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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Enumerative problems (combinatorial problems) in algebraic geometry, Plane and space curves, Real algebraic sets, Combinatorial aspects of tropical varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Lasserre J.-B., Putinar M.: Positivity and optimization for semi-algebraic functions. SIAM. J. Optim. 20, 3364--3383 (2010) Semialgebraic sets and related spaces, Semidefinite programming, Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) G. Valette, Lipschitz triangulations, Illinois J. Math. 49 (2005), no. 3, 953-979. Real algebraic sets, Real-analytic and semi-analytic sets, Triangulation and topological properties of semi-analytic and subanalytic sets, and related questions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) A. Gabrielov. Multiplicity of a zero of an analytic function on a trajectory of a vector field. In: \textit{The Arnoldfest (Toronto, ON, 1997)}, Vol. 24 of \textit{Fields Inst. Commun}. Amer. Math. Soc., Providence (1999), pp. 191-200. Semi-analytic sets, subanalytic sets, and generalizations, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Becher, Karim; Grimm, David; Van Geel, Jan: Sums of squares in algebraic function fields over a complete discretely valued field, Pacific J. Math. 267, No. 2, 257-276 (2014) Quadratic forms over general fields, Forms over real fields, Sums of squares and representations by other particular quadratic forms, Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Transcendental field extensions, Algebraic functions and function fields in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Labs, O.: A list of challenges for real algebraic plane curve visualization software, The IMA volumes in mathematics and its applications 151, 137-164 (2010) Computational aspects of algebraic curves, Special algebraic curves and curves of low genus, Singularities in algebraic geometry, Real algebraic sets, Computer-aided design (modeling of curves and surfaces)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Special algebraic curves and curves of low genus
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Plane and space curves, Real algebraic sets, Topology of real algebraic varieties, Convex sets in \(2\) dimensions (including convex curves), Convex sets in \(3\) dimensions (including convex surfaces), Convex sets in \(n\) dimensions (including convex hypersurfaces)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Mondal, P., Compactifications of \(\mathbb{C}^{2}\) via pencils of jets of curves, C.R. Math. Acad. Sci. Soc. R. Can., 34, 79-96, (2012) Rational and ruled surfaces, Compactification of analytic spaces, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Compactifications; symmetric and spherical varieties, Singularities of curves, local rings, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) L. Bröcker, Families of semialgebraic sets and limits, In: ``Real Algebraic Geometry'' (Rennes 1991), M. Coste - L. Mahé - M.-F. Roy (eds.), Lecture Notes in Math., 1524, Springer-Verlag, Berlin, 1992, pp. 145-162. Zbl0849.14022 MR1226248 Semialgebraic sets and related spaces, Real algebraic sets, Ordered fields
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Izquierdo, M.; Shaska, T., Cyclic curves over the reals, (Beshajs, L.; etal., Advances on Superelliptic Curves and Their Applications, (2015), IOS Press), 70-83 Automorphisms of curves, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) T. Ekedahl, B. Shapiro, and M. Shapiro, ''First steps towards total reality of meromorphic functions,'' Mosc. Math. J., vol. 6, iss. 1, pp. 95-106, 222, 2006. Real algebraic sets, Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) I. Itenberg and E. Shustin, Newton polygons and singular points of real polynomial vector fields , C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 963--968. Toric varieties, Newton polyhedra, Okounkov bodies, Real algebraic sets, Singularities in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Becker, Sums of powers in rings and the real holomorphy ring, J. Reine Angew. Math. 480 pp 71-- (1996) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Algebraic theory of quadratic forms; Witt groups and rings, Real algebraic and real-analytic geometry, Dedekind, Prüfer, Krull and Mori rings and their generalizations
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Convex sets in \(n\) dimensions (including convex hypersurfaces), Multilinear algebra, tensor calculus, Spherical and hyperbolic convexity, Packing and covering in \(n\) dimensions (aspects of discrete geometry), Real algebraic sets, Asymptotic theory of convex bodies
