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Journal articles on the topic 'Harmonic function'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 April 2022

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1

Abi-Khuzam, Faruk F. "Meromorphic functions with harmonic ∗-function." Complex Variables, Theory and Application: An International Journal 12, no. 1-4 (October 1989): 261–65. http://dx.doi.org/10.1080/17476938908814370.

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2

Mustafa, M. T. "Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions." Abstract and Applied Analysis 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/315757.

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For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

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3

Pilipović, Stevan, and Dimitris Scarpalézos. "Harmonic generalized functions in generalized function algebras." Monatshefte für Mathematik 163, no. 1 (December 19, 2009): 81–106. http://dx.doi.org/10.1007/s00605-009-0180-5.

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4

Choudhary, Masood Ahmed, and ToseefAhmed Malik. "Harmonic Convex function and Harmonic Variational Inequalities." International Journal of Mathematics Trends and Technology 54, no. 4 (February 25, 2018): 320–24. http://dx.doi.org/10.14445/22315373/ijmtt-v54p536.

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5

Sebbar, Ahmed. "Harmonic numbers, harmonic series and zeta function." Moroccan Journal of Pure and Applied Analysis 4, no. 2 (December 1, 2018): 122–57. http://dx.doi.org/10.1515/mjpaa-2018-0012.

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AbstractThis paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias. The other parts are devoted to the series $\mathcal{M}{i_s}(z) = \sum\limits_{n = 1}^\infty {{{\mu (n)} \over {{n^s}}}{z^n}} $. A significant result is that the real part f of$$\sum {{{\mu (n)} \over n}{e^{2in\pi \theta }}}$$is an example of a non-trivial real-valued continuous function f on the real line which is 1-periodic, is not odd and has the property $\sum\nolimits_{h = 1}^n {f(h/k) = 0}$ for every positive integer k.

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6

Awan, Muhammad, Muhammad Noor, Marcela Mihai, Khalida Noor, and Nousheen Akhtar. "On approximately harmonic h-convex functions depending on a given function." Filomat 33, no. 12 (2019): 3783–93. http://dx.doi.org/10.2298/fil1912783a.

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A new class of harmonic convex function depending on given functions which is called as ?approximately harmonic h-convex functions? is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.

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7

Matsuoka, Osamu. "Molecular integrals over Laguerre Gaussian-type functions of real spherical harmonics." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 388–92. http://dx.doi.org/10.1139/v92-055.

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Molecular integrals are formulated over the Laguerre Gaussian-type functions (LGTF) of real spherical harmonics. They include the overlap integrals and the energy integrals of kinetic, nuclear attraction, and electron repulsion. For the nuclear-attraction integrals the formulations based on the point as well as the Gaussian nuclear charge distribution models are presented. Integral formulas over the LGTFs of real spherical harmonics are found a little more complicated than those of the LGTFs of complex spherical harmonics due to the summations over magnetic quantum numbers. Keywords: molecular integral, Gaussian-type function, spherical harmonic, solid harmonic, Sonine polynomial.

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8

Xu, Yuan. "Harmonic Polynomials Associated With Reflection Groups." Canadian Mathematical Bulletin 43, no. 4 (December 1, 2000): 496–507. http://dx.doi.org/10.4153/cmb-2000-057-2.

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AbstractWe extend Maxwell’s representation of harmonic polynomials to h-harmonics associated to a reflection invariant weight function hk. Let 𝑫i, 1 ≤ i ≤ d, be Dunkl’s operators associated with a reflection group. For any homogeneous polynomial P of degree n,we prove the polynomial is a h-harmonic polynomial of degree n, where γ = ∑ki and 𝑫 = (𝑫1, … ,𝑫d). The construction yields a basis for h-harmonics. We also discuss self-adjoint operators acting on the space of h-harmonics.

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9

Schaeben, H. "The de la Vallée Poussin Standard Orientation Density Function." Textures and Microstructures 33, no. 1-4 (January 1, 1999): 365–73. http://dx.doi.org/10.1155/tsm.33.365.

