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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.) Nonstandard models in mathematics, Real algebraic sets, Real-analytic and semi-analytic sets, Analytic algebras and generalizations, preparation theorems, Germs of analytic sets, local parametrization
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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.) Skrzyński, M., On basic geometric properties of the cones of nilpotent matrices, Univ. Iagel. Acta Math., 33, 219-228, (1996) Positive matrices and their generalizations; cones of matrices, Real algebraic sets, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Hermitian, skew-Hermitian, and related matrices
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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: 10.1016/S0764-4442(00)01721-3 Real algebraic sets, Complete intersections
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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.) Other nonalgebraically closed ground fields in algebraic geometry, Nash functions and manifolds, Varieties and morphisms, 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.) Parusiński, A.; Szafraniec, Z., Algebraically constructible functions and signs of polynomials, Manuscr. Math., 93, 443-456, (1997) 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.) Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), Real algebraic sets, Rate of convergence, degree of approximation
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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, Integral closure of commutative rings and ideals, Valuations and their generalizations for commutative rings, Dedekind, Prüfer, Krull and Mori rings and their generalizations, Relevant commutative algebra
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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.) Gaffney, T., Araújo dos Santos, R.: Real integral closure and Milnor fibrations. In: Real and Complex Singularities, London Mathematical Society Lecture Note Series, 380, Cambridge University Press, Cambridge, pp. 146-157 (2010) Milnor fibration; relations with knot theory, Topology of analytic spaces, Topology of real algebraic varieties, Local complex singularities, Invariants of analytic local rings, 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.) Lotz, M, On the volume of tubular neighborhoods of real algebraic varieties, Proc. Am. Math. Soc., 143, 1875-1889, (2015) Integral geometry, Real algebraic sets, Geometric probability and stochastic geometry, Conditioning of matrices
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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
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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. I. Degtyarev and V. I. Zvonilov, ''Rigid isotopy classification of real algebraic curves of bidegree (3, 3) on quadrics,'' Mat. Zametki 66(6), 810--815 (1999) [Math. Notes 66 (6), 670--674 (1999) (2000)]. Real algebraic sets, Plane and space curves, 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.) Graded rings, Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Local structure of morphisms in algebraic geometry: étale, flat, etc., Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties, Local complex singularities
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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.) Rational and birational maps, Valuations and their generalizations for commutative rings, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, 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.) Russo, F: The antibirational involutions of the plane and the classification of real del Pezzo surfaces. Algebraic geometry, pp. 289-312. de Gruyter, Berlin (2002) Rational and ruled surfaces, 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.) Bröcker L.: Minimal generation of basic semialgebraic sets. Rky. Mtn. J. Math. 14, 935--938 (1984) Real algebraic and real-analytic geometry, Polynomials in real and complex fields: location of zeros (algebraic theorems), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Enumerative problems (combinatorial problems) 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.) Nash functions and manifolds, 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.) Valuations and their generalizations for commutative rings, 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.) Combinatorial complexity of geometric structures, 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.) Real algebraic sets, Fibrations, degenerations in algebraic geometry, Families, moduli of curves (algebraic)
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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: 10.1016/S0166-8641(98)00084-4 Real algebraic sets, Enumeration in graph theory, Relations of low-dimensional topology with graph theory, Structure of families (Picard-Lefschetz, monodromy, etc.), Riemann surfaces; Weierstrass points; gap sequences
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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.) Kurdyka, K; Rusek, K, Polynomial-rational bijections of \(\mathbb{R}^n\), Proc. Am. Math. Soc., 102, 804-808, (1988) Polynomial rings and ideals; rings of integer-valued polynomials, Rational and birational maps, Real algebraic sets, Real and complex 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.) S.L. Devadoss, \textit{Combinatorial equivalence of real moduli spaces}, \textit{Not. Amer. Math. Soc.}\textbf{51} (2004) 620 [math-ph/0405011]. Real algebraic sets, Families, moduli of curves (algebraic), General geometric structures on low-dimensional 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.) Abhyankar, S; Luengo, I, Spiders and multiplicity sequences, Proc. Amer. Math. Soc., 141, 4071-4085, (2013) Relevant commutative algebra, 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.) ,\textit{Resolution of singularities of threefolds in positive characteristic. II}, J. Algebra 321 (2009), no. 7, 1836--1976.http://dx.doi.org/10.1016/j.jalgebra.2008.11.030.MR2494751 Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties, \(3\)-folds, Rational and birational maps, 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.) Pleśniak, W., Multivariate polynomial inequalities via pluripotential theory and subanalytic geometry methods, Banach center publ., 72, 1, 251-261, (2006) Semi-analytic sets, subanalytic sets, and generalizations, Real algebraic sets, Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs, Plurisubharmonic extremal functions, pluricomplex Green functions, \(C^\infty\)-functions, quasi-analytic functions, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
