Non-uniform dependence on initial data for the generalized Degasperis–Procesi equation on the line

2016 ◽  
Vol 27 (03) ◽  
pp. 1650026
Author(s):  
Yanggeng Fu ◽  
Zanping Yu ◽  
Jianhe Shen
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
High Frequency ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Solution Map ◽  
High Frequency Part ◽  
Uniformly Continuous

In this paper, we show that the solution map of the generalized Degasperis–Procesi (gDP) equation is not uniformly continuous in Sobolev spaces [Formula: see text] for [Formula: see text]. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part. It also exploits the fact that the gDP equation conserves a quantity which is equivalent to the [Formula: see text] norm.

Dynamic relation between global Islamic and conventional sectoral stock and bonds indexes

2020 ◽  
Vol 07 (02) ◽  
pp. 2050006
Author(s):  
Sukriye Tuysuz
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Stock Index ◽  
High Frequency Part ◽  
Dynamic Relation ◽  
The Relationship

This paper examines the relationship between 10 Global sectoral conventional and Islamic assets. For each sector, a conventional, an Islamic stock index and a bond are retained. The analyzed relations are done by taking into account diverse investment horizons by using MODWT and GARCH-DCC-type models. Our results indicate that adding bond indexes into a portfolio composed with conventional stock or Islamic stock is efficient. As for the correlations between conventional and Islamic sectoral indexes, they depend on the sector. Relations between returns of securities are quite similar to the relations between high-frequency part of these series and are very volatile at low frequency.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter out the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain “resolvable condition”, a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered out by the microscope, it is still possible to extract the full information from the low frequency part. On the basis of the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extracts the full information of the sample’s structure directly from the diffraction-blurred image, while the other extracts it directly from part of the observed image’s spectrum (e.g., low frequency part). Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Asymptotic profiles for damped plate equations with rotational inertia terms

2020 ◽  
Vol 17 (03) ◽  
pp. 569-589
Author(s):  
Tomonori Fukushima ◽  
Ryo Ikehata ◽  
Hironori Michihisa
Keyword(s):  
Initial Data ◽  
High Frequency ◽  
Wave Equations ◽  
Splitting Method ◽  
Low Frequency ◽  
Rotational Inertia ◽  
Low Regularity ◽  
Frictional Damping ◽  
The Cauchy Problem ◽  
Plate Equations

We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We derive asymptotic profiles of the solution in [Formula: see text]-sense as [Formula: see text] in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit formula of the solution (high-frequency estimates) and the method due to [R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differential Equations 257 (2014) 2159–2177.] (low-frequency estimates). In this paper, we will introduce a new threshold [Formula: see text] on the regularity of the initial data that divides the property of the corresponding solution to our problem into two parts: one is wave-like, and the other is parabolic-like.

Noise Test and Analysis of Automobile Engine

2013 ◽  
Vol 307 ◽  
pp. 196-199 ◽  
Author(s):  
Yan Liu ◽  
Yan Bin Jia ◽  
Xiao Juan Zhang ◽  
Zong Cai Liu ◽  
Yong Chao Ren ◽  
...  
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Sound Insulation ◽  
Engine Noise ◽  
High Frequency Part ◽  
Speed Measure ◽  
Dash Panel ◽  
Noise Frequency ◽  
Noise Test ◽  
Analysis Engine

To test different car’s noise in a semi-anechoic room with different engine’s speed, measure and analysis engine noise’s characteristics and the dash panel’s sound insulation quantity. The conclusion is that：the engine noise gets bigger 10 dB(A) when engine speeds up every 1000 r/min; engine noise’s frequency mainly distributed in 1600 ~ 4000 Hz; peak part concentrates in the range 100 ~ 400 Hz; engine noise has no direct relation to engine’s displacement; cab noise frequency mainly concentrated in the range 250 ~ 630 Hz and the peaks exist in the intermediate and low frequency part, the high frequency part attenuates obviously which show the car’s dash panel has a good noise insulation and absorption effect in the high frequency part but not too ideal at the intermediate and low frequency especially in the range 250 ~ 630 Hz. These results have high practical value for the design of the automotive to decline noise and vibration.

scholarly journals DECAY OF NONLOCALITY DUE TO ADIABATIC AND QUANTUM NOISE IN THE SOLID STATE

2011 ◽  
Vol 09 (supp01) ◽  
pp. 63-71 ◽  
Author(s):  
B. BELLOMO ◽  
G. COMPAGNO ◽  
A. D'ARRIGO ◽  
G. FALCI ◽  
R. LO FRANCO ◽  
...  
Keyword(s):  
Quantitative Analysis ◽  
Solid State ◽  
High Frequency ◽  
Quantum Noise ◽  
Bell Inequality ◽  
Low Frequency ◽  
Quantum Nonlocality ◽  
High Frequency Part ◽  
Nonlocal Correlations

We study the decay of quantum nonlocality, identified by the violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, for two noninteracting Josephson qubits subject to independent baths with broadband spectra typical of solid state nanodevices. The bath noise can be separated in an adiabatic (low-frequency) and in a quantum (high-frequency) part. We point out the qualitative different effects on quantum nonlocal correlations induced by adiabatic and quantum noise. A quantitative analysis is performed for typical noise figures in Josephson systems. Finally we compare, for this system, the dynamics of nonlocal correlations and of entanglement.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain condition (isolated lighting or named separated lighting), a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered by the microscope, it is still possible to extract the full information from the low frequency part. Based on the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extract the full information of the sample’s structure directly from the diffraction-blurred image, while the other extract it directly from part of the observed image’s spectrum, e.g., low frequency part. Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Full Information ◽  
Structure Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represent its profile, while the high frequency part represent its details. Conventional light microscopes filter the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain condition (isolated lighting or named separated lighting), a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered by the microscope, it is still possible to extract the full information from the low frequency part. Based on the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extract the full information of the sample’s structure information directly from the diffraction-blurred image, while the other extract it directly from part of the observed image’s spectrum, e.g., low frequency part. Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals An Iterative Hybrid Harmonics Detection Method Based on Discrete Wavelet Transform and Bartlett–Hann Window

2020 ◽  
Vol 10 (11) ◽  
pp. 3922 ◽  
Author(s):  
Guishuo Wang ◽  
Xiaoli Wang ◽  
Chen Zhao
Keyword(s):  
Wavelet Transform ◽  
Steady State ◽  
Discrete Wavelet Transform ◽  
High Frequency ◽  
Detection Method ◽  
Low Frequency ◽  
Discrete Wavelet ◽  
Detection Accuracy ◽  
Harmonic Detection ◽  
High Frequency Part

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.

scholarly journals Nonuniform Dependence on Initial Data of a Periodic Camassa-Holm System

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaohuan Wang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Solution Map ◽  
Two Component ◽  
The Cauchy Problem ◽  
Uniformly Continuous

This paper is concerned with some properties of a periodic two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous inHs(𝕊),s>5/2.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter out the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain “resolvable condition”, a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered out by the microscope, it is still possible to extract the full information from the low frequency part. On the basis of the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extracts the full information of the sample’s structure directly from the diffraction-blurred image, while the other extracts it directly from part of the observed image’s spectrum (e.g., low frequency part). Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

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