scholarly journals Some eigenvalue distribution functions of the Laguerre ensemble

1996 ◽  
Vol 29 (23) ◽  
pp. 7561-7579 ◽  
Author(s):  
Y Chen ◽  
S M Manning
Keyword(s):  
Distribution Functions ◽  
Eigenvalue Distribution ◽  
Laguerre Ensemble

Painlevé transcendents

2018 ◽  
Author(s):  
Eugene Kanzieper
Keyword(s):  
Matrix Theory ◽  
Distribution Functions ◽  
Eigenvalue Distribution ◽  
Painlevé Equations ◽  
Modern Theory ◽  
Painleve Equations ◽  
Painlevé Transcendents ◽  
Large N ◽  
Painleve Transcendents ◽  
Second Painlevé Equation

This article discusses the history and modern theory of Painlevé transcendents, with particular emphasis on the Riemann–Hilbert method. In random matrix theory (RMT), the Painlevé equations describe either the eigenvalue distribution functions in the classical ensembles for finite N or the universal eigenvalue distribution functions in the large N limit. This article examines the latter. It first considers the main features of the Riemann–Hilbert method in the theory of Painlevé equations using the second Painlevé equation as a case study before analysing the two most celebrated universal distribution functions of RMT in terms of the Painlevé transcendents using the theory of integrable Fredholm operators as well as the Riemann–Hilbert technique: the sine kernel and the Airy kernel determinants.

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

Obtaining Normalized Atomic Radial Distribution Functions from EELFS Spectra

1997 ◽  
Vol 7 (C2) ◽  
pp. C2-577-C2-578 ◽  
Author(s):  
D. V. Surnin ◽  
D. E. Denisov ◽  
Yu. V. Ruts ◽  
P. M. Knjazev
Keyword(s):  
Radial Distribution ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Atomic Radial Distribution

Calculation of spatially inhomogeneous electron distribution functions

1998 ◽  
Vol 08 (PR7) ◽  
pp. Pr7-33-Pr7-42
Author(s):  
L. L. Alves ◽  
G. Gousset ◽  
C. M. Ferreira
Keyword(s):  
Electron Distribution ◽  
Distribution Functions ◽  
Spatially Inhomogeneous
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