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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. William Helton and Mihai Putinar, Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization, Operator theory, structured matrices, and dilations, Theta Ser. Adv. Math., vol. 7, Theta, Bucharest, 2007, pp. 229 -- 306. Research exposition (monographs, survey articles) pertaining to operator theory, Several-variable operator theory (spectral, Fredholm, etc.), Linear operator methods in interpolation, moment and extension problems, Moment problems, Semialgebraic sets and related spaces, Real algebra, Linear systems in control theory, Positive matrices and their generalizations; cones of matrices, Linear operator inequalities, 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.) Vaquié, M., Extension d'une valuation, Trans. Amer. Math. Soc., 359, 7, 3439-3481, (2007) Valuations and their generalizations for commutative rings, Valued fields, 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.) Ghiloni, R.: Algebraic obstructions and a complete solution of a rational retraction problem. Proc. amer. Math. soc. 130, 3525-3535 (2002) Real algebraic sets, Nash functions and manifolds, Topology of real algebraic varieties, Real-analytic and Nash 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.) Collections of abstracts of lectures, Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Real algebraic and real-analytic geometry, Proceedings, conferences, collections, etc. pertaining to commutative algebra, Real algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Solving polynomial systems; resultants, Determinantal varieties, Computational aspects of algebraic curves, Combinatorial optimization
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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.) Reznick, B.; Tokcan, N., Binary forms with three different relative ranks, arXiv preprint Forms of degree higher than two, Waring's problem and variants, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Enumerative problems (combinatorial problems) 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.) S. Akbulut and H. King, All compact manifolds are homeomorphic to totally algebraic real algebraic sets, Comment. Math. Helv. 66 (1991), no. 1, 139 -- 149. Real algebraic sets, Differential topology
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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.) Suh, DY, Quotients of real algebraic G varieties and algebraic realization problems, Osaka J. Math., 33, 399-410, (1996) Real algebraic sets, Compact Lie groups of differentiable transformations, Differential topology, Group actions on varieties or schemes (quotients)
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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.) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Real algebraic sets, Classical flows, reactions, etc. in chemistry, Differential algebra, Qualitative investigation and simulation of ordinary differential equation models, Cell biology
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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.) Continuity properties of mappings on manifolds, Polynomials in real and complex fields: location of zeros (algebraic theorems), 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.) Affine geometry, Equisingularity (topological and analytic), 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.) 10. O. SIMON, Aspects quantitatifs de Nullstellensätze et de Positivstellensätze. Nombres de Pythagore, Communications in Algebra, 1989, 17, (3), p. 637-667. Zbl0668.14001 MR981475 Relevant commutative algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Quadratic forms over general 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.) V. A. Krasnov, ''On the Brauer group of a real algebraic surface,''Mat. Zametki [Math. Notes],60, No. 6, 935--938 (1996). Special surfaces, Brauer groups of schemes, 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.) Putinar, M; Schmüdgen, K, Multivariate determinateness, Indiana Univ. Math. J., 57, 2931-2968, (2008) Moment problems, Real algebraic sets, Research exposition (monographs, survey articles) pertaining to integral transforms
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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, Local complex singularities
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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. B. Lasserre, \textit{A sum of squares approximation of nonnegative polynomials}, SIAM J. Optim., 16 (2006), pp. 751--765. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, 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.) 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, 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.) Interpolation in approximation theory, Real algebraic sets, Multidimensional problems
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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.) P. Rostalski and B. Sturmfels, \textit{Dualities in convex algebraic geometry}, Rend. Mat. (7), 30 (2010), pp. 285--327. Semidefinite programming, Real algebraic sets, Convex sets without dimension restrictions (aspects of convex 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.) Carlos Andradas and Jesús Ruiz, Low-dimensional sections of basic semialgebraic sets, Illinois J. Math. 38 (1994), no. 2, 303 -- 326. Semialgebraic sets and related spaces, Enumerative problems (combinatorial problems) in algebraic geometry, 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.) Research exposition (monographs, survey articles) pertaining to field theory, 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.) Zieliński, M., Homotopy properties of some real algebraic maps, Homol. Homotopy Appl., 18, 287-294, (2016) 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.) Abhyankar, S; Artal, E, Algebraic theory of curvettes and dicriticals, Proc. Amer. Math. Soc., 141, 4087-4102, (2013) Valuations and their generalizations for commutative rings, Relevant commutative algebra
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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.) Bochnak, J. and Kucharz, W.: Elliptic curves and real algebraic morphisms (to appear); 5?. Elliptic curves and real algebraic morphisms into the 2-sphere,Bull. Amer. Math. Soc. 25 (1991), 81-87. Real algebraic sets, Topology of real algebraic varieties, Real-valued functions in general topology, Birational geometry, Approximation by polynomials, Algebraic topology on manifolds and differential topology
