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pro vyhledávání: '"Abdo Y. Alfakih"'
Autor:
Abdo Y. Alfakih
Publikováno v:
Linear Algebra and its Applications. 594:29-50
A unit spherical Euclidean distance matrix (EDM) D is a matrix whose entries can be realized as the interpoint (squared) Euclidean distances of n points on a unit sphere. In this paper, given such a D and 1 ≤ k l ≤ n , we present a characterizati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::709f0c1014978e742f4d6bd55e6ea371
https://doi.org/10.1016/j.laa.2020.02.013
https://doi.org/10.1016/j.laa.2020.02.013
Autor:
Abdo Y. Alfakih
Publikováno v:
Linear Algebra and its Applications. 556:144-161
An n × n matrix D is a Euclidean distance matrix (EDM) if there exist points p 1 , … , p n in some Euclidean space such that d i j = ‖ p i − p j ‖ 2 for all i , j = 1 , … , n . Let D be an EDM and let E i j be the n × n symmetric matrix w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::13bcdcdb9bd823b663acdc8019fce3fb
https://doi.org/10.1016/j.laa.2018.07.007
https://doi.org/10.1016/j.laa.2018.07.007
Autor:
Abdo Y. Alfakih
Publikováno v:
Discrete Applied Mathematics. 217:707-710
Let G be a graph on n nodes. In this note, we prove that if G is ( r + 1 ) -vertex connected, 1 ź r ź n - 2 , then there exists a configuration p in general position in R r such that the bar framework ( G , p ) is universally rigid. The proof is co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::15e650d408e6ce671c3dcf264f57dd37
https://doi.org/10.1016/j.dam.2016.10.008
https://doi.org/10.1016/j.dam.2016.10.008
Autor:
Abdo Y. Alfakih
Publikováno v:
Journal of Global Optimization. 67:909-924
A bar framework (G, p) in dimension r is a graph G whose nodes are points $$p^1,\ldots ,p^n$$p1,ź,pn in $$\mathbb {R}^r$$Rr and whose edges are line segments between pairs of these points. Two frameworks (G, p) and (G, q) are equivalent if each edge
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8bc5ac50122bb46f847f6d2bed99d125
https://doi.org/10.1007/s10898-016-0448-y
https://doi.org/10.1007/s10898-016-0448-y
Autor:
Abdo Y. Alfakih
Publikováno v:
Linear Algebra and its Applications. 486:504-522
We present a new semidefinite Farkas lemma involving a side constraint on the rank. This lemma is then used to refine and elaborate on a recent characterization, by Connelly and Gortler [7] , of dimensional rigidity of bar frameworks.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::123adc1f05ced31eca3d13d472df1dfc
https://doi.org/10.1016/j.laa.2015.08.030
https://doi.org/10.1016/j.laa.2015.08.030
Autor:
Abdo Y. Alfakih
Publikováno v:
Discrete Mathematics. 343:111587
Let α ≠ β be two positive scalars. A Euclidean representation of a simple graph G in R r is a mapping of the nodes of G into points in R r such that the squared Euclidean distance between any two distinct points is α if the corresponding nodes a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bcebf6923624d3596cd2a4a041569d5a
https://doi.org/10.1016/j.disc.2019.07.003
https://doi.org/10.1016/j.disc.2019.07.003
Autor:
Abdo Y. Alfakih
Publikováno v:
Euclidean Distance Matrices and Their Applications in Rigidity Theory ISBN: 9783319978451
This chapter focuses on two problems concerning the individual entries of an EDM. The first problem is how to determine a missing or an unknown entry of an EDM. We present two methods for solving this problem, the second of which yields a complete cl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fe77b2e69026ba719dceb85e47539623
https://doi.org/10.1007/978-3-319-97846-8_7
https://doi.org/10.1007/978-3-319-97846-8_7
Autor:
Abdo Y. Alfakih
Publikováno v:
Euclidean Distance Matrices and Their Applications in Rigidity Theory ISBN: 9783319978451
Positive semidefinite (PSD) and positive definite (PD) matrices are closely connected with Euclidean distance matrices. Accordingly, they play a central role in this monograph. This chapter reviews some of the basic results concerning these matrices.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::60f89e0057888e9d50ee62be99393460
https://doi.org/10.1007/978-3-319-97846-8_2
https://doi.org/10.1007/978-3-319-97846-8_2
Autor:
Abdo Y. Alfakih
Publikováno v:
Euclidean Distance Matrices and Their Applications in Rigidity Theory ISBN: 9783319978451
This chapter has three parts. Part one addresses the problem of EDM completions. Part two is an introduction to the theory of bar-and-joint frameworks. Such frameworks, which are interesting in their own right, are particularly useful in the study of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6d0f458917e4998f7f00b252e7edbd29
https://doi.org/10.1007/978-3-319-97846-8_8
https://doi.org/10.1007/978-3-319-97846-8_8