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Data inversion of multi-dimensional magnetic resonance in porous media

Magnetic Resonance Letters 2023年第2期3卷 127-139,I0004页

作者： Fangrong Zong Huabing Liu Ruiliang Bai Petrik Galvosas Schoolof Artificial Intelligence Beijing University of Post and TelecommunicationBeijing100876China Beijing Limecho Technology Co Ltd.Beijing102200China Interdisciplinary Institute of Neuroscience and Technology Zhejiang University School of MedicineHangzhou310020China MOE Frontier Science Centerfor Brain Science and Brain-machine Integration School of Brain Science and Brain MedicineZhejiang UniversityHangzhou310030China School of Chemical and Physical Sciences Victoria University of WellingtonWellington6140New Zealand MacDiarmid Institute for Advanced Materials Victoria University of WellingtonWellington6140New Zealand

Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular *** spectroscopy beyond one dimension allows the study of the correlation,exchange processes,and separation of overlapping spectral *** multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous *** from Fourier transform,methods have been developed for processing the multi-dimensional time-domain data,identifying the fluid components,and estimating pore surface permeability via joint relaxation and diffusion *** the resolution of spectroscopic signals with spatial encoding gradients,multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish *** in each voxel are usually expressed as multi-exponential decay,representing microstructures or environments along multiple pore *** separation of contributions from different environments is a common ill-posed problem,which can be resolved ***,the inversion methods and experimental parameters determine the resolution of multi-dimensional *** paper reviews the algorithms that have been proposed to process multidimensional MR datasets in different *** information at the microscopic level,such as tissue components,fluid types and food structures in multi-disciplinary sciences,could be revealed through multi-dimensional MR.

关键词： Multi-dimensional MR Data inversion Porous media Inverse Laplace transform fouriertransform

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A SEMI-ANALYTICAL METHOD FOR THE VIBRATION OF AND SOUND RADIATION FROM A TWO-DIMENTIONAL BEAM-STIFFENED PLATE

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Acta Mechanica Solida Sinica 2011年第3期24卷 231-240页

作者： Haian Zhou Xiaomlng Wang Yulin Mei School of Mechanical Engineering Dalian University of Technology Dalian 116024 China School of Automotive Engineering Dalian University of Technology Dalian 116024 China

A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners, which are assumed to be line forces. The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green＇s function and Fourier transform methods. Using the boundary conditions and space harmonic method, we establish the relationship between the stiffener forces and the vibration displacement of the plate. In this paper, the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement, which are calculated by using a numerical reduction technique. Finally, the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space. Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.

关键词： space harmonics sound radiation stiffened plate wave-number space fouriertransform

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Boundedness for a class of fractional integrals with a rough kernel related to block spaces

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Frontiers of Mathematics in China 2016年第1期11卷 173-187页

作者： Xiao YU Shanzhen LU Department of Mathematics Shangrao Normal University Shangrao 334001 China School of Mathematical Science Beijing Normal University Beijing 100875 China

We prove the boundedness of fractional integral with a rough kernel on Triebel-Lizorkin spaces, where the rough kernel belongs to the block space and does not need to satisfy any moment conditions on the unit sphere.

关键词： Fractional integral block space Triebel-Lizorkin space fouriertransform interpolation

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Multipliers on Vector-valued L^1-spaces for Hypergroups

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Acta Mathematica Sinica,English Series 2018年第7期34卷 1059-1073页

作者： R.SARMA N.Shravan KUMAR Vishvesh KUMAR Department of Mathematics Indian Institute of Technology Delhi

In this article, we extend the well known Wendel＇s theorem to the context of vector-valued L1-spaces on hypergroups. In this regard, various cases have been studied.

关键词： Vector-valued Ll-spaces hypergroups multipliers translation invariant operators fouriertransform

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Stability in the Shephard Problem for L_p-Projection of Convex Bodies

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Wuhan University Journal of Natural Sciences 2014年第4期19卷 283-288页

作者： LI Xinhong MA Tongyi College of Mathematics and Statistics Northwest Normal University College of Mathematics and Statistics Hexi University

In this article, we study the convex bodies associated with Lp-projections in the Brunn-Minkowski-Firey theory, and apply the Fourier analytic methods to prove the linear stability in the Shephard problem for Lp-proje... 详细信息

关键词： stability convex bodies Lp-projections fouriertransform

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