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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, Enumerative problems (combinatorial problems) in algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Topology of real algebraic varieties, Geometric aspects of tropical varieties, Symplectic manifolds (general 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.) Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic sets, Semialgebraic sets and related spaces, 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.) Choi, S.; Park, B.; Park, S., Pseudograph and its associated real toric manifold, Journal of the mathematical society of Japan, 69, 693-714, (2017) Algebraic topology of manifolds, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Toric varieties, Newton polyhedra, Okounkov bodies, Planar graphs; geometric and topological aspects of graph theory, Simplicial sets and complexes in algebraic topology, Enumeration in graph theory, 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.) Ballico, E.: On the field of definition of vector bundles on real varieties,Geom. Dedicata 47 (1993), 317-325. Real algebraic sets, Relevant commutative algebra, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Topological \(K\)-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.) Jia, X.; Wang, W.; Choi, Y.-K.; Mourrain, B.; Tu, C., Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space, J. symb. comput., 73, C, 221-243, (2016) Symbolic computation and algebraic computation, Projective techniques in algebraic geometry, Real algebraic sets, Computational aspects of algebraic 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.) DOI: 10.1023/B:GEOM.0000024691.03080.d8 Real algebraic sets, Integral 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, Semialgebraic sets and related spaces, Real 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.) 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.) Boucksom, Sébastien; Favre, Charles; Jonsson, Mattias, Valuations and plurisubharmonic singularities, Publ. Res. Inst. Math. Sci., 44, 2, 449-494, (2008) Lelong numbers, Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Non-Archimedean analysis, Modifications; resolution of singularities (complex-analytic 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, Real-analytic manifolds, real-analytic spaces, Topology of infinite-dimensional manifolds, Algebraic topology of 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.) B. Bertrand, E. Brugallé, G. Mikhalkin, Tropical open Hurwitz numbers. Rend. Semin. Mat. Univ. Padova 125, 157-171 (2011) Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic sets, Low-dimensional topology of special (e.g., branched) coverings
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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-analytic and semi-analytic sets, Commutative rings and modules of finite generation or presentation; number of generators, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ideals and multiplicative ideal theory in 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.) Rational and birational maps, Varieties and morphisms, 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.) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Sums of squares and representations by other particular quadratic forms, Convexity of real functions of several variables, 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.) Roy, M. -F.: Computation of the topology of a real curve. Astérisque 192, 17-33 (1990) Computational aspects of algebraic 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.) D. E. Dobbs -R. Fedder -M. Fontana,Abstract Riemann surfaces of integral domains and spectral spaces, Ann. Mat. Pura Appl., (4),148 (1987), pp. 101--115. Arithmetic rings and other special commutative rings, General valuation theory for fields, Integral domains, Valuations and their generalizations for commutative rings, Relevant commutative algebra
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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 functions and function fields in algebraic geometry, Arithmetic theory of algebraic function 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.) B. Reznick, \textit{Some concrete aspects of Hilbert's 17th problem}, in Real Algebraic Geometry and Ordered Structures, Contemp. Math. 253, American Mathematical Society, Providence, RI, 2000, pp. 251--272. Forms over real fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Research exposition (monographs, survey articles) pertaining to number theory, History of number theory, Forms of degree higher than two, History of mathematics in the 20th century, Real algebraic and real-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.) 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.) R. Ghiloni, Second order homological obstructions on real algebraic manifolds, Topology Appl. 154 (2007), 3090-3094. 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.) A. Barvinok and G. Blekherman, \textit{Convex geometry of orbits}, in Combinatorial and Computational Geometry, Math. Sci. Res. Inst. Publ. 52, Cambridge University Press, Cambridge, 2005, pp. 51--77. Convex sets in \(n\) dimensions (including convex hypersurfaces), Calibrations and calibrated geometries, Special polytopes (linear programming, centrally symmetric, etc.), 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.) Kucharz, W.: Invertible ideals in real holomorphy rings. J. reine angew. Math. 395, 171-185 (1989) Ideals and multiplicative ideal theory in commutative rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Divisibility and factorizations in 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.) Kucharz, W., Kurdyka, K.: Comparison of stratified-algebraic and topological K-theory. arXiv:1511.04238 [math.AG] Real algebraic sets, Algebraic topology on manifolds and differential topology, Topology of real algebraic varieties, Classical real and complex (co)homology 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.) Real algebraic sets, Real rational functions, Topology of vector bundles and fiber bundles, 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.) Semidefinite programming, 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.) Real algebra, Real algebraic sets, Ordered 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.) Olberding, B., A principal ideal theorem for compact sets of rank one valuation rings, J. Algebra, 489, 399-426, (2017) Valuations and their generalizations for commutative rings, Dedekind, Prüfer, Krull and Mori rings and their generalizations, Schemes and morphisms
