The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Pierre Gilles Lemarié-rieusset - One of the best experts on this subject based on the ideXlab platform.
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Euler Equations and Real Harmonic Analysis
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Pierre Gilles Lemarié-rieussetAbstract:We re-prove various existence theorems of regular solutions for the Euler equations, using classical tools of real Harmonic Analysis such as singular integrals, atomic decompositions and maximal functions.
Milton Ferreira - One of the best experts on this subject based on the ideXlab platform.
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Harmonic Analysis on the Möbius Gyrogroup
Journal of Fourier Analysis and Applications, 2015Co-Authors: Milton FerreiraAbstract:In this paper we propose to develop Harmonic Analysis on the Poincaré ball $${{\mathbb {B}}_{t}^{n}}$$ B t n , a model of the $$n$$ n -dimensional real hyperbolic space. The Poincaré ball $${{\mathbb {B}}_{t}^{n}}$$ B t n is the open ball of the Euclidean $$n$$ n -space $$\mathbb {R}^n$$ R n with radius $$t >0$$ t > 0 , centered at the origin of $$\mathbb {R}^n$$ R n and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in $$\mathbb {R}^n.$$ R n . For any $$t>0$$ t > 0 and an arbitrary parameter $$\sigma \in \mathbb {R}$$ σ ∈ R we study the $$(\sigma ,t)$$ ( σ , t ) -translation, the $$(\sigma ,t)$$ ( σ , t ) -convolution, the eigenfunctions of the $$(\sigma ,t)$$ ( σ , t ) -Laplace–Beltrami operator, the $$(\sigma ,t)$$ ( σ , t ) -Helgason Fourier transform, its inverse transform and the associated Plancherel’s Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic Harmonic Analysis. Moreover, when $$t \rightarrow +\infty $$ t → + ∞ the resulting hyperbolic Harmonic Analysis on $${{\mathbb {B}}_{t}^{n}}$$ B t n tends to the standard Euclidean Harmonic Analysis on $$\mathbb {R}^n,$$ R n , thus unifying hyperbolic and Euclidean Harmonic Analysis. As an application we construct diffusive wavelets on $${{\mathbb {B}}_{t}^{n}}$$ B t n .
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Harmonic Analysis on the Möbius Gyrogroup
Journal of Fourier Analysis and Applications, 2014Co-Authors: Milton FerreiraAbstract:In this paper we propose to develop Harmonic Analysis on the Poincare ball \({{\mathbb {B}}_{t}^{n}}\), a model of the \(n\)-dimensional real hyperbolic space. The Poincare ball \({{\mathbb {B}}_{t}^{n}}\) is the open ball of the Euclidean \(n\)-space \(\mathbb {R}^n\) with radius \(t >0\), centered at the origin of \(\mathbb {R}^n\) and equipped with Mobius addition, thus forming a Mobius gyrogroup where Mobius addition in the ball plays the role of vector addition in \(\mathbb {R}^n.\) For any \(t>0\) and an arbitrary parameter \(\sigma \in \mathbb {R}\) we study the \((\sigma ,t)\)-translation, the \((\sigma ,t)\)-convolution, the eigenfunctions of the \((\sigma ,t)\)-Laplace–Beltrami operator, the \((\sigma ,t)\)-Helgason Fourier transform, its inverse transform and the associated Plancherel’s Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic Harmonic Analysis. Moreover, when \(t \rightarrow +\infty \) the resulting hyperbolic Harmonic Analysis on \({{\mathbb {B}}_{t}^{n}}\) tends to the standard Euclidean Harmonic Analysis on \(\mathbb {R}^n,\) thus unifying hyperbolic and Euclidean Harmonic Analysis. As an application we construct diffusive wavelets on \({{\mathbb {B}}_{t}^{n}}\).
