EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 15 / No 2 (April-June 2009) ESAIM: COCV, 15 2 (2009) 454-470 References
Free Access
Issue
ESAIM: COCV
Volume 15, Number 2, April-June 2009
Page(s) 454 - 470
DOI https://doi.org/10.1051/cocv:2008040
Published online 24 June 2008
  1. T. Andreescu, O. Mushkarov and L. Stoyanov, Geometric problems on maxima and minima. Birkhäuser (2006). [Google Scholar]
  2. M. Atiyah and P. Sutcliffe, The geometry of point particles. Proc. R. Soc. London A 458 (2002) 1089–1115. [CrossRef] [Google Scholar]
  3. M. Atiyah and P. Sutcliffe, Polyhedra in physics, chemistry and geometry. Milan J. Math. 71 (2003) 33–58. [CrossRef] [MathSciNet] [Google Scholar]
  4. R. Bapat, Mixed discriminants of positive semidefinite matrices. Linear Algebra Appl. 126 (1989) 107–124. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Bayart, Épreuve de mathématiques générales du concours d'agrégation de mathématiques 1980. Revue de Mathématiques Spéciales (1980–1981) 220–230. [Google Scholar]
  6. A. Ben Tal, A. Nemirovski and C. Roos, Robust solutions of uncertain quadratic and conic-quadratic problems. SIAM J. Optim. 13 (2002) 535–560. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Bendito, A. Carmona, A.M. Encinas and J.M. Gesto, Estimation of Fekete points. J. Comput. Phys. 225 (2007) 2354–2376. [CrossRef] [MathSciNet] [Google Scholar]
  8. D. Bessis, P. Moussa and M. Villani, Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics. J. Math. Phys. 16 (1975) 2318–2325. [CrossRef] [Google Scholar]
  9. R. Bhatia, Matrix analysis. Springer (1997). [Google Scholar]
  10. J. Bochnak and J. Siciak, Polynomials and multilinear mappings in topological vector spaces. Studia Math. 39 (1971) 59–76. [MathSciNet] [Google Scholar]
  11. G-S. Cheon and I.M. Wanless, An update on Minc's survey of open problems involving permanents. Linear Algebra Appl. 403 (2005) 314–342. [CrossRef] [MathSciNet] [Google Scholar]
  12. H.T. Croft, K.J. Falconer and R.K. Guy, Unsolved problems in geometry. Springer-verlag (1991). [Google Scholar]
  13. K. Derinkuyu and M. Pinar, On the S-procedure and some variants. Math. Meth. Oper. Res. 64 (2006) 55–77. [CrossRef] [Google Scholar]
  14. K. Derinkuyu, M. Pinar and A. Camci, An improved probability bound for the approximate S-lemma. Oper. Res. Lett. 35 (2007) 743–746. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Drmota, W. Schachermayer and J. Teichmann, A hyper-geometric approach to the BMV-conjecture. Monatshefte Math. 146 (2005) 179–201. [CrossRef] [Google Scholar]
  16. S.W. Drury, Essentially Hermitian matrices revisited. Electronic J. Linear Algebra 15 (2006) 285–296. [Google Scholar]
  17. G.P. Egorychev, The solution of Van der Waerden's problem for permanents. Dokl. Akad. Sci. SSSR 258 (1981) 1041–1044 (in Russian), Adv. Math. 42 (1981) 299–305. [Google Scholar]
  18. G.P. Egorychev, Proof of the Van der Waerden conjecture. Siberian Math. J. 22 (1982) 854–859. [CrossRef] [Google Scholar]
  19. L. Elsner and K.D. Ikramov, Normal matrices: an update. Linear Algebra Appl. 285 (1998) 291–303. [CrossRef] [MathSciNet] [Google Scholar]
  20. D.I. Falikman, A proof of the Van der Waerden conjecture on the permanent of a doubly stochastic matrix. Mat. Zametki 29 (1981) 931–938 (in Russian). [MathSciNet] [Google Scholar]
  21. M. Fannes and D. Petz, Perturbation of Wigner matrices and a conjecture. Proc. Amer. Math. Soc. 131 (2003) 1981–1988. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Grone, C.R. Johnson, E.M. Sa and H. Wolkowicz, Normal matrices. Linear Algebra Appl. 87 (1987) 213–225. [CrossRef] [MathSciNet] [Google Scholar]
  23. L. Gurvits, The Van der Waerden conjecture for mixed discriminants. Adv. Math. 200 (2006) 435–454. [CrossRef] [MathSciNet] [Google Scholar]
  24. L. Gurvits, A proof of hyperbolic Van der Waerden conjecture: the right generalization is the ultimate simplification. Preprint (2006). [Google Scholar]
  25. D. Hägele, Proof of the cases Formula of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture. J. Stat. Phys. 127 (2007) 1167–1171. [CrossRef] [MathSciNet] [Google Scholar]
  26. O. Hanner and H. Radstrom, A generalization of a theorem of Fenchel. Proceedings of the American Mathematical Society 2 (1951) 589–593. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Hansen, Trace functions as Laplace transforms. J. Math. Phys. 47 (2006) 043504. [CrossRef] [MathSciNet] [Google Scholar]
  28. D.P. Hardin and E.B. Saff, Discretizing manifolds via minimum energy points. Notices Amer. Math. Soc. 51 (2004) 1186–1194. [MathSciNet] [Google Scholar]
