to the X-rays with a few to a few tens of femtoseconds pulse duration. These facilities have enabled significant breakthrough...
The Navier equations are reformulated to be third-order partial differential equations. New anti-Cauchy-Riemann equations can express a general solution in 2D space for incompressible materials. Based on the third-order solutions in 3D space and the...
We consider a quantum mechanical model for the high-order harmonic generation in bulk solids. The bandgap is assumed to be considerably larger than the exciting photon energy. Using dipole approximation, the dynamical equations for different initial...
Power electronic circuits in modern power supplies have improved the conversion efficiency on the one hand but have also increased harmonic emissions. Harmonic currents from the operation of these units affect the voltage waveforms of the network and...
On the basis of the space voltage vector pulse width modulation (SVPWM) technique, the random pulse width modulation (RPWM) technique, which can reduce harmonics, is investigated based on the vector control system of permanent magnet synchronous moto...
This paper presents a comparative simulation study of the operation of various types of drivers dedicated for use in light-emitting diode (LED)-based light stripes. The study comprises an experimentally verified simulation in view of their influence...
The impedance of the harmonic plane in a dual three-phase permanent magnet synchronous motor (DTP-PMSM) is very low, meaning that even small harmonic voltages can induce significant harmonic currents, particularly at the fifth and seventh harmonic fr...
The rim-driven device (RDD) integrates the motor and the impeller, which can achieve shaftless, modular, and integrated operation of the turbomachinery system and has broad application prospects. To reduce the axial length and radial thickness of the...
The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop...
In
Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are:
The power quality of grid-connected inverters (GCIs) is attracting a lot of attention as the number of distributed generation systems with renewable energy sources are increased. It is well known that the harmonics present in the grid have a lot of d...
Harmonics and interharmonics have a significant impact on the safe operation of power systems, and accurately identifying interharmonics in power systems is the basis of harmonic suppression. The accuracy with which interharmonic components in power...
In this paper, in order to effectively reduce the electromagnetic noise of automotive electronic water pumps, a Hybrid Random Carrier Space Vector Pulse Width Modulation Hybrid Random Carrier Space Vector Pulse Width Modulation, (HRCSVPWM) technique...
The paper presents investigations and analysis of the parameters of the magnetic part of the equivalent circuit of the inductive CT in the frequencies range from 50 Hz to 5 kHz. Therefore, a measuring circuit used to determine the values of the trans...
In this work, we establish some characteristics for a sequence,
Renewable and distributed energy generation includes wind turbines, fuel cells, solar cells, and batteries. These distributed energy sources need special power converters in order to connect them to the grid and make the generated power available for...
In the control system of a permanent magnet synchronous motor (PMSM) driven by an inverter, the conventional space vector pulse width modulation (SVPWM) strategy introduces high-frequency current harmonics at the switching frequency and its multiples...
This paper presents the influences of winding magneto-motive force (MMF) harmonics on the torque characteristics in surface-mounted permanent magnet vernier (SPMV) machines. Based on the magnetic gearing effects, the armature magnetic field of the SP...
The magnetically controlled reactor adjusts its output capacity based on the principle of magnetic saturation. Due to the iron core working in the saturated region, higher harmonics will be generated in the working current. A large number of harmonic...
A grid-forming converter (GFM) controls power output by adjusting the phase angle and amplitude of its output voltage, providing voltage and frequency support to the power system and effectively enhancing system stability. However, it has limitations...
We study coaxial superpositions of Gaussian optical vortices described by a geometric progression. The topological charge (TC) is obtained for all variants of such superpositions. The TC can be either integer or half-integer in the initial plane. How...
Quantum-optical spectrometry is a recently developed shot-to-shot photon correlation-based method, namely using a quantum spectrometer (QS), that has been used to reveal the quantum optical nature of intense laser–matter interactions and connect the...
Material nonlinearity is explored for the assessment of structural integrity. Crack–wave interactions are of particular interest. The major focus is on higher-order harmonics, generated in propagating shear horizontal (SH) waves. These harmonic...
In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where “generalized” indicates that a boundary functi...
Bolted joints are fundamental to numerous structural components in engineering practice. Nevertheless, their failure or even their loosening can lead to insufficient performance and reduced structural safety. This study presents a theoretical develop...
of 8