Response of Cylindrical Cavity to Traveling Load in Bore

1974 ◽  
Vol 41 (3) ◽  
pp. 800-801
Author(s):  
M. Kojima
Keyword(s):  
Fourier Transform ◽  
Dynamic Response ◽  
Stress Analysis ◽  
Cylindrical Cavity ◽  
Loading Condition ◽  
Infinite Medium ◽  
Transient Solution ◽  
The Past ◽  
The Fourier Transform ◽  
The Relationship

Stress analysis was carried out on a cylindrical cavity in an infinite medium. The normal tractions, which act along the circumference of the bore, rotate continuously or change their rotating directions at t = 0. In this analysis, the Fourier-transform technique according to the theory of distributions was employed to investigate the relationship between the loading condition of traveling traction and the dynamic response. The theory of distributions verified the past solutions and in this analysis it also revealed the possibility of some transient solution.

Computers and infrared spectroscopy: evolution and revolution

1991 ◽  
Vol 69 (11) ◽  
pp. 1781-1785 ◽  
Author(s):  
D. J. Moffatt ◽  
J. K. Kauppinen ◽  
H. H. Mantsch
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Key Words ◽  
Maximum Entropy ◽  
Input Data ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
History Of ◽  
The Fourier Transform ◽  
The Relationship

A brief history of the relationship between computer and infrared spectroscopist is given with emphasis on the use of the Fourier transform. Subsequently, an algorithm is developed that may be used to devise an objective Fourier self-deconvolution procedure which depends only on the input data and is not subject to the biases that are often introduced in such subjective techniques. Key words: deconvolution, Fourier transform, maximum entropy method.

scholarly journals Temperature-Dependent Broadening of the Ultraviolet Photoelectron Spectrum of Au(110)

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5969
Author(s):  
Tomonari Nishida ◽  
Ikuo Kinoshita ◽  
Juntaro Ishii
Keyword(s):  
Fourier Transform ◽  
Temperature Dependence ◽  
Photoelectron Spectroscopy ◽  
Photoelectron Spectrum ◽  
Thermodynamic Temperature ◽  
Temperature Dependent ◽  
Photoelectron Emission ◽  
The Fourier Transform ◽  
The Relationship

To determine the thermodynamic temperature of a solid surface from the electron energy distribution measured by photoelectron spectroscopy, it is necessary to accurately evaluate the energy broadening of the photoelectron spectrum and investigate its temperature dependence. Broadening functions in the photoelectron spectrum of Au(110)’s surface near the Fermi level were estimated successfully using the relationship between the Fourier transform and the convolution integral. The Fourier transform could simultaneously reduce the noise of the spectrum when the broadening function was derived. The derived function was in the form of a Gaussian, whose width depended on the thermodynamic temperature of the sample and became broader at higher temperatures. The results contribute to improve accuracy of the determination of thermodynamic temperature from the photoelectron spectrum and provide useful information on the temperature dependence of electron scattering in photoelectron emission processes.

scholarly journals The Relationship Between ϵ-Kronecker Sets and Sidon Sets

2016 ◽  
Vol 59 (3) ◽  
pp. 521-527 ◽  
Author(s):  
Kathryn Hare ◽  
L. Thomas Ramsey
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Dual Group ◽  
Sidon Sets ◽  
Sidon Set ◽  
Arithmetic Properties ◽  
The Fourier Transform ◽  
The Relationship ◽  
Discrete Abelian Group

AbstractA subset E of a discrete abelian group is called ϵ-Kronecker if all E-functions of modulus one can be approximated to within ϵ by characters. E is called a Sidon set if all bounded E-functions can be interpolated by the Fourier transform of measures on the dual group. As ϵ-Kronecker sets with ϵ < 2 possess the same arithmetic properties as Sidon sets, it is natural to ask if they are Sidon. We use the Pisier net characterization of Sidonicity to prove this is true.

scholarly journals Ruin Probabilities and Complex Analysis

2021 ◽  
Author(s):  
Andrew Leung
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Complex Analysis ◽  
Inverse Fourier Transform ◽  
Ruin Probabilities ◽  
Heavy Tailed Distributions ◽  
Complex Functions ◽  
Heavy Tailed ◽  
The Fourier Transform ◽  
The Relationship

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

scholarly journals Design of Wideband Multifunction Antenna Array Based on Multiple Interleaved Subarrays

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Longjun Li ◽  
Buhong Wang
Keyword(s):  
Fourier Transform ◽  
Antenna Array ◽  
Antenna Arrays ◽  
Linear Antenna ◽  
Energy Distributions ◽  
Low Sidelobe ◽  
Pattern Similarity ◽  
The Fourier Transform ◽  
The Relationship ◽  
Linear Antenna Arrays

A new Modified Iterative Fourier Technique (MIFT) is proposed for the design of interleaved linear antenna arrays which operate at different frequencies with no grating lobes, low-sidelobe levels, and wide bandwidths. In view of the Fourier transform mapping between the element excitations and array factor of uniform linear antenna array, the spectrum of the array factor is first acquired with FFT and its energy distributions are investigated thoroughly. The relationship between the carrier frequency and the element excitation is obtained by the density-weighting theory. In the following steps, the element excitations of interleaved subarrays are carefully selected in an alternate manner, which ensures that similar patterns can be achieved for interleaved subarrays. The Peak Sidelobe Levels (PSLs) of the interleaved subarrays are further reduced by the iterative Fourier transform algorithm. Numerical simulation results show that favorable design of the interleaved linear antenna arrays with different carrier frequencies can be obtained by the proposed method with favorable pattern similarity, low PSL, and wide bandwidths.