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The de la Vallée Poussin standard orientation density function νκ(ω)=C(κ)cos⁡2κ(ω/2) is discussed with emphasis on the finiteness of its harmonic series expansion which, advantageously distinguishes it from other known standard functions. Given its halfwidth, the de la Vallée Poussin standard orientation density function allows, for example, to tabulate the degree of series expansion into harmonics required for its exact representation.

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10

STEVIĆ, Stevo. "On harmonic function spaces." Journal of the Mathematical Society of Japan 57, no. 3 (July 2005): 781–802. http://dx.doi.org/10.2969/jmsj/1158241935.

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11

Macek, J. H., S. Yu Ovchinnikov, and D. B. Khrebtukov. "Harmonic oscillator Green’s function." Radiation Physics and Chemistry 59, no. 2 (August 2000): 149–53. http://dx.doi.org/10.1016/s0969-806x(00)00285-1.

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12

Begehr, H., and T. Vaitekhovich. "Modified harmonic Robin function." Complex Variables and Elliptic Equations 58, no. 4 (October 12, 2011): 483–96. http://dx.doi.org/10.1080/17476933.2011.625092.

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13

Nassim Kraimia, Mohamed, and Mohamed Boudour. "Harmonic interaction of a static Var compensator with AC power system containing multiple non-linear loads." Engineering review 40, no. 3 (May 21, 2020): 21–31. http://dx.doi.org/10.30765/er.40.3.03.

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In this paper a study of the impact of the harmonics generated by a static Var compensator (SVC) is presented. The SVC is modeled, in the harmonic domain, as a coupled current source by using the complex Fourier transforms. Then, this model is converted to polar form to be integrated into the harmonic power flow program. This approach has been carried out on the IEEE 14 bus test power system, in order to show its effectiveness in evaluating the impact of harmonics, injected by the shunt compensating devices, and its interaction with the AC transmission system, in meshed power networks. Since the SVC consists of a thyristorcontrolled reactor (TCR) and a fixed capacitor, the harmonic currents are functions of the TCR thyristors firing angles. The variation of the total voltage harmonic distortion as function of firing angle changes and location of nonlinear loads is clearly presented and discussed.

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14

Yin, Songting. "Some Remarks on Harmonic Functions in Minkowski Spaces." Mathematics 7, no. 2 (February 19, 2019): 196. http://dx.doi.org/10.3390/math7020196.

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We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean.

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15

Liu, Liyan, Carlos Lozano, and Dan Iredell. "Time–Space SST Variability in the Atlantic during 2013: Seasonal Cycle." Journal of Atmospheric and Oceanic Technology 32, no. 9 (September 2015): 1689–705. http://dx.doi.org/10.1175/jtech-d-15-0028.1.

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AbstractA 2-yr-long daily gridded field of sea surface temperature (SST) in the Atlantic centered for the year 2013 is projected onto orthogonal components: its mean, six harmonics of the year cycle, the slow-varying contribution, and the fast-varying contribution. The periodic function defined by the year harmonics, referred to here as the seasonal harmonic, contains most of the year variability in 2013. The seasonal harmonic is examined in its spatial and temporal distribution by describing the amplitude and phase of its maxima and minima, and other associated parameters. In the seasonal harmonic, the ratio of the duration of warming period to cooling period ranges from 0.2 to 2.0. There are also differences in the spatial patterns and dominance of the year harmonics—in general associated with regions with different insolation, oceanic, and atmospheric regimes. Empirical orthogonal functions (EOFs) of the seasonal harmonic allow for a succinct description of the seasonal evolution for the Atlantic and its subdomains. The decomposition can be applied to model output, allowing for a more incisive model validation and data assimilation. The decorrelation time scale of the rapidly varying signal is found to be nearly independent of the time of the year once four or more harmonics are used. The decomposition algorithm, here implemented for a single year cycle, can be applied to obtain a multiyear average of the seasonal harmonic.

