Andrei Gabrielov
Publications listed in MathSciNet
| [1] | A. Eremenko, A. Gabrielov, M. Shapiro, and A. Vainshtein. Rational functions and real Schubert calculus. Proc. Amer. Math. Soc., 134(4):949-957 (electronic), 2006. |
| [2] | Ilya Zaliapin, Henry Hang Lam Wong, and Andrei Gabrielov. Inverse cascade in a percolation model: hierarchical description of time-dependent scaling. Phys. Rev. E (3), 71(6):066118, 13, 2005. |
| [3] | Andrei Gabrielov and Nicolai Vorobjov. Betti numbers of semialgebraic sets defined by quantifier-free formulae. Discrete Comput. Geom., 33(3):395-401, 2005. |
| [4] | Ilya Zaliapin, Andrei Gabrielov, and Vladimir Keilis-Borok. Multiscale trend analysis. Fractals, 12(3):275-292, 2004. |
| [5] | Andrei Gabrielov and Nicolai Vorobjov. Complexity of computations with Pfaffian and Noetherian functions. In Normal forms, bifurcations and finiteness problems in differential equations, volume 137 of NATO Sci. Ser. II Math. Phys. Chem., pages 211-250. Kluwer Acad. Publ., Dordrecht, 2004. |
| [6] | A. Gabrielov, N. Vorobjov, and T. Zell. Betti numbers of semialgebraic and sub-Pfaffian sets. J. London Math. Soc. (2), 69(1):27-43, 2004. |
| [7] | Andrei Gabrielov. Relative closure and the complexity of Pfaffian elimination. In Discrete and computational geometry, volume 25 of Algorithms Combin., pages 441-460. Springer, Berlin, 2003. |
| [8] | Andrei Gabrielov and Thierry Zell. On the number of connected components of the relative closure of a semi-Pfaffian family. In Algorithmic and quantitative real algebraic geometry (Piscataway, NJ, 2001), volume 60 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 65-75. Amer. Math. Soc., Providence, RI, 2003. |
| [9] | A. Eremenko and A. Gabrielov. Degrees of real Wronski maps. Discrete Comput. Geom., 28(3):331-347, 2002. |
| [10] | A. Eremenko and A. Gabrielov. Counterexamples to pole placement by static output feedback. Linear Algebra Appl., 351/352:211-218, 2002. Fourth special issue on linear systems and control. |
| [11] | A. Eremenko and A. Gabrielov. Pole placement static output feedback for generic linear systems. SIAM J. Control Optim., 41(1):303-312 (electronic), 2002. |
| [12] | A. Eremenko and A. Gabrielov. Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry. Ann. of Math. (2), 155(1):105-129, 2002. |
| [13] | Alexandre Eremenko and Andrei Gabrielov. The Wronski map and Grassmannians of real codimension 2 subspaces. Comput. Methods Funct. Theory, 1(1):1-25, 2001. |
| [14] | Andrei Gabrielov and Nicolai Vorobjov. Complexity of cylindrical decompositions of sub-Pfaffian sets. J. Pure Appl. Algebra, 164(1-2):179-197, 2001. Effective methods in algebraic geometry (Bath, 2000). |
| [15] | Andrei Gabrielov. Multiplicity of a zero of an analytic function on a trajectory of a vector field. In The Arnoldfest (Toronto, ON, 1997), volume 24 of Fields Inst. Commun., pages 191-200. Amer. Math. Soc., Providence, RI, 1999. |
| [16] | A. Gabrielov, W. I. Newman, and D. L. Turcotte. Exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling. Phys. Rev. E (3), 60(5, part A):5293-5300, 1999. |
| [17] | Andrei Gabrielov and Askold Khovanskii. Multiplicity of a Noetherian intersection. In Geometry of differential equations, volume 186 of Amer. Math. Soc. Transl. Ser. 2, pages 119-130. Amer. Math. Soc., Providence, RI, 1998. |
| [18] | Andrei Gabrielov, Frédéric Jean, and Jean-Jacques Risler. Multiplicity of polynomials on trajectories of polynomial vector fields in C3. In Singularities Symposium-ojasiewicz 70 (Kraków, 1996; Warsaw, 1996), volume 44 of Banach Center Publ., pages 109-121. Polish Acad. Sci., Warsaw, 1998. |
| [19] | A. Gabrielov. Frontier and closure of a semi-Pfaffian set. Discrete Comput. Geom., 19(4):605-617, 1998. |
| [20] | Andrei Gabrielov. Complements of subanalytic sets and existential formulas for analytic functions. Invent. Math., 125(1):1-12, 1996. |
| [21] | Andrei Gabrielov. Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy. Math. Res. Lett., 2(4):437-451, 1995. |
