On Constructing Distribution Functions; with Applications to Lommel Polynomials and Bessel Functions

1968 ◽  
Vol 130 (2) ◽  
pp. 281 ◽  
Author(s):  
Daniel Maki
Keyword(s):  
Bessel Functions ◽  
Distribution Functions ◽  
Lommel Polynomials

scholarly journals Turán inequalities for symmetric orthogonal polynomials

1997 ◽  
Vol 20 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Joaquin Bustoz ◽  
Mourad E. H. Ismail
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Relation ◽  
Bessel Functions ◽  
Sum Of Squares ◽  
Weighted Sum ◽  
Pollaczek Polynomials ◽  
Lommel Polynomials ◽  
Three Term Recurrence Relation

A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials andq-Bessel functions.

scholarly journals (BESSEL-)WEIGHTED ASYMMETRIES

2011 ◽  
Vol 04 ◽  
pp. 126-134
Author(s):  
B. U. MUSCH ◽  
A. PROKUDIN
Keyword(s):  
Bessel Functions ◽  
Pion Mass ◽  
Natural Generalization ◽  
Distribution Functions ◽  
High Momentum ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Soft Factor ◽  
Fragmentation Functions ◽  
Soft Factors

Semi-inclusive deep inelastic scattering experiments allow us to probe the motion of quarks inside the proton in terms of so-called transverse momentum dependent parton distribution functions (TMD PDFs), but the information is convoluted with fragmentation functions (TMD FFs) and soft factors. It has long been known that weighting the measured event counts with powers of the hadron momentum before forming angular asymmetries de-convolutes TMD PDFs and TMD FFs in an elegant way, but this also entails an undesirable sensitivity to high momentum contributions. Using Bessel functions as weights, we find a natural generalization of weighted asymmetries that preserves the de-convolution property and features soft-factor cancellation, yet allows us to be less sensitive to high transverse momenta. The formalism also relates to TMD quantities studied in lattice QCD. We briefly show preliminary lattice results from an exploratory calculation of the Boer-Mulders shift using lattices generated by the MILC and LHP collaborations at a pion mass of 500 MeV.

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.

Sign in / Sign up

Export Citation Format

Share Document