Literature DB >> 24293780

RIEMANN ZEROS AND THE INVERSE PHASE PROBLEM.

David S Tourigny1.   

Abstract

Finding a universal method of crystal structure solution and proving the Riemann hypothesis are two outstanding challenges in apparently unrelated fields. For centrosymmetric crystals however, a connection arises as the result of a statistical approach to the inverse phase problem. It is shown that parameters of the phase distribution are related to the non-trivial Riemann zeros by a Mellin transform.

Entities:  

Keywords:  Mellin transform; Riemann hypothesis; Riemann zeta function; X-ray diffraction; crystallography; maximum likelihood; structure factor

Year:  2013        PMID： 24293780      PMCID： PMC3841715          DOI： 10.1142/S021798491350187X

Source DB:  PubMed          Journal:  Mod Phys Lett B        ISSN： 0217-9849            Impact factor:   1.668


  11 in total

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Authors:  M G Rossmann
Journal:  Acta Crystallogr D Biol Crystallogr       Date:  2001-09-21

2.  Refinement of macromolecular structures by the maximum-likelihood method.

Authors:  G N Murshudov; A A Vagin; E J Dodson
Journal:  Acta Crystallogr D Biol Crystallogr       Date:  1997-05-01

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5.  [23] Bayesian statistical viewpoint on structure determination: Basic concepts and examples.

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Journal:  Methods Enzymol       Date:  1997       Impact factor: 1.600

6.  The structure of a centrosymmetric protein crystal.

Authors:  L E Zawadzke; J M Berg
Journal:  Proteins       Date:  1993-07

7.  Magnetic excitation spectra of Sr2IrO4 probed by resonant inelastic x-ray scattering: establishing links to cuprate superconductors.

Authors:  Jungho Kim; D Casa; M H Upton; T Gog; Young-June Kim; J F Mitchell; M van Veenendaal; M Daghofer; J van den Brink; G Khaliullin; B J Kim
Journal:  Phys Rev Lett       Date:  2012-04-23       Impact factor: 9.161

8.  Introduction to phasing.

Authors:  Garry L Taylor
Journal:  Acta Crystallogr D Biol Crystallogr       Date:  2010-03-24

9.  Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4.

Authors:  B J Kim; H Ohsumi; T Komesu; S Sakai; T Morita; H Takagi; T Arima
Journal:  Science       Date:  2009-03-06       Impact factor: 47.728

10.  Racemic crystallography of synthetic protein enantiomers used to determine the X-ray structure of plectasin by direct methods.

Authors:  Kalyaneswar Mandal; Brad L Pentelute; Valentina Tereshko; Vilasak Thammavongsa; Olaf Schneewind; Anthony A Kossiakoff; Stephen B H Kent
Journal:  Protein Sci       Date:  2009-06       Impact factor: 6.725
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