| [22] | A. Gabrièlov. Multiplicities of Pfaffian intersections, and the lojasiewicz inequality. Selecta Math. (N.S.), 1(1):113-127, 1995. |
| [23] | A. Gabrièlov and N. Vorobjov. Complexity of stratifications of semi-Pfaffian sets. Discrete Comput. Geom., 14(1):71-91, 1995. |
| [24] | Andrei Gabrielov, Jean-Marie Lion, and Robert Moussu. Ordre de contact de courbes intégrales du plan. C. R. Acad. Sci. Paris Sér. I Math., 319(3):219-221, 1994. |
| [25] | Andrei Gabrielov. Avalanches, sandpiles and Tutte decomposition. In The Gelfand Mathematical Seminars, 1990-1992, pages 19-26. Birkhäuser Boston, Boston, MA, 1993. |
| [26] | Andrei Gabrielov. Abelian avalanches and Tutte polynomials. Phys. A, 195(1-2):253-274, 1993. |
| [27] | I. G. Petrovski\i. Izbrannye trudy. “Nauka”, Moscow, 1986. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaya geometriya. [Systems of partial differential equations. Algebraic geometry], Edited and with a preface by V. I. Arnold, N. N. Bogolyubov, A. N. Kolmogorov, O. A. Ole\i nik, S. L. Sobolev and A. N. Tikhonov, Compiled by Ole\i nik, With commentaries by Kolmogorov, L. R. Volevich, V. Ya. Ivri\i, I. M. Gelfand, G. E. Shilov, Ole\i nik, V. P. Palamodov, A. M. Gabrièlov and V. M. Kharlamov. |
| [28] | L. Gording. Sharp fronts of paired oscillatory integrals. Uspekhi Mat. Nauk, 38(6(234)):85-96, 1983. Translated from the English by A. M. Gabrièlov. |
| [29] | A. M. Gabrièlov. Polar curves and intersection matrices of singularities. Invent. Math., 54(1):15-22, 1979. |
| [30] | A. M. Gabrièlov. Characteristic Pontrjagin cycles in a Cech complex. Funktsional. Anal. i Prilozhen., 13(2):1-10, 96, 1979. |
| [31] | A. M. Gabrièlov. Combinatorial formulas for Pontrjagin classes and GL-invariant chains. Funktsional. Anal. i Prilozhen., 12(2):1-7, 95, 1978. |
| [32] | D. B. Fuchs, A. M. Gabrièlov, and I. M. Gelfand. The Gauss-Bonnet theorem and the Atiyah-Patodi-Singer functionals for the characteristic classes of foliations. Topology, 15(2):165-188, 1976. |
| [33] | A. M. Gabrièlov, I. M. Gelfand, and M. V. Losik. Atiyah-Patodi-Singer functionals for the characteristic classes of a tangent bundle. Funkcional. Anal. i Prilozen., 10(2):13-28, 1976. |
| [34] | A. M. Gabrièlov, I. M. Gelfand, and M. V. Losik. A local combinatorial formula for the first Pontrjagin class. Funkcional. Anal. i Prilozen., 10(1):14-17, 1976. |
| [35] | A. M. Gabrièlov and A. G. Kušnirenko. Description of deformations with constant Milnor number for homogeneous functions. Funkcional. Anal. i Prilozen., 9(4):67-68, 1975. |
| [36] | A. M. Gabrièlov, I. M. Gelfand, and M. V. Losik. Combinatorial computation of characteristic classes. I, II. Funkcional. Anal. i Prilozen., 9(2):12-28; ibid. 9 (1975), no. 3, 5-26, 1975. |
| [37] | A. M. Gabrièlov. Bifurcations, Dynkin diagrams and the modality of isolated singularities. Funkcional. Anal. i Prilozen., 8(2):7-12, 1974. |
| [38] | A. M. Gabrièlov. Dynkin diagrams of unimodal singularities. Funkcional. Anal. i Prilozen., 8(3):1-6, 1974. |
| [39] | A. M. Gabrièlov, I. M. Gelfand, and M. V. Losik. The combinatorial computation of characteristic classes. Funkcional. Anal. i Prilozen., 9(1):54-55, 1974. |
| [40] | A. M. Gabrièlov. Formal relations among analytic functions. Izv. Akad. Nauk SSSR Ser. Mat., 37:1056-1090, 1973. |
| [41] | A. M. Gabrièlov. Intersection matrices for certain singularities. Funkcional. Anal. i Prilozen., 7(3):18-32, 1973. |
| [42] | B. Malgranz. Analytic spaces. Uspehi Mat. Nauk, 27(1(163)):159-184, 1972. Translated from the English (Enseignement Math. (2) 14(1968), 1-28) by A. M. Gabrièlov. |
| [43] | A. M. Gabrièlov. The formal relations between analytic functions. Funkcional. Anal. i Prilozen., 5(4):64-65, 1971. |
| [44] | A. M. Gabrièlov. A certain theorem of Hörmander. Funkcional. Anal. i Prilozen, 4(2):18-22, 1970. |
| [45] | A. M. Gabrièlov. Projections of semianalytic sets. Funkcional. Anal. i Prilozen., 2(4):18-30, 1968. |