Fourier transforms of irregular mixed homogeneous hypersurface measures

Greenblatt, Michael

doi:10.1002/mana.201700017

Cited by 4 publications

(1 citation statement)

References 16 publications

(23 reference statements)

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“…e Fourier transform is a good solution for the problem [22]. e acceleration-time curves were transferred to amplitude-frequency curves (shown in Figure 17), and the natural frequency of specimen was obtained.…”

Section: Testing Process and Data Dealmentioning

confidence: 99%

Method Improvements of Testing Modulus of Soil Based on Free‐Vibration Column

Jin

Huang

Wang

et al. 2019

Advances in Civil Engineering

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It is difficult to directly measure the dynamic elastic modulus of soils when the strain is less than 10−4, though the dynamic shear modulus can be easily obtained by the free-vibration testing method. Some improvements were adapted to the traditional free-vibration column for measuring dynamic elastic modulus of soil precisely with lateral vibration in small strain (10−4∼10−6). Differing from the traditional lateral vibration theory, a new dynamic elastic modulus testing method based on bending vibration equation of cantilever beam was put forward based on the improved free-vibration column of GZZ-50. Firstly, some descriptions about calibration process of needed testing parameter (moment of inertia of drive board) were made, and then, Poisson’s ratio of standardized column was used to confirm the measured results. Four main improvements were applied, including the shape of drive board which made the bending vibration equation solved, laser displacement sensors for correcting specimen’s height parameter with uncontacted manner which can reduce the influence of specimen, a hoop with plug used to make the split mould be removed, and air duct used when installing drive board to increase the success rate of installing specimen. Finally, standard process of installing specimen was described, which can be used as reference of similar test.

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Section: Testing Process and Data Dealmentioning

confidence: 99%

Method Improvements of Testing Modulus of Soil Based on Free‐Vibration Column

Jin

Huang

Wang

et al. 2019

Advances in Civil Engineering

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$$L^p$$ L p Sobolev Regularity for a Class of Radon and Radon-Like Transforms of Various Codimension

Greenblatt

2018

J Fourier Anal Appl

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Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals

Greenblatt

2021

Math. Ann.

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In a well-known paper by Bruna, Nagel and Wainger [BNW], Fourier transform decay estimates were proved for smooth hypersurfaces of finite line type bounding a convex domain. In this paper, we generalize their results in the following ways. First, for a surface that is locally the graph of a convex real analytic function, we show that a natural analogue holds even when the surface in question is not of finite line type. Secondly, we show a result for a general surface that is locally the graph of a convex C 2 function, or a piece of such a surface defined through real analytic equations, that implies an analogous Fourier transform decay theorem in many situations where the oscillatory index is less than 1. This result has implications for lattice point discrepancy problems, which we describe.

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Fourier transforms of irregular mixed homogeneous hypersurface measures

Cited by 4 publications

References 16 publications

Method Improvements of Testing Modulus of Soil Based on Free‐Vibration Column

Method Improvements of Testing Modulus of Soil Based on Free‐Vibration Column

$$L^p$$ L p Sobolev Regularity for a Class of Radon and Radon-Like Transforms of Various Codimension

Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals

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