scholarly journals The phase problem of ultraflat unimodular polynomials: The resolution of the conjecture of Saffari

2001 ◽  
Vol 321 (4) ◽  
pp. 905-924 ◽  
Author(s):  
Tamás Erdélyi
Keyword(s):  
Phase Problem ◽  
Unimodular Polynomials

scholarly journals Solutions for parametric double phase Robin problems

2021 ◽  
Vol 121 (2) ◽  
pp. 159-170 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Boundary Condition ◽  
Existence Theorems ◽  
Robin Boundary Condition ◽  
Phase Problem ◽  
Double Phase ◽  
Robin Boundary ◽  
Double Phase Problem

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .

Detonation-propelled shocks in tubular charges as a two-phase problem

2012 ◽  
Vol 340 (11-12) ◽  
pp. 900-909 ◽  
Author(s):  
Irina Brailovsky ◽  
Gregory Sivashinsky
Keyword(s):  
Phase Problem ◽  
Two Phase

scholarly journals ARCIMBOLDOon coiled coils

2018 ◽  
Vol 74 (3) ◽  
pp. 194-204 ◽  
Author(s):  
Iracema Caballero ◽  
Massimo Sammito ◽  
Claudia Millán ◽  
Andrey Lebedev ◽  
Nicolas Soler ◽  
...  
Keyword(s):  
Coiled Coil ◽  
Coiled Coils ◽  
Translational Symmetry ◽  
Command Line ◽  
Phase Problem ◽  
Final Solution ◽  
Resolution Limit ◽  
Helical Structures ◽  
Small Model ◽  
Test Pool

ARCIMBOLDOsolves the phase problem by combining the location of small model fragments usingPhaserwith density modification and autotracing usingSHELXE. Mainly helical structures constitute favourable cases, which can be solved using polyalanine helical fragments as search models. Nevertheless, the solution of coiled-coil structures is often complicated by their anisotropic diffraction and apparent translational noncrystallographic symmetry. Long, straight helices have internal translational symmetry and their alignment in preferential directions gives rise to systematic overlap of Patterson vectors. This situation has to be differentiated from the translational symmetry relating different monomers.ARCIMBOLDO_LITEhas been run on single workstations on a test pool of 150 coiled-coil structures with 15–635 amino acids per asymmetric unit and with diffraction data resolutions of between 0.9 and 3.0 Å. The results have been used to identify and address specific issues when solving this class of structures usingARCIMBOLDO. Features fromPhaserv.2.7 onwards are essential to correct anisotropy and produce translation solutions that will pass the packing filters. As the resolution becomes worse than 2.3 Å, the helix direction may be reversed in the placed fragments. Differentiation between true solutions and pseudo-solutions, in which helix fragments were correctly positioned but in a reverse orientation, was found to be problematic at resolutions worse than 2.3 Å. Therefore, after every new fragment-placement round, complete or sparse combinations of helices in alternative directions are generated and evaluated. The final solution is once again probed by helix reversal, refinement and extension. To conclude, density modification andSHELXEautotracing incorporating helical constraints is also exploited to extend the resolution limit in the case of coiled coils and to enhance the identification of correct solutions. This study resulted in a specialized mode withinARCIMBOLDOfor the solution of coiled-coil structures, which overrides the resolution limit and can be invoked from the command line (keyword coiled_coil) orARCIMBOLDO_LITEtask interface inCCP4i.

scholarly journals A General Strategy to Solve the Phase Problem in RNA Crystallography

Structure ◽  
2007 ◽  
Vol 15 (7) ◽  
pp. 761-772 ◽  
Author(s):  
Amanda Y. Keel ◽  
Robert P. Rambo ◽  
Robert T. Batey ◽  
Jeffrey S. Kieft
Keyword(s):  
General Strategy ◽  
Phase Problem ◽  
Rna Crystallography

Solution to the phase problem using x-ray interferometry

1985 ◽  
Vol 31 (10) ◽  
pp. 6420-6423 ◽  
Author(s):  
J. T. Hutton ◽  
G. T. Trammell ◽  
J. P. Hannon
Keyword(s):  
Phase Problem ◽  
X Ray
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