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Enumerative problems (combinatorial problems) in algebraic geometry, Classical problems, Schubert calculus, Grassmannians, Schubert varieties, flag manifolds, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Delzell, C.N.; González-Vega, L.; Lombardi, H., A continuous and rational solution to hilbert's 17th problem and several cases of the positivstellensatz, (), 61-75 Relevant commutative algebra, Polynomial rings and ideals; rings of integer-valued polynomials, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Andrzej Łȩcki and Zbigniew Szafraniec, An algebraic method for calculating the topological degree, Topology in nonlinear analysis (Warsaw, 1994) Banach Center Publ., vol. 35, Polish Acad. Sci. Inst. Math., Warsaw, 1996, pp. 73 -- 83. Degree, winding number, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) E. Mukhin and V. Tarasov, \textit{Lower bounds for numbers of real solutions in problems of Schubert calculus}, 2014, arXiv:1404.7194. Classical problems, Schubert calculus, Grassmannians, Schubert varieties, flag manifolds, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Kharlamov, Viatcheslav; Răsdeaconu, Rareş, Counting real rational curves on \(K3\) surfaces, Int. Math. Res. Not. IMRN, 14, 5436-5455, (2015) Enumerative problems (combinatorial problems) in algebraic geometry, \(K3\) surfaces and Enriques surfaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1007/BF02677463 Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Local analytic geometry, Computational aspects of higher-dimensional varieties, Real algebraic sets, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Plane and space curves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Bajaj C.L., Xu G.L.: Piecewise rational approximations of real algebraic curves. J. Comput. Math. 15, 55--71 (1997) Computer-aided design (modeling of curves and surfaces), Real algebraic sets, Approximation by rational functions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) González-Vega, Laureano; Lombardi, Henri, A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field, J. Pure Appl. Algebra, 90, 2, 167-188, (1993) Ordered fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Hoffmann, D. W., \textit{motivic equivalence and similarity of quadratic forms}, Doc. Math., Extra Volume, 265-275, (2015) Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), (Equivariant) Chow groups and rings; motives
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Damour, S.: Sur l'algébricité des applications holomorphes. C. R. Acad. sci. Paris, ser. I 332, 491-496 (2001) Real algebraic sets, Real submanifolds in complex manifolds, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Polynomial optimization, Nonlinear programming, Combinatorial aspects of matroids and geometric lattices, Convex sets in \(n\) dimensions (including convex hypersurfaces)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Topology of real algebraic varieties, Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic sets, Geometric probability and stochastic geometry, Random matrices (probabilistic aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Basu, S., Roy, M.F., Safey El Din, M., Schost, É.: A baby step-giant step roadmap algorithm for general algebraic sets. Found. Comput. Math. 14(6), 1117--1172 (2014) Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic sets, Symbolic computation and algebraic computation
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Collections of abstracts of lectures, Proceedings of conferences of miscellaneous specific interest, Field arithmetic, Valuations and their generalizations for commutative rings, Diophantine equations, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic problems in algebraic geometry; Diophantine geometry, Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations, Decidability of theories and sets of sentences, Model theory, Computability and recursion theory
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Sottile, F., Some real and unreal enumerative geometry for flag manifolds, Michigan math. J., 48, 573-592, (2000) Enumerative problems (combinatorial problems) in algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Real algebraic sets, Computational aspects in algebraic geometry, Numerical aspects of computer graphics, image analysis, and computational geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Viro, O.; Turaev, V. (ed.); Vershik, A. (ed.), Encomplexing the writhe, 241-256, (2001), Providence, RI Plane and space curves, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [HJ3] D. Haran and M. Jarden,The absolute Galois group of a pseudo real closed algebraic field, Pacific J. Math.123 (1986), 55--69. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Separable extensions, Galois theory, Rational points, Limits, profinite groups
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Polynomials in real and complex fields: location of zeros (algebraic theorems)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) C. T. C. Wall, ''Duality of real projective plane curves: Klein's equation,'' Preprint. Singularities of curves, local rings, Real algebraic sets, Computational aspects of algebraic curves, Projective techniques in algebraic geometry, Grassmannians, Schubert varieties, flag manifolds
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Nabutovsky, Isotopies and nonrecursive functions in real algebraic geometry in Real Analytic and Algebraic Geometry pp 194-- (1990) Real algebraic sets, Isotopy in differential topology, Applications of computability and recursion theory, Homotopy theory and fundamental groups in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J.-J. Risler, Construction d'hypersurfaces réelles (d'après Viro) , Astérisque 216 (1993), 69--86., Séminaire Bourbaki 1992/93, exp. no. 763. Topology of real algebraic varieties, Real algebraic sets, Hypersurfaces and algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Seppälä, M, Real algebraic curves in the moduli space of complex curves, Compositio Math., 74, 259-283, (1990) Families, moduli of curves (algebraic), Real algebraic sets, Complex-analytic moduli problems, Algebraic moduli of abelian varieties, classification