  29. S. He, Z.-Q. Luo, J. Nie and S. Zhang, Semidefinite relaxation bounds for indefinite homogeneous quadratic optimization. Technical report, Department of systems engineering and engineering management, the Chinese University of Hong-Kong (2007). [Google Scholar]
  30. C. Hillar, Advances on the Bessis-Moussa-Villani trace conjecture. Linear Algebra Appl. 426 (2007) 130–142. [CrossRef] [MathSciNet] [Google Scholar]
  31. C. Hillar and C.R. Johnson, On the positivity of the coefficients of a certain polynomial defined by two positive definite matrices. J. Statist. Phys. 118 (2005) 781–789. [CrossRef] [Google Scholar]
  32. J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273. [CrossRef] [MathSciNet] [Google Scholar]
  33. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I, Grundlehren der mathematischen Wissenschaften 305. Springer-Verlag (1993); 2nd edition in 1996. [Google Scholar]
  34. R. Holzman and D.J. Kleitman, On the product of sign vectors and unit vectors. Combinatorica 12 (1992) 303–316. [CrossRef] [MathSciNet] [Google Scholar]
  35. R.A. Horn and C.R. Johnson, Matrix analysis. Cambridge University Press (1985). [Google Scholar]
  36. H.-X. Huang, P. Pardalos and Z.-J. Shen, A point balance algorithm for the spherical code problem. J. Global Optim. 19 (2001) 329–344. [CrossRef] [MathSciNet] [Google Scholar]
  37. C.R. Johnson and C.J. Hillar, Eigenvalues of words in two positive definite letters. SIAM J. Matrix Anal. Appl. 23 (2002) 916–928. [CrossRef] [MathSciNet] [Google Scholar]
  38. C.R. Johnson, S. Leichenauer, P. McNamara and R. Costas, Principal minor sums of Formula . Linear Algebra Appl. 411 (2005) 386–389. [CrossRef] [MathSciNet] [Google Scholar]
  39. H. Joris, Le chasseur perdu dans la forêt : un problème de géométrie plane. Elem. Math. 35 (1980) 1–14. [MathSciNet] [Google Scholar]
  40. D. Knuth, A permanent inequality. Amer. Math. Monthly 88 (1981) 731–740. [CrossRef] [MathSciNet] [Google Scholar]
  41. A.B.J. Kuijlaars and E.B. Saff, Asymptotics for minimal discrete energy on the sphere. Trans. Amer. Math. Soc. 350 (1998) 523–538. [CrossRef] [MathSciNet] [Google Scholar]
  42. J.C. Lagarias, The Van der Waerden conjecture: two soviet solutions. Notices Amer. Math. Soc. 29 (1982) 130–133. [Google Scholar]
  43. E.H. Lieb and R. Seiringer, Equivalent forms of the Bessis-Moussa-Villani conjecture. J. Statist. Phys. 115 (2004) 185–190. [CrossRef] [MathSciNet] [Google Scholar]
  44. M. Marcus and M. Newman, On the minimum of the permanent of a doubly stochastic matrix. Duke Math. J. 26 (1959) 61–72. [CrossRef] [MathSciNet] [Google Scholar]
  45. H. Minc, Permanents, Encyclopedia of Mathematics and its Applications 6. Addison-Wesley, Reading, Mass (1978). [Google Scholar]
  46. A. Mouchet, Bounding the ground-sate energy of a many-body system with the differential method. Nuclear Phys. A 765 (2006) 319–341. [CrossRef] [Google Scholar]
  47. A. Mouchet, Upper and lower bounds for an eigenvalue associated with a positive eigenvector J. Math. Phys. 47 (2006) 022109. [Google Scholar]
  48. P. Moussa, On the representation of Formula as a Laplace transform. Rev. Math. Phy. 12 (2000) 621–655. [Google Scholar]
  49. P.J. Nahin, When least is best. Princeton University Press (2004). [Google Scholar]
  50. Y. Nesterov and A. Nemirovski, Interior-point polynomial algorithms in convex programming. SIAM Studies in Applied Mathematics (1994). [Google Scholar]
  51. D. Niven, Maxima and minima without calculus. Reprinted by the Mathematical Association of America (2006). [Google Scholar]
  52. J.D. Pinter, Globally optimized spherical point arrangements: model variants and illustrative results. Ann. Oper. Res. 104 (2001) 213–230. [CrossRef] [MathSciNet] [Google Scholar]
  53. E.A. Rakhmanov, E.B. Saff and Y. Zhou, Minimal discrete energy on the sphere. Math. Res. Lett. 1 (1994) 647–662. [MathSciNet] [Google Scholar]
  54. E.B. Saff and A.B.J. Kuijlaars, Distributing many points on the sphere. Math. Intelligencer 19 (1997) 5–11. [Google Scholar]
  55. S. Smale, Mathematical problems for the next century. Math. Intelligencer 20 (1998) 7–15. [CrossRef] [MathSciNet] [Google Scholar]
  56. W.J.H. Stortelder, J.J.B. de Swart and J.D. Pinter, Finding elliptic Fekete points sets: two numerical approaches. J. Comput. Appl. Math. 130 (2001) 205–216. [CrossRef] [MathSciNet] [Google Scholar]
  57. P.L. Takouda, Problèmes d'approximation linéaires coniques : Approches par projections et via Optimisation sous contraintes de semidéfinie positivité. Ph.D. thesis, Paul Sabatier University, Toulouse, France (2003). [Google Scholar]
  58. J.H. Van Lint, Notes on Egorychev's proof of the Van der Waerden conjecture. Linear Algebra Appl. 39 (1981) 1–8. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.