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16

Prasath, V., S. Vijayalakshmi, and R. Jain Anush. "PMSG Based WECS with PR Control Strategy for Grid Control." Applied Mechanics and Materials 573 (June 2014): 267–72. http://dx.doi.org/10.4028/www.scientific.net/amm.573.267.

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In this paper, a current feedback control scheme is proposed using Proportional Resonant (PR) for a grid-connected converter with an LCL Filter; PR controller with harmonic compensators has high gain at the desired frequencies for decrease harmonic distortion in the alternative voltage or current. Harmonic compensators of PR controller are limited to several low-order harmonics due to the system instability when the compensated frequency is out of system control loop’s bandwidth. The average value of current flow through inductors of LCL filter is feedback to the PR current regulator. Zero D-axis Control (ZDC) is to control the generator side converter to reduce the DC-link ripples, multi-loop harmonic current controllers are applied to regulate the higher-order harmonics by PR regulators. Consequently control strategy with LCL filter is to reduce third-order function to first-order function. By this way large control loop gain can be chosen to obtain control loop for the required harmonic components of the PR controller. The simulation and experimental results have been illustrated to validate the effectiveness of the proposed method in MATLAB Simulink.

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17

Wang, Guishuo, Xiaoli Wang, and Chen Zhao. "An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window." Applied Sciences 10, no. 11 (June 5, 2020): 3922. http://dx.doi.org/10.3390/app10113922.

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The current signal harmonic detection method(s) cannot reduce the errors in the analysis and extraction of mixed harmonics in the power grid. This paper designs a harmonic detection method based on discrete Fourier transform (DFT) and discrete wavelet transform (DWT) using Bartlett–Hann window function. It improves the detection accuracy of the existing methods in the low frequency steady-state part. In addition, it also separates the steady harmonics from the attenuation harmonics of the high frequency part. Simulation results show that the proposed harmonic detection method improves the detection accuracy of the steady-state part by 1.5175% compared to the existing method. The average value of low frequency steady-state amplitude detection of the proposed method is about 95.3375%. At the same time, the individual harmonic components of the signal are accurately detected and recovered in the high frequency part, and separation of the steady-state harmonics and the attenuated harmonics is achieved. This method is beneficial to improve the ability of harmonic analysis in the power grid.

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18

Foskolos, Georgios. "Measurement-Based Current-Harmonics Modeling of Aggregated Electric-Vehicle Loads Using Power-Exponential Functions." World Electric Vehicle Journal 11, no. 3 (July 28, 2020): 51. http://dx.doi.org/10.3390/wevj11030051.

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This paper presents an aggregate current-harmonic load model using power exponential functions and built from actual measurement data during the individual charging of four different fully electric vehicles. The model is based on individual emitted current harmonics as a function of state of charge (SOC), and was used to deterministically simulate the simultaneous charging of six vehicles fed from the same bus. The aggregation of current harmonics up to the 11th was simulated in order to find the circumstances when maximal current-harmonic magnitude occurs, and the phase-angle location. The number of possible identical vehicles was set to four, while battery SOC, the start of charging, and the kind of vehicle were randomized. The results are presented in tables, graphs, and polar plots. Even though simulations did not consider the surrounding harmonics, supply-voltage variation, or network impedance, this paper presents an innovative modeling approach that gives valuable information on the individual current-harmonic contribution of aggregated electric-vehicle loads. With the future implementation of vehicle-to-grid technology, this way of modeling presents new opportunities to predict the harmonic outcome of multiple electric vehicles charging.

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19

Almaita, Eyad K., and Jumana Al shawawreh. "Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm. (On-Line Harmonics Estimation Application)." International Journal of Renewable Energy Development 6, no. 1 (March 22, 2017): 9–17. http://dx.doi.org/10.14710/ijred.6.1.9-17.