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) D.J. Bates, F. Sottile, Khovanskii--Rolle continuation for real solutions. www.math.tamu.edu/\(\sim\)sottile/stories/Rolle/ , www.nd.edu/\(\sim\)dbates1/Rolle/ . Real algebraic sets, Computational aspects in algebraic geometry, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) G. W. Brumfiel, Witt rings and \?-theory, Rocky Mountain J. Math. 14 (1984), no. 4, 733 -- 765. Ordered fields and real algebraic geometry (Boulder, Colo., 1983). Real algebraic and real-analytic geometry, General binary quadratic forms, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real-analytic and semi-analytic sets, Real algebra, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ghezzi, L.; Tài Hà, H.; Kashcheyeva, O., Toroidalisation of generating sequences in dimension two function fields, J. Algebra, 301, 838-866, (2006) Local structure of morphisms in algebraic geometry: étale, flat, etc., Valuations and their generalizations for commutative rings, Rational and birational maps, Singularities in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Elliptic curves, Real algebraic sets, Special divisors on curves (gonality, Brill-Noether theory), Divisors, linear systems, invertible sheaves, Projective analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Extension theory of commutative rings, Valuation rings, Local structure of morphisms in algebraic geometry: étale, flat, etc., Valuations and their generalizations for commutative rings, Commutative ring extensions and related topics, Morphisms of commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Jeffrey, LC; Mare, A-L, Products of conjugacy classes in SU(2), Canad. Math. Bull., 48, 90, (2005) Algebraic moduli problems, moduli of vector bundles, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Algebraic cycles, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Specification and verification (program logics, model checking, etc.), Logic in computer science, Interpolation, preservation, definability, Real algebraic sets, Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) --------, Invariants of real symplectic \(4\)-manifolds and lower bounds in real enumerative geometry, Invent. Math. 162 (2005), 195--234. Enumerative problems (combinatorial problems) in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Symplectic manifolds (general theory), Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fernando, On open and closed morphisms between semialgebraic sets, Proc. Amer. Math. Soc. 140 (4) pp 1207-- (2012) Semialgebraic sets and related spaces, Real-valued functions in general topology, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Chain conditions, finiteness conditions in commutative ring theory
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) John P. D'Angelo, Real and complex geometry meet the Cauchy-Riemann equations, Analytic and algebraic geometry, IAS/Park City Math. Ser., vol. 17, Amer. Math. Soc., Providence, RI, 2010, pp. 77 -- 182. Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Holomorphic mappings and correspondences, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Plane and space curves, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) V. Powers, \textit{Positive Polynomials and Sums of Squares: Theory and Practice}, (2015). Formal methods and deformations in algebraic geometry, Real algebraic sets, Sums of squares and representations by other particular quadratic forms, Semidefinite programming
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Algebraic moduli problems, moduli of vector bundles, Structure of modular groups and generalizations; arithmetic groups, Discrete subgroups of Lie groups, Real algebraic sets, Period matrices, variation of Hodge structure; degenerations, Relations with algebraic geometry and topology, Relations with arrangements of hyperplanes, Structure of families (Picard-Lefschetz, monodromy, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Dajano Tossici, \emph{Essential dimension of group schemes over a local scheme}, J. Algebra 492 (2017), 1--27. DOI 10.1016/j.jalgebra.2017.07.023; zbl 06794858; MR3709138; arxiv 1602.07187 Group schemes, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Algebraic moduli of abelian varieties, classification, Real algebraic sets, Homogeneous spaces and generalizations, Classical groups (algebro-geometric aspects), Linear algebraic groups over the reals, the complexes, the quaternions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) S. Podkorytov, ''The mean value of the Euler characteristic of a random algebraic hypersurface,'' Algebra Analiz, 11, 185--193 (1999). Real algebraic sets, Group actions on varieties or schemes (quotients), Real-analytic and semi-analytic sets, Hypersurfaces and algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Divisors, linear systems, invertible sheaves, Global theory and resolution of singularities (algebro-geometric aspects), Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Z.~Izhakian, M.~Knebusch, and L.~Rowen, Dominance and transmissions in supertropical valuation theory, {\em Comm. in Algebra}, 41(7):2736--2782, 2013 Valuations and their generalizations for commutative rings, Valuation rings, Valuations, completions, formal power series and related constructions (associative rings and algebras), Semirings, Logical aspects of lattices and related structures, Complete lattices, completions, Semifields
