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fourier transform of anisotropic mixed-norm Hardy spaces

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Frontiers of Mathematics in China 2021年第1期16卷 119-139页

作者： Long HUANG Der-Chen CHANG Dachun YANG Laboratory of Mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China Department of Mathematics and Statistics Georgetown UniversityWashingtonDC 20057USA Graduate Institute of Business Adminstration College of ManagementFu Jen Catholic UniversityNew Teipei City 242China

Let a:=(a1,…,an)∈[1,∞)n,p:=(p1,…,pn)∈(0,1]n,Hpa(R^(n))be the anisotropic mixed-norm Hardy space associated with adefined via the radial maximal function,and let f belong to the Hardy space Hpa(R^(n)).In this article,we show that the fourier transform fcoincides with a continuous function g onℝn in the sense of tempered distributions and,moreover,this continuous function g,multiplied by a step function associated with a,can be pointwisely controlled by a constant multiple of the Hardy space norm of *** proofs are achieved via the known atomic characterization of Hpa(R^(n))and the establishment of two uniform estimates on anisotropic mixed-norm *** applications,we also conclude a higher order convergence of the continuous function gat the ***,a variant of the Hardy-Littlewood inequality in the anisotropic mixed-norm Hardy space setting is also *** these results are a natural generalization of the well-known corresponding conclusions of the classical Hardy spaces Hp(R^(n))with p∈0,1],and are even new for isotropic mixed-norm Hardy spaces on∈n.

关键词： Anisotropic(mixed-norm)Hardy space fourier transform Hardy-Littlewood inequality

Estimation of particle depth from two defocused images using the fourier transform

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Particuology 2020年第2期18卷 48-54页

作者： Wu Zhou Xu Luo Benting Chen Yukun Zhang Xiaoshu Cai School of Energy and Power Engineering University of Shanghai for Science and TechnologyShanghai 200093China Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering Shanghai 200093China

Depth from defocus is one technology for depth *** estimate particle depth information from two defocused images captured simultaneously by two coaxial cameras with different imaging *** images are processed with the fourier transform to obtain the characteristic parameter(i.e.,the standard deviation of the relative blur kernel of these two defocused images).First,we theoretically analyze the functional relationship between the object depth and the standard deviation or variation of the relative blur ***,we verify the relationship *** analyze the influence of particle size,window size and image noise on the calibration curves using both numerical simulations and *** obtain the depth range and accuracy of this measurement system *** the verification experiments,we use a sample of glass microbeads and the irregularly-shaped dust particles on a microscope *** of these experiments present a suitable depth measurement ***,we apply the measuring system to the depth estimation of drops from a small anti-fogging *** results show that our system and image processing algorithm are robust for different types of particles,facilitating the in-line three-dimensional positioning of particles.

关键词： Depth from two defocused images fourier transform Standard deviation of relative blur kernel Drops depth measurement Sensitivity and accuracy analysis

Optical scaled Fresnel-fourier transform obtained via intermediate coordinate-momentum representation

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Chinese Physics B 2010年第1期19卷 66-71页

作者：李迟生罗汉文 Department of Electronic Engineering Shanghai Jiao Tong University

Using the intermediate coordinate-momentum representation {x}s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator F （r, s） and the fourier transform operator F- by decomposing U. We also find that the matrix element s,r 〈x｜U｜f） just corresponds to an optical scaled Presnel fourier transform.