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In this paper, an adaptive Radial Basis Function Neural Networks (RBFNN) algorithm is used to estimate the fundamental and harmonic components of nonlinear load current. The performance of the adaptive RBFNN is evaluated based on the difference between the original signal and the constructed signal (the summation between fundamental and harmonic components). Also, an extensive investigation is carried out to propose a systematic and optimal selection of the Adaptive RBFNN parameters. These parameters will ensure fast and stable convergence and minimum estimation error. The results show an improving for fundamental and harmonics estimation comparing to the conventional RBFNN. Also, the results show how to control the computational steps and how they are related to the estimation error. The methodology used in this paper facilitates the development and design of signal processing and control systems.Article History: Received Dec 15, 2016; Received in revised form Feb 2nd 2017; Accepted 13rd 2017; Available onlineHow to Cite This Article: Almaita, E.K and Shawawreh J.Al (2017) Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm (On-Line Harmonics Estimation Application). International Journal of Renewable Energy Develeopment, 6(1), 9-17.http://dx.doi.org/10.14710/ijred.6.1.9-17

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20

Tsorng-Juu Liang, R. M. O'Connell, and R. G. Hoft. "Inverter harmonic reduction using Walsh function harmonic elimination method." IEEE Transactions on Power Electronics 12, no. 6 (November 1997): 971–82. http://dx.doi.org/10.1109/63.641495.

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21

Li, Zhenhua, Tinghe Hu, and Ahmed Abu-Siada. "A Minimum Side-Lobe Optimization Window Function and Its Application in Harmonic Detection of an Electricity Gird." Energies 12, no. 13 (July 8, 2019): 2619. http://dx.doi.org/10.3390/en12132619.

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Several window functions are currently applied to improve the performance of the discrete Fourier transform (DFT) harmonic detection method. These window functions exhibit poor accuracy in measuring the harmonic contents of a signal with high-order and weak-amplitude components when the power frequency fluctuates within a small range. In this paper, a minimum side-lobe optimization window function that is aimed at overcoming the abovementioned issue is proposed. Moreover, an improved DFT harmonic detection algorithm based on the six-term minimum side-lobe optimization window and four-spectrum-line interpolation method is proposed. In this context, the minimum side-lobe optimization window is obtained by optimizing the conventional cosine window function according to the optimization rules, and the characteristics of the new proposed window are provided to analyze its performance. Then, the proposed optimization window function is employed to improve the DFT harmonic detection algorithm based on the six-term minimum side-lobe optimization window and four-spectrum-line interpolation method. The proposed technique is used to detect harmonics of an electricity gird in which the six-term minimum side-lobe optimization window is utilized to eliminate the influence of spectrum leakage caused by nonsynchronous sampling of signal processing. The four-spectrum-line interpolation method is employed to eliminate or mitigate the fence effect caused by the inherent measurement error of the DFT method. Simulation experiments in two complex conditions and an experiment test are carried out to validate the improved performance of the proposed window. Results reveal that the six-term minimum side-lode optimization window has the smallest peak side lobe when compared with existing windows, which can effectively reduce the interaction influence of spectrum leakage, improve the measurement accuracy of the DFT harmonic detection method, and meet the standard requirement of harmonic measurement in complex situations.

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22

Gangadharan, Murugusundaramoorthy, Vijaya Kaliyappan, Hijaz Ahmad, K. H. Mahmoud, and E. M. Khalil. "Mapping properties of Janowski-type harmonic functions involving Mittag-Leffler function." AIMS Mathematics 6, no. 12 (2021): 13235–46. http://dx.doi.org/10.3934/math.2021765.

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<abstract><p>In this paper, we examine a connotation between certain subclasses of harmonic univalent functions by applying certain convolution operator regarding Mittag-Leffler function. To be more precise, we confer such influences with Janowski-type harmonic univalent functions in the open unit disc $ \mathbb{D}. $</p></abstract>

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23

Chen, Wen-Hua. "Harmonic Disturbance Observer for Nonlinear Systems." Journal of Dynamic Systems, Measurement, and Control 125, no. 1 (March 1, 2003): 114–17. http://dx.doi.org/10.1115/1.1543551.

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A nonlinear harmonic disturbance observer for nonlinear systems subject to harmonics is designed and stability of the proposed observer is established using passivity approach. A systematic procedure to choose the nonlinear gain function in the observer is proposed. The proposed nonlinear disturbance observer can be integrated with a linear/nonlinear controller to improve its disturbance attenuation ability for nonlinear systems under harmonics.

