A. Y. Alfakih

Dept of Mathematics and Statistics, University of Winsdsor

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Completed or Submitted Papers

Refereed Papers

  • A. Y. Alfakih , Local, dimensional and universal rigidities: A unified Gram matrix approach. Rigidity and Symmetry. R. Connelly, W. Whiteley and A. Weiss Editors. Fields Institute Communications, Vol=70, pages 41--60. Springer, (2014)

  • A. Y. Alfakih and V-H Nguyen , On affine motions and universal rigidity of tensegrity frameworks. . Linear Algebra Appl. Vol 439, 3134--3147 (2013)

  • A. Y. Alfakih and Y. Ye , On affine motions and bar frameworks in general positions. . Linear Algebra Appl. vol 438, 31--36, (2013)

  • A. Y. Alfakih, N. Taheri and Y. Ye , On stress matrices of (d+1)-lateration frameworks in general position. . Math. Program. vol 137, 1--17, (2013)

  • A. Y. Alfakih, On bar frameworks, stress matrices and semidefinite programming . Math. Program. Ser. B vol 129, 113--128, (2011)

  • A. Y. Alfakih, On the universal rigidity of generic bar frameworks.
    Contribution Disc. Math. vol 5, no 1, 7--17, (2010)

  • A. Y. Alfakih, On the dual rigidity matrix. Linear Algebra Appl. 428, 962--972, (2008).

  • A. Y. Alfakih, On the eigenvalues of Euclidean distance matrices.
    Comput. Appl. Math. Vol 27, no 3, 237--250, (2008)

  • A. Y. Alfakih and H. Wolkowicz, Some necessary and some sufficient trace
    inequalities for Euclidean distance matrices. Linear Mult. Algebra . 55, 499--506, (2007).

  • A. Y. Alfakih, On dimensional rigidity of joint-and-bar frameworks.
    Discrete Appl. Math. 155, 1244-1253, (2007).

  • A. Y. Alfakih, On the nullspace, the rangespace and the characteristic polynomial
    of Euclidean distance matrices. Linear Algebra Appl . 416, 348-354, (2006).

  • A. Y. Alfakih, A remark of the faces of the cone of Euclidean Distance Matrices.
    Linear Algebra Appl . 414, 266-270, (2006).

  • A. Y. Alfakih, On the Uniqueness of Euclidean Distance Matrix Completions:
    the case of points in general position. Linear Algebra Appl ., 397, 265-277 (2005).

  • A. Y. Alfakih, On the Uniqueness of Euclidean Distance Matrix Completions.
    Linear Algebra Appl ., 370, 1--14 (2003).

  • A. Y. Alfakih and H. Wolkowicz, Two Theorems on Euclidean Distance Matrices
    and Gale Transform. Linear Algebra Appl ., 340, 149--154 (2002).

  • A. Y. Alfakih, On Rigidity and Realizability of Weighted Graphs.
    Linear Algebra Appl. , 325, 57--70 (2001).

  • A. Y. Alfakih, Graph Rigidity via Euclidean Distance Matrices.
    Linear Algebra Appl ., 310, 149--165 (2000).

  • A. Y. Alfakih, A. Khandani and H. Wolkowicz, Solving Euclidean Distance Matrix
    Completion Problems via Semidefinite Programming. Comput. Optim. Appl. , 12, 13--30 (1999).

  • A. Y. Alfakih, T. Yi and K. G. Murty, Some Facets of an Assignment Problem
    with a 0--1 Side Constraint. J. of Comb. Optim. , 4, 365--388 (2000).

  • A. Y. Alfakih and K. G. Murty, Adjacency on the Constrained Assignment Problem.
    Discrete Appl. Math. , 87, 269--274 (1998).

Research Reports:

Chapters in Books:

  • A. Y. Alfakih , Universal rigidity bar frameworks in general position: A Euclidean distance matrix approach in . "Distance Geometry: Theory, methods and applications", A Mucherino et al editors. 3--22, Springer (2013)

  • A. Y. Alfakih and H. Wolkowicz, Matrix Completion Problems. In Handbook of Semidefinite Programming: Theory, Algorithms, and Applications.
    H. Wolkowicz, R. Saigal, and L. Vandenberghe editors, Kluwer Academic Publishers,
    Boston. pp 533--546 (2000).