Shapiro and Shapiro: Bibliography

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Bibliography

[BB]	R. Brockett and C. Byrnes, Multivariable Nyquist criteria, root loci and pole placement: A geometric viewpoint , IEEE Trans. Automat. Control., AC-26 (1981), 271-284.
[BFZ]	A. Berenstein, S. Fomin, and A. Zelevinsky, Parametrizations of canonical bases and totally positive matrices. Adv. Math., 122 (1996), 49-149.
[By]	C. Byrnes, Pole assignment by output feedback, in Three Decades of Mathematical Systems Theory, H. Nijmeijer and J. M. Schumacher, eds., vol. 135 of Lecture Notes in Control and Inform. Sci., Springer-Verlag, Berlin, 1989, pp. 31-78.
[D]	P. Deitmaier, The Stewart-Gough platform of general geometry can have 40 real postures, in Advances in Robot Kinematics: Analysis and Control, Jordan Lenancic, and Manfred Husty, eds., Kluwer, 1998, pp. 1-10.
[EH]	D. Eisenbud and J. Harris, Divisors on general curves and cuspidal rational curves, Invent. Math., 74 (1983), pp. 371-418.
[EG]	A. Eremenko and A. Gabrielov, Rational functions with real critical points and B. and M. Shapiro conjecture in real enumerative geometrys, Mss., December 1999.
[FRZ]	J.-C. Faugère, Fabrice Rouillier, and Paul Zimmermann, Private communication, 1998.
[Fu]	W. Fulton, Introduction to Intersection Theory in Algebraic Geometry, CBMS 54, AMS, 1996. second edition.
[G-VRRT]	L. Gonzalez-Vega, F. Rouillier, M.F. Roy, and G. Trujillo, Symbolic Recipes for Real Solutions, in Some Tapas of Computer Algebra, A.M. Cohen, H. Cuypers, and H. Sterk, eds., Springer-Verlag, 1999. pp. 34-65.
[HP]	W.V.D. Hodge and D. Pedoe, Methods of Algebraic Geometry, Volume II, Cambridge University Press, 1952.
[HSS]	B. Huber, F. Sottile, and B. Sturmfels, Numerical Schubert Calculus, J. Symb. Comp., 26 (1998), pp. 767-788.
[Kh]	V. Kharlamov, Private communication.
[Kl]	S. Kleiman, The transversality of a general translate, Comp. Math., 28 (1974), pp. 287-297.
[Lö]	C. Löwner, On totally positive matrices, math. Zeitschr., 63 (1955), pp. 266-267.
[RTV]	F.Ronga, A.Tognoli, and T.Vust, The number of conics tangent to 5 given conics: the real case, Rev. Mat. Univ. Complut. Madrid, 10 (1997), pp. 391-421.
[RS]	J. Rosenthal and F. Sottile, Some remarks on real and complex output feedback, Sys. and Control Lett., 33 (1998), pp. 73-80. Documentation of the system we found that is not controllable with real output feedback
[Sc]	H. Schubert, Beziehungen zwischen den linearen Räumen auferlegbaren charakteristischen Bedingungen, Math. Ann., 38 (1891), pp. 588-602.
[So94]	F. Sottile, Real Enumerative Geometry for the Grassmannian of Lines in Projective Space, Ph.D. Thesis, University of Chicago, 1994.
[So96]	, Pieri's formula for flag manifolds and Schubert polynomials, Annales de l'Institut Fourier, 46 (1996), pp. 89-110.
[So97a]	, Enumerative geometry for the real Grassmannian of lines in projective space, Duke Math. J., 87 (1997), pp. 59-85.
[So97b]	, Real enumerative geometry and effective algebraic equivalence, J. Pure Appl. Alg., 117 & 118 (1997), pp. 601-615. Proc., MEGA'96.
[So97c]	, Enumerative geometry for real varieties, in Algebraic Geometry, Santa Cruz 1995, J. Kollár, R. Lazarsfeld, and D. Morrison, eds., vol. 62, Part 1 of Proc. Sympos. Pure Math., Amer. Math. Soc., 1997, pp. 435-447.
[So99]	, The Special Schubert calculus is real, ERA of the AMS, 5 (1999), 35-39.
[So00]	, Real Scubert calculus: Polynomial systems and a conjecture of Shapiro and Shapiro, Experimental Mathematics 9:2 (2000), pp. 161-182.
[So00a]	, Real Rational Curves in Grassmannians, J. Amer. Math. Soc. 13 (2000), 333-341.
[So00b]	, Some real and unreal enumerative geometry for flag manifolds, Michigan Math.J., to appear, 2000.
[St]	B. Sturmfels, Polynomial equations and convex polytopes, Amer. Math. Monthly, 105, (1998), 907--922.
[V]	J. Verschelde, Numerical evidence for a conjecture in real algebraic geometry, Experimental Mathematics, to appear. 1998.