关键词： Fresnel transform Fresnel operator fourier transform intermediate coordinatemomentum representation

Ghost imaging-based optical cryptosystem for multiple images using integral property of the fourier transform

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Chinese Physics B 2021年第12期30卷 441-449页

作者： Yi Kang Leihong Zhang Hualong Ye Dawei Zhang Songlin Zhuang University of Shanghai for Science and Technology Shanghai 200093China

A novel ghost imaging-based optical cryptosystem for multiple images using the integral property of the fourier transform is *** from other multiple-image encryption schemes,we mainly construct the modulation patterns related to the plaintext images to realize the encrypted transmission of multiple *** encryption process,the first image is encrypted by the ghost imaging encryption scheme,and the intensity sequence obtained by the bucket detector is used as the *** modulation patterns of other images are constructed by using the integral property of the fourier transform and used as the ***,the ciphertext and keys are transmitted to the receiver to complete the encryption *** decryption,the receiver uses different keys to decrypt the ciphertext and gets different plaintext images,and decrypted images have no image aliasing *** and simulations verify the feasibility,security,and robustness of the proposed *** scheme has high scalability and broad application prospect,which provides a new idea for optical information encryption.

关键词： ghost imaging image encryption fourier transform

THE fourier transform FOR HOMOGENEOUS VECTOR BUNDLES OVER QUATERNION UNIT DISK

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Chinese Annals of Mathematics,Series B 2000年第3期21卷 343-350页

作者： LIU JIANMING (School of Mathematical Sciences, Peking University, Beijing 100871. China.) E-mail: liujm@math. *** or liujm@sxx0.math.pku. *** School of Mathematical Sciences Peking University Beijing 100871 China

The fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.

关键词： fourier transform Homogeneous vector bundles Quaternion unit disk

Arithmetic and fourier transform for the PYXIS multi-resolution digital Earth model

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International Journal of Digital Earth 2009年第1期2卷 59-79页

作者： A.Vince X.Zheng Department of Mathematics University of FloridaGainesvilleFL 32611-8105USA Department of Arts and Sciences Voorhees CollegeDenmarkSC 29042USA

This paper investigates a multi-resolution digital Earth model called PYXIS,which was developed by PYXIS Innovation *** PYXIS hexagonal grids employ an efficient hierarchical labeling scheme for addressing *** provide a recursive definition of the PYXIS grids,a systematic approach to the labeling,an algorithm to add PYXIS labels,and a discussion of the discrete fourier transform on PYXIS grids.

关键词： discrete grid digital Earth fourier transform

A Boundary Meshless Method for Solving Heat Transfer Problems Using the fourier transform

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Advances in Applied Mathematics and Mechanics 2011年第5期3卷 572-585页

作者： A.Tadeu C.S.Chen J.Antonio Nuno Simoes Department of Civil Engineering Faculty of Sciences and TechnologyUniversity of CoimbraPolo II-Pinhal de Marrocos3030-290 CoimbraPortugal Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA

fourier transform is applied to remove the time-dependent variable in the diffusion *** non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation,which is solved by the method of fundamental solutions and the method of particular *** particular solution of Helmholtz equation is available as shown in[4,15].The approximate solution in frequency domain is then inverted numerically using the inverse fourier transform *** frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static *** numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

关键词： Transient heat transfer meshless methods method of particular solutions method of fundamental solutions frequency domain fourier transform

A DISTRIBUTION SPACE FOR fourier transform

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Applied Mathematics(A Journal of Chinese Universities) 2007年第2期22卷 229-234页

作者： Zhou Chaoying Yang Lihua Huang Daren School of Mathematics and Computing Science Sun Yat-sen University Guangzhou 510275 China

A space Df is constructed and some characterizations of space Df are given. It is shown that the classical fourier transform is extended to the distribution space Df, which can be embedded into the Schwartz distribution space D＇ continuously. It is also shown that D＇f is the biggest embedded subspace of D on which the extended fourier transform, f, is a homeomorphism of D＇f onto itself.

关键词： fourier transform distribution conjugate operator

fourier transform Moire Deflectometry for Measuring the 3-D Temperature Field

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Chinese Journal of Lasers 2000年第1期 35-41页

作者： MA Li WANG Ming LIU Song QI Xiaopin (Basic Department, Nanchang University, Nanchang 330029, China)

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关键词： fourier transform Moire deflectometry 3 D temperature field