Search results for "Distortion"
showing 10 items of 309 documents
Assessing energy forecasting inaccuracy by simultaneously considering temporal and absolute errors
2017
Abstract Recent years have seen a growing trend in wind and solar energy generation globally and it is expected that an important percentage of total energy production comes from these energy sources. However, they present inherent variability that implies fluctuations in energy generation that are difficult to forecast. Thus, forecasting errors have a considerable role in the impacts and costs of renewable energy integration, management, and commercialization. This study presents an important advance in the task of analyzing prediction models, in particular, in the timing component of prediction error, which improves previous pioneering results. A new method to match time series is defined…
A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group
2017
We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group $\mathbb{H}_1$. Several auxiliary properties of quasiconformal mappings between subdomains of $\mathbb{H}_1$ are proven, including distortion of balls estimates and local BMO-estimates for the logarithm of the Jacobian of a quasiconformal mapping. Applications of the Koebe theorem include diameter bounds for images of curves, comparison of integrals of the average derivative and the operator norm of the horizontal differential, as well as the study of quasiconformal densities and metrics in domains in $\mathbb{H}_1$. The theorems are discussed for…
Mappings of finite distortion: the degree of regularity
2005
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)⩾1 be a measurable function defined on a domain Ω⊂Rn,n⩾2, and such that exp(βK(x))∈Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|n⩽K(x)J(x,f) for a.e. x∈Ω and such that the Jacobian determinant J(x,f) is locally in L1log−c1(n)βL. Then automatically J(x,f) is locally in L1logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite disto…
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
2019
AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.
Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings
2010
Abstract We investigate how the integrability of the derivatives of Orlicz–Sobolev mappings defined on open subsets of R n affect the sizes of the images of sets of Hausdorff dimension less than n. We measure the sizes of the image sets in terms of generalized Hausdorff measures.
Mappings of finite distortion: The sharp modulus of continuity
2003
We establish an essentially sharp modulus of continuity for mappings of subexponentially integrable distortion.
Introducing the Temporal Distortion Index to perform a bidimensional analysis of renewable energy forecast
2016
Abstract Wind has been the largest contributor to the growth of renewal energy during the early 21st century. However, the natural uncertainty that arises in assessing the wind resource implies the occurrence of wind power forecasting errors which perform a considerable role in the impacts and costs in the wind energy integration and its commercialization. The main goal of this paper is to provide a deeper insight in the analysis of timing errors which leads to the proposal of a new methodology for its control and measure. A new methodology, based on Dynamic Time Warping, is proposed to be considered in the estimation of accuracy as attribute of forecast quality. A new dissimilarity measure…
A low cost and easy re-configurable instrument for power quality survey
2004
In this document the development of a low cost and user friendly PC-based instrument for power quality measurement is proposed, according to IEC 61000-4-7 and standard IEC 61000-4-30. It is an easily re-configurable instrument able to measure harmonics, interharmonics and amplitude disturbances and supply unbalance. In order to verify its accuracy, the instrument has been tested according standard test procedures, by means of a built-up calibration test bench.
On the methodologies for the calibration of static electricity meters in the presence of harmonic distortion
2010
This paper is focused on the problems related to the calibration of static electricity meters with nonsinusoidal test waveforms. This is an up-to-date issue since the harmonic distortion levels are ever increasing, especially in low-voltage power systems, and in such conditions the performances of the modern static electricity meters can be negatively affected, depending on the implemented measurement algorithm. Thus it is important to test the meters with nonsinusoidal waveforms. The paper analyzes the problems related to both the choice of the test signals to be used for calibration and the implemented metric, with a particular focus on the reactive energy meters. The analysis is supporte…
Measurement Uncertainty of Harmonic Emission Indicators based on IEEE Std. 1459-2010
2020
The study presented in this paper is aimed at analyzing the measurement uncertainty impact on the evaluation of some power ratio parameters for harmonic emissions assessment based on IEEE Std. 1459-2010 apparent power decomposition. In addition to power factors for line utilization and harmonic pollution levels evaluation defined in the Standard, the study covers also some new parameters, which have been introduced by the authors as IEEE Std. 1459-2010 power quantities ratios. The measurement of the aforesaid parameters is implemented on a PC-based wattmeter, in order to investigate the measurement uncertainty impact on the evaluation of the power ratios. The obtained results show that, in …