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Secant varieties, tensor rank, varieties of sums of powers, Projective techniques in algebraic geometry, Real algebraic sets, Computational aspects in algebraic geometry, Multilinear algebra, tensor calculus
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valuations and their generalizations for commutative rings, General valuation theory for fields, Complete rings, completion, Global theory and resolution of singularities (algebro-geometric aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Homological dimension and commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valuations and their generalizations for commutative rings, Ramification problems in algebraic geometry, Birational geometry, Formal power series rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Schicho, J.: Elementary theory of del Pezzo surfaces. Computational methods for algebraic spline surfaces, 77-94 (2005) Rational and ruled surfaces, Computational aspects of algebraic surfaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Topology of real algebraic varieties, Plane and space curves, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) A. B. Korchagin and G. M. Polotovskii (Polotovskiy), ''On arrangements of a plane real quintic curve with respect to a pair of lines,'' Commun. Contemp. Math., 5, 1--24 (2003). Real algebraic sets, Plane and space curves, Topology of real algebraic varieties, Questions of classical algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.), Other designs, configurations, Association schemes, strongly regular graphs, Real algebraic sets, Combinatorial aspects of matrices (incidence, Hadamard, etc.), Combinatorial aspects of finite geometries, Extremal set theory, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) N. \textsc{Bourbaki}, \textit{Algèbre commutative}, Masson, Paris, 1985, chapitres 1 à 7. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Valuations and their generalizations for commutative rings, Divisors, linear systems, invertible sheaves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Abiev, N.A., Arvanitoyeorgos, A., Nikonorov, Y.G., Siasos, P.: The dynamics of the Ricci flow on generalized Wallach spaces. Differ. Geom. Appl. \textbf{35}(Suppl.), 26-43 (2014) Differential geometry of homogeneous manifolds, Dynamics induced by flows and semiflows, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) R. Ghiloni, Rigidity and moduli space in Real Algebraic Geometry, Math. Ann. 335 (2006), 751-766. Zbl1098.14045 MR2232015 Real algebraic sets, Nash functions and manifolds
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1007/BF03322485 Field extensions, Model theory of fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Decidability of theories and sets of sentences, Model-theoretic algebra, Ordered fields, Quantifier elimination, model completeness, and related topics, Algebraic number theory: local fields, Dedekind, Prüfer, Krull and Mori rings and their generalizations
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Vector bundles on curves and their moduli, Real algebraic sets, Coverings of curves, fundamental group
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Plane and space curves, Curves in Euclidean and related spaces, Real algebraic sets, Projective techniques in algebraic geometry, Classical problems, Schubert calculus
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Mir, Nordine, Artin's approximation theorems and Cauchy-Riemann geometry, Methods Appl. Anal., 1073-2772, 21, 4, 481-502, (2014) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, CR structures, CR operators, and generalizations, Analysis on CR manifolds, Real submanifolds in complex manifolds, Real-analytic manifolds, real-analytic spaces, Real-analytic sets, complex Nash functions, Real algebraic sets, Real-analytic and semi-analytic sets, Nash functions and manifolds
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Effectivity, complexity and computational aspects of algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Putinar, M., Scheiderer, C.: Multivariate moment problems: geometry and indeterminateness. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) \textbf{5}(2), 137-157 (2006) Moment problems, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valued fields, Semialgebraic sets and related spaces, Polynomials in real and complex fields: location of zeros (algebraic theorems), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Effectivity, complexity and computational aspects of algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Syzygies, resolutions, complexes and commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fernando, JF, On the sustitution theorem for rings of semi-algebraic functions, J. Inst. Math. Jussieu, 14, 857-894, (2015) Semialgebraic sets and related spaces, Real-valued functions in general topology, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Chain conditions, finiteness conditions in commutative ring theory