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Harmonic Analysis on the Einstein Gyrogroup
2014Co-Authors: Milton FerreiraAbstract:In this paper we study Harmonic Analysis on the Einstein gyrogroup of the open ball of R$^n$, $n \in N,$ centered at the origin and with arbitrary radius $t \in R^+,$ associated to the generalised Laplace-Beltrami operator $$ L_{\sigma,t} = \disp \left( 1 - \frac{\|x\|^2}{t^2} \right) \!\left( \Delta - \sum_{i,j=1}^n \frac{x_i x_j}{t^2} \frac{\partial^2}{\partial x_i \partial x_j} - \frac{\kappa}{t^2} \sum_{i=1}^n x_i \frac{\partial}{\partial x_i} + \frac{\kappa(2-\kappa)}{4t^2} \right)$$ where $\kappa=n+\sigma$ and $\sigma \in {\mathbb R}$ is an arbitrary parameter. The generalised Harmonic Analysis for $L_{\sigma,t}$ gives rise to the $(\sigma,t)$-translation, the $(\sigma,t)$-convolution, the $(\sigma,t)$-spherical Fourier transform, the $(\sigma,t)$-Poisson transform, the $(\sigma,t)$-Helgason Fourier transform, its inverse transform and Plancherel's Theorem. In the limit of large $t,$ $t \rightarrow +\infty,$ the resulting hyperbolic Harmonic Analysis tends to the standard Euclidean Harmonic Analysis on $R^n,$ thus unifying hyperbolic and Euclidean Harmonic Analysis
Wang Junhua - One of the best experts on this subject based on the ideXlab platform.
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Harmonic Analysis based on time domain mutual-multiplication window
Journal of Modern Power Systems and Clean Energy, 2016Co-Authors: Tan Tianyuan, Chen Wenjuan, Liu Kaipei, Xiong Niu, Junmin Zhang, Wang JunhuaAbstract:The signal spectral leakage and fence effect are prone to take place during the power Harmonic Analysis by fast fourier transform (FFT) under asynchronous sampling. The inhibiting ability of classical window functions is restricted by side-lobe behaviors. A new type window function called time domain mutual-multiplication window, is obtained by multiplication operation of several window functions. A novel approach of Harmonic Analysis is developed through analyzing performances of main-lobe and side-lobe of the new window. Simulation results show that the time domain mutual-multiplication window can significantly suppress frequency spectral leakage and improve the accuracy of Harmonic parameter estimation.
T.t. Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Parametric Harmonic Analysis
IEE Proceedings - Generation Transmission and Distribution, 1997Co-Authors: T.t. NguyenAbstract:Harmonics in power systems is now a subject of wide ramifications. One particular aspect is that of capturing Harmonic data at selected locations in a power network and processing it to identify Harmonics and to quantify their magnitudes and arguments. Circumstances are encountered in practice for which the discrete Fourier transform (DFT) cannot be relied on to achieve valid Harmonic component identification. These are where there are subHarmonics, Harmonics which are not integer multiples of the supply frequency, and where two or more Harmonics have only small frequency separations between them. The paper reports a new procedure which fulfils the requirements of practical Harmonic Analysis. It avoids altogether the limitations of the DFT algorithm and is based on the nomination of a distorted waveform model expressed in terms of a sum of sinusoidal functions. Model parameters are the frequencies, magnitudes and arguments of the Harmonics in the waveform it represents. The error between this model waveform and the actual one represented in captured form is minimised. At the minimum, the parameters of the model are those of the waveform for which Harmonic Analysis is required. A key advance in this parametric form of Analysis is that of a partitioning of the data for the waveform to be analysed into a training set and a test set. This partitioned form of generalised parametric Harmonic Analysis is thus developed. Key concepts are clarified via a numerical example to illustrate how this approach can excel for the Harmonic Analysis in power systems.
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Data partitioning in parametric Harmonic Analysis
Electronics Letters, 1996Co-Authors: T.t. NguyenAbstract:The key feature of the advance in parametric Harmonic Analysis reported that of partitioning the data series into a training set and a test set. Test errors are monitored in successive training error minimisations. The Analysis procedure achieves high resolution between frequency components, and minimises the data window required in Harmonic Analysis.
Li Peng - One of the best experts on this subject based on the ideXlab platform.
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Power System Harmonic Analysis Based on RPROP ANNs
Journal of Zhejiang Water Conservancy and Hydropower College, 2011Co-Authors: Li PengAbstract:For improving the speed and accuracy of Harmonic Analysis,a Harmonic Analysis method based on RPROP neural network is proposed.Hanning-windowed interpolation Harmonic Analysis algorithm is used to obtain initial weight and bias values of ANNs(Artificial Neural Networks)and the network takes RPROP algorithm as a training algorithm derived number.Different from the BP(Back Propagation)algorithm,the algorithm adjusts the parameters of ANNs by sign information of first-order partial derived number,which avoids the influence of amplitude information of first-order partial derived number which is useless for parameters adjustment.In the meantime,the algorithm does not have the problem of parameters selection.Therefore,the convergence speed,accuracy and real-time performance of power system Harmonic Analysis can be improved.Finally,BP ANNs and RPROP ANNs are used to analyze signal,and the comparison of the results verifies the conclusion.
