Bibliografia


  1. R. Baier, Extrapolation methods for the computation of set-valued integrals and reachable sets of linear differential inclusions, Zeitschr. Angew. Math. Mech. 74, 1994, No6, 555-557.

  2. R. Baier, Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen, Dissertation, Universitat Bayreuth, Bayreuther Mathematische Schriften, Heft 50 (1995).

  3. R. Baier, E. Farkhi, Directed Sets and Differences of Convex Compact Sets, in Proceedings of the 18 th IFIP Conference on System Modelling and Optimization, Detroit, July 1997.

  4. R. Baier, F. Lempio, Computing Aumann's integral, in Modeling techniques for uncertain systems, Proceedings of a conference held in Sopron, (Ed. A. Kurzhanski, et al.), Sopron, Hungary, July 6-10, 1992, Birkhauser. Prog. Syst. Control Theory. 18, 71-92.

  5. R. Baier, F. Lempio, Approximating reachable sets by extrapolation methods, in Curves and surfaces in geometric design, Papers from the 2nd international conference on curves and surfaces, (Ed. J.-P. Laurent), held in Chamonix-Mont-Blanc, France, June 10-16, 1993, Wellesley.

  6. Chr. Bauer, Minimal and reduced pairs of convex bodies, Geom. Dedicata 62, No.2, 179-192 (1996)

  7. V. F. Demyanov, A. M. Rubinov, Quasidifferential calculus, Optimization Software Inc., Publications Division, New York, (1986).

  8. P. Diamond, P. Kloeden, A. Rubinov, A. Vladimirov, Comperative properties of three metrics in the space of compact convex sets, Set-Valued Analysis 5, 1997, No.3, 267-289

  9. G. Ewald, Combinatorial Convexity and Algebraic Geometry, Graduate Texts in Mathematics, Vol. 168, Springer Verlag, Berlin, Heidelberg, New York (1996).

  10. J. Grzybowski, Minimal pairs of compact convex sets, Archiv der Mathematika 63 (1994) pp. 173-181.

  11. J. Grzybowski, Summands of compact convex sets, Mathematika, 43 (1996), 286-294.

  12. J. Grzybowski, D. Pallaschke, R. Urbański (1999), Minimal pairs representing selections of four linear functions in R 3, submitted to Journal of Convex Analysis

  13. J. Grzybowski, R. Urbański, Minimal pairs of bounded closed convex sets, Studia Math. 126 (1997), 95-99.

  14. J. Grzybowski, R. Urbański, On Convex Class of Pairs of Convex Bodies, Proc. Amer. Math. Soc. 125 (1997), 3397-3401.

  15. J. Grzybowski, R. Urbański, M. Wiernowolski, On Common Summands and Anti-summands of Compact Convex Sets, Bull. Polish Acad. Sci. Math. 47 (1999), 69-76.

  16. L. Hormander, Sur la fonction d' appui des ensembles convexes dans un espace localement convex, Arkiv for Matematik 3 pp. 181-186 (1954).

  17. S. Kaczmarek, Minimal pairs in classes of frustums, Comment. Math. (1999), to uppear.

  18. P. McMullen, The Polytope Algebra. Advances in Mathematics {78} 76-130 (1989).

  19. D. Pallaschke, S. Rolewicz, Sublinear functions which generate the group of normal forms of piecewise smooth Morse functions, Optimization 45 pp. 223-226 (1999).

  20. D. Pallaschke, S. Scholtes, R. Urbański, On minimal pairs of compact convex sets, Bull. Polish Acad. Sci. Math. 39 pp. 1-5 (1991).

  21. D. Pallaschke, S. Scholtes, R. Urbański, The space of convex bodies and quasidifferentiable functions, Function Spaces, Proc. of the Second International Conf. Poznań 1989, Teubner-Texte zur Mathematik, Vol. 120 (1991), 128-132.

  22. D. Pallaschke, R. Urbański, Quasidifferentiable functions and minimal pairs of compact convex sets, Dissertationes Math. 340 (1995), 207-221.

  23. D. Pallaschke, R. Urbański, Quasidifferentiable Functions and Pairs of Convex Compact Sets, Acta math. Vietnamica 22 (1997), 223-245.

  24. D. Pallaschke, R. Urbański, Some criteria for the minimality of pairs of compact convex sets, Zeitschrift fur Operations Research 37 pp. 129-150 (1993).

  25. D. Pallaschke, R. Urbański, Reduction of quasidifferentials and minimal representations, Mathem. Programming, (Series A) 66 pp. 161-180 (1994).

  26. D. Pallaschke, R. Urbański, A continuum of minimal pairs of compact convex sets which are not connected by translations, Journal of Convex Analysis 3, pp. 83-95 (1996).

  27. D. Pallaschke, W. Urbańska, R. Urbański, C-Minimal Pairs of Compact Convex Sets, Journal of Convex Analysis 4, pp. 1-26 (1997).

  28. D. Pallaschke, R. Urbański, Decompositions of Compact Convex Sets, Journal of Convex Analysis 4, pp. 333-342 (1998).

  29. D. Pallaschke, R. Urbański, Invariants of Pairs of Compact Convex Sets, erscheint in Journal of Convex Analysis, (1999).

  30. A. G. Pinsker, The space of convex sets of a locally convex space, Trudy Leningrad Engineering-Economic Institute, 63 (1966) pp. 13-17.

  31. A. M. Rubinov, I. S. Akhundov, Differences of compact sets in the sense of Demyanov and its Application to Non-Smooth Analysis, Optimization 23 (1992) 179-189.

  32. S. Scholtes, On Convex Bodies and Some Applications to Optimization, Mathematical Systems in Economics, Vol.119 (1990), Verlag Anton Hain, Frankfurt am Main.

  33. S. Scholtes, Minimal pairs of convex bodies in two dimensions, Mathematika 39 pp. 267-273 (1992).

  34. R. Urbański, A generalization of the Minkowski-Radstrom-Hormander Theorem, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 24 (1976) pp. 709-715.

  35. R. Urbański, On a family of pairwise convex sets, Comment. Math. 37 (1997), 165-172.

  36. R. Urbański, On Cutting Frustum, Funct. Approximatio. Comment. Math. 25 (1997), 165-172.

  37. R. Urbański, On minimal fractions, Comment. Math. 38 (1998), 149-161.

  38. R. Urbański, On minimal convex pairs of convex compact sets, Archiv der Mathematik 67 pp. 226-238 (1996).

  39. R. Urbański, Pairs of sets with convex union, Collect. Math. 48 (1997), 791-798.

  40. M. Wiernowolski, A criterion for the minimality of pairs of convex compact sets, Comment. Math. 34 (1994), 247-252.

  41. M. Wiernowolski, Minimality in asymmetry classes, Studia Math. 124 (1997), 149-154.

  42. M. Wiernowolski, On Amount of Minimal Pairs, Funct. Approx. Comment. Math. 23 (1994), 35-39.




* Czy istnieją pary minimalne zbiorów wypukłych? * Czy pary minimalne zbiorów wypukłych są jedyne? *
* A co z wielościanami wypukłymi? * Jakie są niezmienniki par minimalnych zbiorów wypukłych? *
* Jak pary minimalne wiążą się z ułamkami? *
* Historia par minimalnych wypukłych zbiorów zwartych *
* Jak się zainteresowaliśmy parami zbiorów wypukłych? *
* Bibliografia * Definicje *
* Strona główna *