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).

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.

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

2011 ◽  
Vol 3 (5) ◽  
pp. 572-585 ◽  
Author(s):  
A. Tadeu ◽  
C. S. Chen ◽  
J. António ◽  
Nuno Simões
Keyword(s):  
Fourier Transform ◽  
Helmholtz Equation ◽  
Initial Conditions ◽  
Inverse Fourier Transform ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Static Response ◽  
Particular Solution ◽  
The Fourier Transform ◽  
Transfer Problems

AbstractFourier transform is applied to remove the time-dependent variable in the diffusion equation. Under 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 solutions. The 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 algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

scholarly journals Inversion of Fourier Transforms by Means of Scale-Frequency Series

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Nassar H. S. Haidar
Keyword(s):  
Fourier Transform ◽  
Nonlinear Programming ◽  
Fourier Transforms ◽  
Inverse Fourier Transform ◽  
Double Series ◽  
Nonlinear Programming Problem ◽  
Continuous Scale ◽  
Free Parameters ◽  
The Fourier Transform ◽  
Dual Scale

We report on inversion of the Fourier transform when the frequency variable can be scaled in a variety of different ways that improve the resolution of certain parts of the frequency domain. The corresponding inverse Fourier transform is shown to exist in the form of two dual scale-frequency series. Upon discretization of the continuous scale factor, this Fourier transform series inverse becomes a certain nonharmonic double series, a discretized scale-frequency (DSF) series. The DSF series is also demonstrated, theoretically and practically, to be rate-optimizable with respect to its two free parameters, when it satisfies, as an entropy maximizer, a pertaining recursive nonlinear programming problem incorporating the entropy-based uncertainty principle.

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 effect of spatial coherence of sources on synthetic aperture mapping

1991 ◽  
Vol 131 ◽  
pp. 10-14
Author(s):  
Daniel F.V. James
Keyword(s):  
Fourier Transform ◽  
Inverse Fourier Transform ◽  
Spatial Coherence ◽  
Full Description ◽  
Coherent Light ◽  
Partially Coherent ◽  
Interference Fringes ◽  
Partially Coherent Light ◽  
The Fourier Transform ◽  
Coherence Area

The interferometric mapping of astronomical objects relies on the van-Cittert Zernike theorem, one of the major results of the theory of partially coherent light [see, Bom and Wolf (1980), chapter 10]. This theorem states that the degree of spatial coherence of the field from a distant spatially incoherent source is proportional to the Fourier transform of the intensity distribution across the source. Measurement of the degree of spatial coherence, by, for example, measuring the visibility of interference fringes, allows the object to be mapped by making an inverse Fourier transform. (For a full description of this technique see Thompson, Moran and Swenson, 1986.)In this paper I present a summary of the results an investigation into what happens when the distant source is not spatially coherent (James, 1990). Using a heuristic model of a spherically symmetric partially coherent source, an analytic expression for the error in the measurement of the effective radius, expressed as a function of coherence area, can be obtained.

Discrete Time, Discrete Frequency

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Continuous Time ◽  
Time Varying ◽  
Discrete Frequency ◽  
The Fourier Transform ◽  
Definition Of ◽  
The Time Domain

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

scholarly journals Calculation of ruin probabilities for a dense class of heavy tailed distributions

2014 ◽  
Vol 2015 (7) ◽  
pp. 573-591 ◽  
Author(s):  
Mogens Bladt ◽  
Bo Friis Nielsen ◽  
Gennady Samorodnitsky
Keyword(s):  
Ruin Probabilities ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Dense Class

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.

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