Complex Integral Equations of the Direct Approach

2002 ◽  
pp. 56-70
Author(s):  
A. M. Linkov
Keyword(s):  
Integral Equations ◽  
Direct Approach ◽  
Complex Integral

Diffraction by a cylinder of finite length

1956 ◽  
Vol 52 (2) ◽  
pp. 322-335 ◽  
Author(s):  
W. E. Williams ◽  
M. J. Lighthill
Keyword(s):  
Approximate Solution ◽  
Circular Cylinder ◽  
Explicit Expression ◽  
Integral Equations ◽  
Finite Length ◽  
Sound Wave ◽  
Wave Number ◽  
Resonant System ◽  
Cylinder Length ◽  
Complex Integral

ABSTRACTThe diffraction of a plane harmonic sound wave by a hollow circular cylinder of finite length is considered. The problem is treated by using Laplace transforms and is reduced to the solution of two complex integral equations. An approximate solution is obtained for these equations when the product of the wave number (k) and the cylinder length (l) is large. The resonance of the system is considered and an equation derived for the resonant lengths which is then solved approximately for kl large. An explicit expression is obtained for the end correction of an. r–resonant system (i.e. kl ≈ rπ), and also comparison is made with experimental results.

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

Direct Approach for Jugular Paraganglioma by Enlarged Mastoidectomy and Hypotympanotomy without Middle Ear Obliteration

2016 ◽  
Vol 77 (S 02) ◽  
Author(s):  
Kazimierz Niemczyk ◽  
Robert Bartoszewicz ◽  
Krzysztof Morawski ◽  
Izabela Popieluch
Keyword(s):  
Middle Ear ◽  
Direct Approach
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