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24

Nobile, Drew. "Harmonic Function in Rock Music." Journal of Music Theory 60, no. 2 (October 2016): 149–80. http://dx.doi.org/10.1215/00222909-3651838.

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25

CHU, CHO-HO. "HARMONIC FUNCTION SPACES ON GROUPS." Journal of the London Mathematical Society 70, no. 01 (July 23, 2004): 182–98. http://dx.doi.org/10.1112/s0024610704005265.

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26

Manzo, V. J. "Software-assisted harmonic function discrimination." Journal of Music, Technology and Education 7, no. 1 (May 1, 2014): 23–37. http://dx.doi.org/10.1386/jmte.7.1.23_1.

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27

Dziok, Jacek. "Harmonic Function with Correlated Coefficients." Acta Mathematica Scientia 39, no. 6 (September 27, 2019): 1661–73. http://dx.doi.org/10.1007/s10473-019-0615-6.

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28

Kavitha, R., and Rani Thottungal. "WTHD minimisation in hybrid multilevel inverter using biogeographical based optimisation." Archives of Electrical Engineering 63, no. 2 (June 1, 2014): 187–96. http://dx.doi.org/10.2478/aee-2014-0015.

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Abstract Harmonic minimisation in hybrid cascaded multilevel inverter involves complex nonlinear transcendental equation with multiple solutions. Hybrid cascaded multilevel can be implemented using reduced switch count when compared to traditional cascaded multilevel inverter topology. In this paper Biogeographical Based Optimisation (BBO) technique is applied to Hybrid multilevel inverter to determine the optimum switching angles with weighted total harmonic distortion (WTHD) as the objective function. Optimisation based on WTHD combines the advantage of both OMTHD (Optimal Minimisation of Total Harmonic Distortion) and SHE (Selective Harmonic Elimination) PWM. WTHD optimisation has the benefit of eliminating the specific lower order harmonics as in SHEPWM and minimisation of THD as in OMTHD. The simulation and experimental results for a 7 level multilevel inverter were presented. The results indicate that WTHD optimization provides both elimination of lower order harmonics and minimisation of Total Harmonic Distortion when compared to conventional OMTHD and SHE PWM. Experimental prototype of a seven level hybrid cascaded multilevel inverter is implemented to verify the simulation results.

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29

Becker, W., S. Long, and J. K. Mclver. "Nonperturbative Behavior of Higher-Harmonic Production in a Model Atom." Zeitschrift für Naturforschung A 52, no. 1-2 (February 1, 1997): 105–7. http://dx.doi.org/10.1515/zna-1997-1-224.

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Abstract The emission of very high harmonics of a laser field irradiating a model atom defined by a three-dimensional delta function is considered and several nonperturbative features of the harmonic spectrum are discussed.

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30

Montolalu, Chriestie E. J. C. "ENERGY FUNCTIONAL OF ROTATIONALLY SYMMETRIC HARMONIC MAPS FROM A BALL INTO A SPHERE." JURNAL ILMIAH SAINS 16, no. 1 (June 24, 2016): 35. http://dx.doi.org/10.35799/jis.16.1.2016.12534.

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ABSTRACT A study in Rotationally Symmetric Harmonic Maps has been conducted in the past few decades. One of its well-known study is its application from a ball into a sphere in three dimensional space. This has been shown to be accurate by showing its energy function. This paper will show how to find an energy function for this case. Keywords: Rotationally Symmetric Harmonic Maps, Energy Functional FUNGSI ENERGI DARI PEMETAAN ROTASI HARMONIK SIMETRIS DARI BOLA KE SPHERE ABSTRAK Studi tentang Pemetaan Rotasi Harmonik yang simetris telah dilakukan selama beberapa dekade terakhir ini. Salah satunya yang paling dikenal adalah aplikasinya dari bola ke sphere dalam ruang dimensi tiga. Hal ini telah dapat ditunjukkan dengan akurat dengan membuktikan fungi energinya. Tulisan ini akan menunjukkan cara menemukan fungsi energi untuk masalah ini. Kata-kata kunci: Pemetaan Rotasi Harmonik Simetris, Fungsi Energi

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31

Yao, Jianjun, Chenguang Xiao, Zhenshuai Wan, Shiqi Zhang, and Xiaodong Zhang. "Acceleration Harmonics Identification for an Electro-Hydraulic Servo Shaking Table Based on a Nonlinear Adaptive Algorithm." Applied Sciences 8, no. 8 (August 9, 2018): 1332. http://dx.doi.org/10.3390/app8081332.