Principles of Practical Advantages and Limitations of Light Microscopic 3d Deconvolution

1997 ◽  
Vol 3 (S2) ◽  
pp. 373-374
Author(s):  
T.J. Holmes ◽  
N.J. O’Connor ◽  
M. Wang ◽  
C. Wang ◽  
J.N. Turner
Keyword(s):  
Fourier Transform ◽  
Graduate Students ◽  
Confocal Microscopy ◽  
Confocal Microscope ◽  
Resolving Power ◽  
Fourier Optics ◽  
Axial Resolution ◽  
Basic Principles ◽  
The Past ◽  
The Fourier Transform

There has been much provocative discussion over the past few years about the advantages and limitations of deconvolution methods. In this tutorial we will provide a reasonable understanding of the underlying theoretical principles of deconvolution, with an aim at understanding expected advantages and limitations. These principles will be presented for a mixed audience composed of biologists, neuroscientists, engineers, physicists and other scientists and graduate students. These principles will be presented in the context of both widefield and confocal microscopy deconvolution.The basic principles of Fourier optics will be presented. From these principles, we can explain why it is that the confocal microscope provides a superior in-plane and axial (z-axis) resolving power, compared to the widefield microscope. In particular, for example, the Fourier transform of a 3D widefield image contains a missing cone region (to be explained in the tutorial), and this missing cone region effectively spoils the axial resolution of unprocessed widefield data.

scholarly journals On the Fourier transform of a compact semisimple Lie group

1994 ◽  
Vol 56 (1) ◽  
pp. 64-116 ◽  
Author(s):  
N. J. Wildberger
Keyword(s):  
Fourier Transform ◽  
Irreducible Representation ◽  
Lie Group ◽  
Spherical Trigonometry ◽  
Semisimple Lie Group ◽  
Symbol Calculus ◽  
Naturally Occurring ◽  
Type Character ◽  
The Fourier Transform ◽  
The Relationship

AbstractWe develop a concrete Fourier transform on a compact Lie group by means of a symbol calculus, or *-product, on each integral co-adjoint orbit. These *-products are constructed by means of a moment map defined for each irreducible representation. We derive integral formulae for these algebra structures and discuss the relationship between two naturally occurring inner products on them. A global Kirillov-type character is obtained for each irreducible representation. The case of SU(2) is treated in some detail, where some interesting connections with classical spherical trigonometry are obtained.

Using Attenuated Total Reflection Fourier Transform Infrared Spectroscopy (ATR FT-IR) to Study the Molecular Conformation of Parchment Artifacts in Different Macroscopic States

2013 ◽  
Vol 67 (2) ◽  
pp. 158-162 ◽  
Author(s):  
Lee Gonzalez ◽  
Matthew Wade ◽  
Nancy Bell ◽  
Kate Thomas ◽  
Tim Wess
Keyword(s):  
Molecular Structure ◽  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Fourier Transform Infrared Spectroscopy ◽  
Molecular Conformation ◽  
Chemical Change ◽  
Fourier Transform Infrared ◽  
Ft Ir ◽  
The Fourier Transform ◽  
The Relationship

Maintaining appropriate temperatures and relative humidity is considered essential to extending the useful life of parchment artifacts. Although the relationship between environmental factors and changes to the physical state of artifacts is reasonably understood, an improved understanding of the relationship between the molecular conformation and changes to the macroscopic condition of parchment is needed to optimize environmental conditions. Using Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR FT-IR) analysis, the conformation of the molecular structure in selected parchment samples with specific macroscopic conditions, typically discoloration and planar deformations (e.g., cockling and tearing), have been made. The results of this investigation showed that the Fourier transform infrared signal differs for parchment samples exhibiting different macroscopic conditions. In areas exhibiting planar deformation, a change in the Fourier Transform Infrared signal was observed that indicates unfolding of the molecular conformation. In comparison, the discolored samples showed a change in molecular conformation that indicates a chemical change within the collagen molecular structure. This paper discusses the possible causal associations and implications of these findings for the conservation and preservation of parchment artifacts.

The on-line use of histogram data for high-speed correction and alignment of electron microscope images

1984 ◽  
Vol 42 ◽  
pp. 556-557
Author(s):  
William Krakow
Keyword(s):  
Power Spectrum ◽  
High Speed ◽  
Direct Memory Access ◽  
Digital Television ◽  
Contrast Transfer Function ◽  
The Past ◽  
High Resolution Tem ◽  
On Line ◽  
Correction Of Astigmatism ◽  
The Fourier Transform

In the past few years on-line digital television frame store devices coupled to computers have been employed to attempt to measure the microscope parameters of defocus and astigmatism. The ultimate goal of such tasks is to fully adjust the operating parameters of the microscope and obtain an optimum image for viewing in terms of its information content. The initial approach to this problem, for high resolution TEM imaging, was to obtain the power spectrum from the Fourier transform of an image, find the contrast transfer function oscillation maxima, and subsequently correct the image. This technique requires a fast computer, a direct memory access device and even an array processor to accomplish these tasks on limited size arrays in a few seconds per image. It is not clear that the power spectrum could be used for more than defocus correction since the correction of astigmatism is a formidable problem of pattern recognition.

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