scholarly journals Solution to the Pompeiu problem and the related symmetry problem

2017 ◽  
Vol 63 ◽  
pp. 28-33 ◽  
Author(s):  
A.G. Ramm
Keyword(s):  
Pompeiu Problem ◽  
Symmetry Problem

scholarly journals Symmetry Problems for PDE

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2240
Author(s):  
Alexander G. Ramm
Keyword(s):  
Harmonic Analysis ◽  
New Method ◽  
General Interest ◽  
Pompeiu Problem ◽  
Symmetry Problem

The results of this paper allow one to derive several results of general interest: to prove the Schiffer’s conjecture, to solve the Pompeiu problem, to prove two symmetry results in harmonic analysis and to give a new method for solving an old symmetry problem.

Elastic photon scattering fromHe4: Charge symmetry problem

1992 ◽  
Vol 46 (2) ◽  
pp. 449-454 ◽  
Author(s):  
D. P. Wells ◽  
D. S. Dale ◽  
R. A. Eisenstein ◽  
F. J. Federspiel ◽  
M. A. Lucas ◽  
...  
Keyword(s):  
Photon Scattering ◽  
Charge Symmetry ◽  
Symmetry Problem

On Broken Symmetry

2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Vladimir Zelevinsky
Keyword(s):  
Point Of View ◽  
Low Energy ◽  
Broken Symmetry ◽  
Symmetry Problem ◽  
Energy Physics

From the practical position of a quantum theoretician working in low-energy physics, here is a more modest point of view on the symmetry problem, including its various manifestations and violations.

scholarly journals The Pompeiu problem

2013 ◽  
Vol 1 (1) ◽  
Author(s):  
Alexander G. Ramm
Keyword(s):  
Pompeiu Problem

On the Pompeiu problem and its generalizations

1993 ◽  
Vol 45 (10) ◽  
pp. 1623-1628 ◽  
Author(s):  
V. V. Volchkov
Keyword(s):  
Pompeiu Problem

scholarly journals Novel dynamic residue network analysis approaches to study homodimeric allosteric modulation in SARS-CoV-2 Mpro and in its evolutionary mutations

2021 ◽  
Author(s):  
Olivier Sheik Amamuddy ◽  
Rita Afriyie Baoteng ◽  
Victor Barozi ◽  
Dorothy Wavinya Nyamai ◽  
Ozlem Tastan Bishop
Keyword(s):  
Binding Site ◽  
Laboratory Strain ◽  
Allosteric Modulators ◽  
Allosteric Communication ◽  
Katz Centrality ◽  
Symmetry Problem ◽  
The Stability ◽  
Allosteric Mechanisms ◽  
Domain I ◽  
Communication Path

The rational search for allosteric modulators and the allosteric mechanisms of these modulators in the presence of evolutionary mutations, including resistant ones, is a relatively unexplored field. Here, we established novel in silico approaches and applied to SARS-CoV-2 main protease (Mpro). First, we identified six potential allosteric modulators (SANC00302, SANC00303, SANC00467, SANC00468, SANC00469, SANC00630) from the South African Natural Compounds Database (SANCDB) bound to the allosteric pocket of Mpro that we determined in our previous work. We also checked the stability of these compounds against Mpro of laboratory strain HCoV-OC43 and identified differences due to residue changes between the two proteins. Next, we focused on understanding the allosteric effects of these modulators on each protomer of the reference Mpro protein, while incorporating the symmetry problem in the functional homodimer. In general, asymmetric behavior of multimeric proteins is not commonly considered in computational analysis. We introduced a novel combinatorial approach and dynamic residue network (DRN) analysis algorithms to examine patterns of change and conservation of critical nodes, according to five independent criteria of network centrality (betweenness centrality (BC), closeness centrality (CC), degree centrality (DC), eigencentrality (EC) and katz centrality (KC)). The relationships and effectiveness of each metric in characterizing allosteric behavior were also investigated. We observed highly conserved network hubs for each averaged DRN metric on the basis of their existence in both protomers in the absence and presence of all ligands, and we called them persistent hubs (residues 17, 111, 112 and 128 for averaged BC; 6, 7, 113, 114, 115, 124, 125, 126, 127 and 128 for averaged CC; 36, 91, 146, 150 and 206 for averaged DC; 7, 115 and 125 for EC; 36, 125 and 146 for KC). We also detected ligand specific signal changes some of which were in or around functional residues (i.e. chameleon switch PHE140). Using EC persistent hubs and ligand introduced hubs we identified a residue communication path between allosteric binding site and catalytic site. Finally, we examined the effects of the mutations on the behavior of the protein in the presence of selected potential allosteric modulators and investigated the ligand stability. The hit compounds showed various levels of stability in the presence of SARS-CoV-2 Mpro mutations, being most stable in A173V, N274D and R279C, and least stable in R60C, N151D V157I, C160S and A255V. SANC00468 was the most stable compound in the 43 mutant protein systems. We further used DRN metric analysis to define cold spots as being those regions that are least impacted, or not impacted, by mutations. One crucial outcome of this study was to show that EC centrality hubs form an allosteric communication path between the allosteric ligand binding site to the active site going through the interface residues of Domain I and II; and this path was either weakened or lost in the presence of some of the mutations. Overall, the results of this study revealed crucial aspects that need to be considered in drug discovery in COVID-19 specifically and in general for rational computational drug design purposes.

scholarly journals POMPEIU PROBLEM FOR THE HEISENBERG BALL

2011 ◽  
Vol 15 (6) ◽  
pp. 2503-2531 ◽  
Author(s):  
Wayne M. Eby
Keyword(s):  
Pompeiu Problem

application to the Pompeiu problem

1994 ◽  
Vol 73 (3) ◽  
pp. 561-582 ◽  
Author(s):  
Peter Ebenfelt
Keyword(s):  
Pompeiu Problem
Sign in / Sign up

Export Citation Format

Share Document