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Since the electro-hydraulic servo shaking table came into existence, many nonlinear elements, such as, dead zone, friction and backlash, as well as its acceleration response has higher harmonics which result in acceleration harmonic distortion, when the electro-hydraulic system is excited by sinusoidal signal. For suppressing the harmonic distortion and precisely identify harmonics, a combination of the adaptive linear neural network and least mean M-estimate (ADALINE-LMM), is proposed to identify the amplitude and phase of each harmonic component. Specifically, the Hampel’s three-part M-estimator is applied to provide thresholds for detecting and suppressing the impulse noise. Harmonic generators are used by this harmonic identification scheme to create input vectors and the value of the identified acceleration signal is subtracted from the true value of the system acceleration response to construct the criterion function. The weight vector of the ADALINE is updated iteratively by the LMM algorithm, and the amplitude and phase of each harmonic, even the results of harmonic components, can be computed directly online. The simulation and experiment are performed to validate the performance of the proposed algorithm. According to the experiment result, the above method of harmonic identification possesses great real-time performance and it has not only good convergence performance but also high identification precision.

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Hoflund, Maria, Jasper Peschel, Marius Plach, Hugo Dacasa, Kévin Veyrinas, Eric Constant, Peter Smorenburg, et al. "Focusing Properties of High-Order Harmonics." Ultrafast Science 2021 (August 29, 2021): 1–8. http://dx.doi.org/10.34133/2021/9797453.

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Many applications of the extreme ultraviolet (XUV) radiation obtained by high-order harmonic generation (HHG) in gases require a small focus area in order to enable attosecond pulses to reach a high intensity. Here, high-order harmonics generated in Ar with a multiterawatt laser system in a loose focusing geometry are focused to a few micrometers using two toroidal mirrors in a Wolter configuration with a high demagnification factor. Using a knife-edge measurement technique, we determine the position and size of the XUV foci as a function of harmonic order. We show that the focus properties vary with harmonic order and the generation conditions. Simulations, based on a classical description of the harmonic dipole phase and assuming that the individual harmonics can be described as Gaussian beams, reproduce the experimental behavior. We discuss how the generation geometry affects the intensity and duration of the focused attosecond pulses.

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33

Nicolau, Artur. "Radial behaviour of Bloch Harmonic functions and their area function." Indiana University Mathematics Journal 48, no. 4 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1662.

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34

Eriksson, Sirkka-Liisa, Marko Kotilainen, and Visa Latvala. "Hyperbolic Harmonic Functions: Weak Approach with Applications in Function Spaces." Advances in Applied Clifford Algebras 17, no. 3 (May 29, 2007): 425–36. http://dx.doi.org/10.1007/s00006-007-0043-x.

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35

MacGillivray, John, and Victor Sparrow. "Greens function modified spherical harmonic analysis." Journal of the Acoustical Society of America 108, no. 5 (November 2000): 2593. http://dx.doi.org/10.1121/1.4743644.

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36

Ershov, A. A. "Mixed problem for a harmonic function." Computational Mathematics and Mathematical Physics 53, no. 7 (July 2013): 908–19. http://dx.doi.org/10.1134/s0965542513070087.

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37

Fang, Shao C., and Santosh S. Venkatesh. "A Threshold Function for Harmonic Update." SIAM Journal on Discrete Mathematics 10, no. 3 (August 1997): 482–98. http://dx.doi.org/10.1137/s0895480195283701.