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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.) Izhakian Z., Supertropical monoids: Basics and canonical factorization Valuations and their generalizations for commutative rings, Complete lattices, completions, Valuation rings, Logical aspects of lattices and related structures, Semifields, Valuations, completions, formal power series and related constructions (associative rings and algebras), Semirings
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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.) Software, source code, etc. for problems pertaining to algebraic geometry, Real algebraic sets, Geometric aspects of numerical algebraic geometry, 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.) Real algebraic sets
| 0
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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, Graphical methods in statistics, Rigidity and flexibility of structures (aspects of discrete 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. Verschelde, ''Numerical evidence for a conjecture in real algebraic geometry,'' Experiment. Math., vol. 9, iss. 2, pp. 183-196, 2000. Computational aspects of higher-dimensional varieties, Numerical computation of solutions to systems of equations, Real algebraic sets, 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.) Coste, M.; Kurdyka, K.: Le discriminant d'un morphisme de variétés algébriques réelles. Topology 37, No. 2, 393-399 (1998) Topology of real algebraic varieties, Topological properties in algebraic geometry, 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 functions and function fields in algebraic geometry, Vector bundles on curves and their moduli, Valuations and their generalizations for commutative rings, Elliptic curves, Riemann-Roch theorems, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to commutative algebra, Arithmetic ground fields for 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.) Rigid analytic geometry, Valuation rings, Non-Archimedean valued fields, Non-Archimedean analysis, Valuations and their generalizations for commutative rings, Non-Archimedean function 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.) \beginbarticle \bauthor\binitsE. \bsnmMukhin, \bauthor\binitsE. \bsnmTarasov and \bauthor\binitsA. \bsnmVarchenko, \batitleOn reality property of Wronski maps, \bjtitleConfluentes Math. \bvolume1 (\byear2009), no. \bissue2, page 225-\blpage247. \endbarticle \OrigBibText E. Mukhin. E. Tarasov and A. Varchenko, On reality property of Wronski maps, Confluentes Math. 1 (2009), no. 2, 225-247. \endOrigBibText \bptokstructpyb \endbibitem Groups and algebras in quantum theory and relations with integrable systems, Real algebraic sets, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Exactly solvable models; Bethe ansatz
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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.) Semidefinite programming, Numerical mathematical programming methods, Nonconvex programming, global optimization, Coloring of graphs and hypergraphs, 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.) Coverings of curves, fundamental group, 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.) 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.) H. King, ''Planar Linkages and Algebraic Sets,'' Turkish J. Math. 23(1), 33--56 (1999). Discriminantal varieties and configuration spaces in algebraic topology, Real algebraic sets, General low-dimensional topology
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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.) Bröcker, L.: Semialgebraische geometrie. Jber. d. Dt. Math.-Verein. 97, 130--156 (1995) Semialgebraic sets and related spaces, 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.) Coquand, T., \textit{space of valuations}, Annals of Pure and Applied Logic, 157, 97-109, (2009) Other constructive mathematics, Frames, locales, Valuations and their generalizations for commutative rings, Applications of logic to commutative algebra, Schemes and morphisms
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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.) Rational and birational maps, Birational automorphisms, Cremona group and generalizations, Real algebraic sets, Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties, Abstract finite 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.) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Polynomials in general fields (irreducibility, etc.), Real algebra, Moment problems
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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. Causa and R. Re, \textit{On the maximum rank of a real binary form}, Ann. Mat. Pura. Appl. (4), 190 (2011), pp. 55--59. Real algebraic sets, Projective techniques in algebraic geometry, Canonical forms, reductions, 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.) B. Bank, M. Giusti, J. Heintz, and L. M. Pardo, \textit{Generalized polar varieties and an efficient real elimination}, Kybernetika \textbf{40} (2004), no. 5, 519-550. Real algebraic sets, Singularities in algebraic geometry, Symbolic computation and algebraic computation, Analysis of algorithms and problem complexity
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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, Real algebraic sets, Real-analytic and semi-analytic sets, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Kinematics of mechanisms and robots
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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. M. Guseĭn-Zade and N. N. Nekhoroshev, On singularities of type \?_{\?} on simple curves of fixed degree, Funktsional. Anal. i Prilozhen. 34 (2000), no. 3, 69 -- 70 (Russian, with Russian summary); English transl., Funct. Anal. Appl. 34 (2000), no. 3, 214 -- 215. Local complex singularities, Singularities in algebraic geometry, 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, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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.) Lasserre J.B.: Representation of nonnegative convex polynomials. Arch. Math. 91(2), 126--130 (2008) Semialgebraic sets and related spaces, Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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.) Nash functions and manifolds, Real algebraic sets, Semialgebraic sets and related spaces, Linear function spaces and their duals
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