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Applied Mathematics and Mechanics(English Edition) 2006年第6期27卷 781-792页

作者： Rajneesh Kumar Praveen Ailawalia Department of Mathematics Kurukshetra University KurukshetraHaryanaINDIA136119 Department of Applied Sciences Institute of Engineering and Emerging Technologies MakhnumajraBaddi Distt. SolanH.PINDIA173205

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.

关键词： time harmonic thermoelastic micropolar medium cubic symmetry microrotation fourier transform

Texture classification based on EMD and FFT

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第9期7卷 1516-1521页

作者： XIONG Chang-zhen XU Jun-yi ZOU Jian-cheng QI Dong-xu School of Information Science and Technology Sun Yat-sen University Guangzhou 510275 China Information Science School Guangdong University of Business Studies Guangzhou 510320 China College of Science North China University of Technology Beijing 100041 China

Empirical mode decomposition (EMD) is an adaptive and approximately orthogonal filtering process that reflects human’s visual mechanism of differentiating textures. In this paper, we present a modified 2D EMD algorithm using the FastRBF and an appropriate number of iterations in the shifting process (SP), then apply it to texture classification. Rotation-invariant texture feature vectors are extracted using auto-registration and circular regions of magnitude spectra of 2D fast fourier transform (FFT). In the experiments, we employ a Bayesion classifier to classify a set of 15 distinct natural textures selected from the Brodatz album. The experimental results, based on different testing datasets for images with different orientations, show the effectiveness of the proposed classification scheme.

关键词： Texture classification Empirical mode decomposition (EMD) fourier transform Auto-registration Rotationinvariant

BOUNDEDNESS OF THE CALDER´ON COMMUTATOR WITH A ROUGH KERNEL ON TRIEBEL-LIZORKIN SPACES

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Acta Mathematica Scientia 2023年第4期43卷 1618-1632页

作者：胡国恩刘洁 Center of Fundamental Science Huanghe Science and Technology UniversityZhengzhou 450063China

In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1

关键词： Calder´on commutator fourier transform Littlewood-Paley theory Calder´on reproducing formula

LAPLACE transformS FOR ANALYTIC FUNCTIONS IN TUBULAR DOMAINS

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Acta Mathematica Scientia 2021年第6期41卷 1938-1948页

作者： Guantie DENG Qian FU Hui CAO Laboratory of Mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing100875China

Assume that 0 详细信息

Assume that 0transform of some function f∈L(R^(n)).

关键词： Laplace transforms fourier transform tubular domain regular cone

Frame Wavelets with Compact Supports for L^2(R^n)

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Acta Mathematica Sinica,English Series 2007年第2期23卷 349-356页

作者： De Yun YANG Xing Wei ZHOU Zhu Zhi YUAN Department of Information Taishan University Department of Automation Nankai University Department of Mathematics and LPMC Nankai University

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.

关键词： fourier transform frame wavelet expansive matrix

Correction to the crustal thickness of the northwestern China using the data of seis-mic tomography

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Acta Seismologica Sinica(English Edition) 2005年第6期18卷 643-650,749页

作者：许萍傅容珊黄建平戴志阳查显杰 University of Science and Technology of China Hefei 230026 China

Considering the influence of the density anomaly of the crust and upper mantle on the gravity, we provide a new arithmetic to invert the crustal thickness. Applying the result of seismic tomography, we calculated the lateral density heterogeneity of the crust and upper mantle and the gravity anomalies caused by such lateral density heterogeneity, and then subtracted gravity anomalies caused by mentioned density anomalies from observational Bouguer anomalies, finally in view of the correction on the initial crustal thickness based on the hypothesis of isostasy, inverted the regional crustal thickness. Using the data of seismic tomography from XU et al, we inverted the Moho depth beneath northwestern China. It is shown that the gravity anomalies on the surface of the earth are -6 × 10-4 m/s2 - 3 × 10-4 m/s2. Compared with the result inverted directly using Bouguer anomalies, this method can bring correction of 6 km to the Moho depth. And this method make it further mature in theory and feasible in practice to invert the thickness of the crust using data of gravity and provide a new arithmetic for us to understand the conformation of the Moho.