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38

Weiling, Peng. "Hyperbolic Harmonic Function in Minkowski Space." Advances in Applied Clifford Algebras 17, no. 2 (December 22, 2006): 273–79. http://dx.doi.org/10.1007/s00006-006-0012-9.

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39

Bernasconi, A. "Harmonic analysis and Boolean function complexity." Calcolo 35, no. 3 (November 1, 1998): 149–86. http://dx.doi.org/10.1007/s100920050014.

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40

DRAGOVICH, BRANKO. "ADELIC HARMONIC OSCILLATOR." International Journal of Modern Physics A 10, no. 16 (June 30, 1995): 2349–65. http://dx.doi.org/10.1142/s0217751x95001145.

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Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of the simplest vacuum state leads to the well-known functional relation for the Riemann zeta function. Some expectation values are calculated. The existence of adelic matter at very high energies is suggested.

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41

Claessens, S. J. "Spherical harmonic analysis of a harmonic function given on a spheroid." Geophysical Journal International 206, no. 1 (April 4, 2016): 142–51. http://dx.doi.org/10.1093/gji/ggw126.

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42

Nazir, Refdinal, Krismadinata Krismadinata, and Rizka Amalia. "The Camparison of Harmonic Distortion Self-Excited Induction Generator with Isolated Synchronous Generator under Non-linear Loads." International Journal of Power Electronics and Drive Systems (IJPEDS) 6, no. 4 (December 1, 2015): 759. http://dx.doi.org/10.11591/ijpeds.v6.i4.pp759-771.

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In this paper, the harmonic distortion for Self-Excited Induction Generator (SEIG) and an isolated synchronous generator (ISG) under non-linear load during steady state conditions are analyzed. The voltage and current harmonics distortion for both generators are calculated using the transfer function method in frequency domain for SEIG and phasor diagram method for ISG. This analysis is done independently one by one component for all harmonic components appear. The analysis results for both generators are verified to the laboratory test results. For loading with the same non-linear load to both generators, the harmonics distortion on the stator windings of SEIG was smaller than compare ISG. In addition, the harmonic distortion effects on other loads connected to PCC point of SEIG was lower than the other loads connected to ISG.

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SHOJAEI, M. R., A. A. RAJABI, and H. HASANABADI. "HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE." International Journal of Modern Physics E 17, no. 06 (June 2008): 1125–30. http://dx.doi.org/10.1142/s0218301308010398.

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In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

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Kumar, Devendra. "Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3." gmj 15, no. 1 (March 2008): 99–110. http://dx.doi.org/10.1515/gmj.2008.99.

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Abstract We study the growth of functions which are harmonic in any number of variables. The results are expressed in terms of spherical harmonic coefficients as well as by the approximation error of the harmonic function with (𝑝, 𝑞)-growth.

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Armitage, D. H., and C. S. Nelson. "A harmonic quadrature formula characterizing open strips." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 1 (January 1993): 147–51. http://dx.doi.org/10.1017/s0305004100075836.

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Let γn denote n-dimensional Lebesgue measure. It follows easily from the well-known volume mean value property of harmonic functions that if h is an integrable harmonic function on an open ball B of centre ξ0 in ℝn, where n ≥ 2, thenA converse of this result is due to Kuran [8]: if D is an open subset of ℝn such that γn(D) < + ∞ and if there exists a point ξo∈D such thatfor every integrable harmonic function h on D, then D is a ball of centre ξ0. Armitage and Goldstein [2], theorem 1, showed that the same conclusion holds under the weaker hypothesis that (1·2) holds for all positive integrable harmonic functions h on D.

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Zygarlicki, Jarosław, and Janusz Mroczka. "Method of testing and correcting signal amplifiers’ transfer function using prony analysis." Metrology and Measurement Systems 19, no. 3 (October 1, 2012): 489–98. http://dx.doi.org/10.2478/v10178-012-0042-7.