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Topology of real algebraic varieties, Linear algebraic groups over the reals, the complexes, the quaternions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Singularities in algebraic geometry, Complex surface and hypersurface singularities, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ch. Ferrier, Hubert's 17th problem and best dual bounds in quadratic minimization. Cybernetics and System Analysis 5 ( 1998) 76-91. Zbl0972.13017 MR1712046 Real algebra, Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Gouveia, J.; Thomas, R. R.: Spectrahedral approximations of convex hulls of algebraic sets, MOS-SIAM series on optimization 13, 293-340 (2012) Semidefinite programming, Computational aspects of higher-dimensional varieties, Real algebraic sets, Convex programming
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) I. Meguerditchian, Géométrie du discriminant réel et des polynômes hyperboliques, Thèse de doctorat, Univ. de Rennes I, soutenue le 24.01.1991 Differentiable maps on manifolds, Theory of singularities and catastrophe theory, Low-dimensional topology of special (e.g., branched) coverings, Real algebraic sets, Elementary questions in algebraic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Algebraic theory of quadratic forms; Witt groups and rings, Real-analytic and semi-analytic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Topology of real algebraic varieties, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Spivakovsky, M.: Valuations, the linear Artin approximation theorem and convergence of formal functions. Álxebra 54, 237-254 (1990) Valuations and their generalizations for commutative rings, Local deformation theory, Artin approximation, etc.
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Singularities of holomorphic vector fields and foliations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Dynamical aspects of holomorphic foliations and vector fields, Structure of families (Picard-Lefschetz, monodromy, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Lerario, A; Lundberg, E, Statistics on hilbert's sixteenth problem, Int. Math. Res. Not., 2015, 4293-4321, (2015) Real algebraic sets, Topology of real algebraic varieties, Geometric probability and stochastic geometry, Spherical harmonics
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Symbolic computation and algebraic computation, Solving polynomial systems; resultants, Real algebraic sets, Semidefinite programming
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Heintz, J., Roy, M.-F., Solernó, P.: Single exponential path finding in semialgebraic sets. I. The case of a regular bounded hypersurface. In: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Tokyo, 1990). Lecture Notes in Computer Science, vol. 508, pp. 180-196. Springer, Berlin (1991) Real algebraic sets, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), Semialgebraic sets and related spaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Polynomials, rational functions in real analysis, Real algebraic sets, Real-analytic functions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Bochnak and W. Kucharz, The Weierstrass approximation theorem and a characterization of the unit circle, Proc. Amer. Math. Soc. 127 (1999), 1571-1574. Zbl0912.14024 MR1653417 Real algebraic sets, Rational and birational maps
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Spivakovsky (M.).- Valuations in function fields of surfaces. Amer. J. Math., 112(1):107-156 (1990). Zbl0716.13003 MR1037606 Valuations and their generalizations for commutative rings, Surfaces and higher-dimensional varieties, Local rings and semilocal rings, Commutative Noetherian rings and modules
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Plane and space curves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) C. Scheiderer, \textit{Distinguished representations of non-negative polynomials,} J. Algebra, 289 (2005), pp. 558--573. Real algebraic sets, Real algebra, Sums of squares and representations by other particular quadratic forms
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Bajaj C. and Royappa A. (1995). Finite representations of real parametric curves and surfaces.Technical Report, CAPO report CER-92-28, Purdue University. Also in International J. Comput. Geometry Appl. 5: 313--326 Computational aspects of algebraic curves, Computer graphics; computational geometry (digital and algorithmic aspects), Real algebraic sets, Computational aspects of algebraic surfaces, Computational aspects of higher-dimensional varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Discriminantal varieties and configuration spaces in algebraic topology, Real algebraic sets, Classification of homotopy type, Artificial intelligence for robotics
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) D'Angelo, J.P., Invariant CR mappings, (Complex analysis, Trends math., (2010), Birkhäuser/Springer Basel AG Basel), 95-107 Real submanifolds in complex manifolds, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, Proper holomorphic mappings, finiteness theorems, Real algebraic sets
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