关键词： seismic tomography fourier transform Bouguer anomalies Moho

General solutions to a class of time fractional partial differential equations

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Applied Mathematics and Mechanics(English Edition) 2010年第7期31卷 815-826页

作者：黄凤辉郭柏灵 Department of Mathematics School of SciencesSouth China University of Technology Institute of Applied Physics and Computational Mathematics

A class of time fractional partial differential equations is considered, which in- cludes a time fractional diffusion equation, a time fractional reaction-diffusion equation, a time fractional advection-diffusion equation, and their corresponding integer-order partial differential equations. The fundamental solutions to the Cauchy problem in a whole-space domain and the signaling problem in a half-space domain are obtained by using fourier- Laplace transforms and their inverse transforms. The appropriate structures of the Green functions are provided. On the other hand, the solutions in the form of a series to the initial and boundary value problems in a bounded-space domain are derived by the sine- Laplace or cosine-Laplace transforms. Two examples are presented to show applications of the present technique.

关键词： fractional differential equation Caputo fractional derivative Green function Laplace transform fourier transform sine (cosine) transform

An Application of BMO-type Space to Chemotaxis-fluid Equations

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1650-1666页

作者： Ming Hua YANG Yu Mei ZI Zun Wei FU Department of Mathematics Jiangxi University of Finance and EconomicsNanchang 330032P.R.China Department of Mathematics Linyi UniversityLinyi 276005P.R.China College of Information Technology The University of SuwonBongdameupHwaseong-siGyeonggi-do445-743Korea

We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional *** prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3),where Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3) is a subspace of bmo^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p) (R^(3))×(B˙_(q,∞)^(3/q) (R^(3))∩L^(∞)(R^(3))).Furthermore,we obtain that the system exists a unique global solution for any small initial data(u0,n0,c0)∈BMO^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p)(R^(3))×(B_(q,∞)^(3/q)(R^(3))∩L^(∞)(R^(3))).For the difference between these spaces and known ones,our results may be regarded as a new existence theorem on the system.

关键词： BMO-type space fourier transform Besov space Keller-Segel equation Navier-Stokes equation

L^p Boundedness for Parabolic Littlewood-Paley Operators with Rough Kernels Belonging to Block Spaces

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Acta Mathematica Sinica,English Series 2010年第2期26卷 277-286页

作者： Dong Xiang CHEN Shan Zhen LU School of Mathematics Beijing Normal University Beijing 100875 P. R. China and Department of Mathematics Jiangxi Normal University Nanchang 330022 P. R. China School of Mathematics Beijing Normal University Beijing 100875 P. R. China

This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved.

关键词： parabolic Littlewood-Paley operator fourier transform rough kernel block space

Analysis and Process of Music Signals to Generate Two-Dimensional Tabular Data and a New Music

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Computers, Materials & Continua 2020年第5期63卷 553-566页

作者： Oakyoung Han Jaehyoun Kim Sungkyun Software Education Institute Sungkyunkwan UniversitySeoul03063Korea Department of Computer Education Sungkyunkwan UniversitySeoul03063Korea

The processing of sound signals is significantly improved *** for sound signal processing focusing on music beyond speech area is getting attention due to the development of deep learning *** study is for analysis and process of music signals to generate tow-dimensional tabular data and a new *** analysis and process part,we represented normalized waveforms for each of input data via frequency domain *** we looked into shorted segment to see the difference wave pattern for different *** transform is applied to get spectrogram of the music *** is applied to represent the spectrogram based on the human ear instead of the distance on the frequency dimension,and the final spectrogram has been plotted by Mel *** generating part,we created two-dimensional tabular data for data *** the 2D data,any kind of analysis can be done since it has digit values for the music ***,we generated a new music by applying LSTM toward the song audience preferred *** the result,it has been proved that the created music showed the similar waveforms with the original *** study made a step forward for music signal *** this study expands further,it can find the pattern that listeners like so music can be generated within favorite singer’s voice in the way that the listener prefers.

关键词： Frequency domain signals spectrogram fourier transform filterbank long short-term memory