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Abstract This article presents a way of analyzing the transfer function of electronic signal amplifiers. It also describes the possibility of using signal precorrection which improves the parasitic harmonics in the THD (Total Harmonic Distortion) of the amplified signal by correcting linearity of the tested amplifier’s transfer function. The proposed method of analyzing and presenting the transfer function allows to diagnose the causes of generating parasitic harmonics, what makes it a useful tool when designing low distortion amplifier systems, such as e.g. amplifiers in measurement systems. The presented THD correction can be used in e.g. amplifier systems that cooperate with arbitrary generators.

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WU, YIPENG, ZHILONG CHEN, XIA ZHANG, and XUDONG ZHAO. "MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET." Fractals 28, no. 05 (August 2020): 2050077. http://dx.doi.org/10.1142/s0218348x20500772.

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Harmonic functions possess the mean value property, that is, the value of the function at any point is equal to the average value of the function in a domain that contain this point. It is a very attractive problem to look for analogous results in the fractal context. In this paper, we establish a similar results of the mean value property for the harmonic functions on the higher-dimensional Sierpinski gasket.

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Noor, Muhammad, Khalida Noor, and Sabah Iftikhar. "Integral inequalities for differentiable p-harmonic convex functions." Filomat 31, no. 20 (2017): 6575–84. http://dx.doi.org/10.2298/fil1720575n.

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In this paper, we consider a new class of harmonic convex functions, which is called p-harmonic convex function. Several new Hermite-Hadamard, midpoint, Trapezoidal and Simpson type inequalities for functions whose derivatives in absolute value are p-harmonic convex are obtained. Some special cases are discussed. The ideas and techniques of this paper may stimulate further research.

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Noor, M. A., K. I. Noor, and S. Iftikhar. "Some inequalities for strongly $(p,h)$-harmonic convex functions." Carpathian Mathematical Publications 11, no. 1 (June 30, 2019): 119–35. http://dx.doi.org/10.15330/cmp.11.1.119-135.

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In this paper, we show that harmonic convex functions $f$ is strongly $(p, h)$-harmonic convex functions if and only if it can be decomposed as $g(x) = f(x) - c (\frac{1}{x^p})^2,$ where $g(x)$ is $(p, h)$-harmonic convex function. We obtain some new estimates class of strongly $(p, h)$-harmonic convex functions involving hypergeometric and beta functions. As applications of our results, several important special cases are discussed. We also introduce a new class of harmonic convex functions, which is called strongly $(p, h)$-harmonic $\log$-convex functions. Some new Hermite-Hadamard type inequalities for strongly $(p, h)$-harmonic $log$-convex functions are obtained. These results can be viewed as important refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

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Tian, Mingxing, Yaomin Wang, and Jun Li. "Comprehensive Harmonic Responsibility Calculation Based on Different Weighting Methods." Energies 12, no. 23 (November 22, 2019): 4449. http://dx.doi.org/10.3390/en12234449.

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Dividing the responsibility of harmonics between customer and utility sides is necessary to improve the objectivity, rationality, and scientificalness of power measurement and power quality evaluation. On the basis of expert experience and customer needs and considering the background harmonic fluctuation, this study proposes two reasonable conditions to evaluate harmonic responsibility. At the same time, the reference index of harmonic responsibility calculation and the problem of different frequency harmonics are considered in the comprehensive calculation. On the basis of the IEEE Std. 1459–2010 power theory, the index set of harmonic responsibility is established, and several common subjective and objective weighting methods are used to weigh each index. On the basis of optimization theory, an optimization model is established by constructing a Lagrange function in finding the condition extremum to unify the subjective and objective information. Finally, the calculation method is verified by a Norton equivalent model, and the harmonic responsibility of each index is calculated by the harmonic current vector method; thus, calculating the actual impedance of customer and utility sides is unnecessary, making the calculation simple and effective. Results of the comparative analysis show that the comprehensive evaluation method of harmonic responsibility with the combinatorial weighting method can not only meet the different needs of different groups for harmonic indicators but also reflect the background harmonic fluctuations sensitively. In this manner, the subjective and objective information are unified, and the shortcomings of a single weighting method are overcome. Hence, the evaluation results are accurate, practical, and reasonable.

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