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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 Riemannian 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.) Ghiloni, R., On the space of morphisms into generic real algebraic varieties, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 5, 419-438, (2006) 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.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebra, Intersection theory, characteristic classes, intersection multiplicities 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.) Coste M. and Diop M.\ M., Real algebraic 1-cocycles are Nash coboundaries, Boll. Un. Mat. Ital. A (7) 6 (1992), no. 2, 249-254. Real algebraic sets, Nash functions and manifolds, (Co)homology theory 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.) Topology of real algebraic varieties, Plane and space curves, Local complex singularities, Modifications; resolution of singularities (complex-analytic aspects), Singularities of curves, local rings, Real algebraic sets, Critical points and critical submanifolds in 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, Nash functions and manifolds, 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.) L. Pharamond Dit D'COSTA, Géométrie réelle des dessins d'enfant . Journal de théorie des nombres de Bordeaux 16 ( 2004 ), 639 - 691 . Numdam | MR 2144962 | Zbl 1078.14089 Topology of real algebraic varieties, Real algebraic sets, Coverings of curves, fundamental group, 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.) Numerical algebraic geometry, Geometric aspects of numerical algebraic geometry, Plane and space curves, Computational aspects of algebraic curves, Real algebraic sets, Symbolic computation and algebraic computation, Numerical aspects of computer graphics, image analysis, and computational geometry, Computational real algebraic geometry, Computer graphics; computational geometry (digital and algorithmic 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.) L. P. Bos, N. Levenberg, and B. A. Taylor, ``Characterization of smooth, compact algebraic curves in \Bbb R2,'' in Topics in Complex Analysis (Warsaw, 1992), P. Jakóbczak and W. Pleśniak, Eds., vol. 31 of Banach Center Publ., pp. 125-134, Polish Academy of Sciences, Warsaw, 1995. Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), 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.) Sums of squares and representations by other particular quadratic forms, 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., van Hamel J.: Transcendental manifolds in real projective space and Stiefel--Whitney classes. Ann. Sc. Norm. Super. Pisa Cl. Sci. 5(8), 267--277 (2009) Real algebraic sets, Algebraic cycles, Characteristic classes and numbers in 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, Semialgebraic sets and related spaces, 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.) Singularities in algebraic geometry, Morphisms of commutative rings, Ramification and extension theory, Valuations and their generalizations for commutative rings, Valuation 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.) S.D. Cutkosky, Introduction to algebraic geometry, preprint. Valuations and their generalizations for commutative rings, Relevant commutative algebra, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or 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.) Topology of real algebraic varieties, Jacobians, Prym 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.) Little J.: The ubiquity of order domains for the construction of error control codes. Adv. Math. Commun. \textbf{1}(1), 151-171 (2007). Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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.) Pecker, D., On the elimination of algebraic inequalities, Pacific J. Math., 146, 2, 305-314, (1990) 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.) Huisman, J., Correction to ``A real algebraic bundle is strongly algebraic whenever its total space is affine'', Contemp. Math., 253, 179, (2000) 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: 10.3842/sigma.2013.062 Real algebraic sets, Discontinuous groups of transformations, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic 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.) Tancredi, A; Tognoli, A, On the products of Nash subvarieties by spheres, Proc. Am. Math. Soc., 134, 983-987, (2006) Real algebraic sets, Nash functions and manifolds, 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.) Piltant, O.: An axiomatic version of Zariski's pathching theorem. Universidad de Valladolid. Preprint (2008) Global theory and resolution of singularities (algebro-geometric aspects), Modifications; resolution of singularities (complex-analytic aspects), Global theory of complex singularities; cohomological properties, Valuations and their generalizations for commutative rings, Singularities of vector fields, topological 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.) Singularities in algebraic geometry, Singularities of curves, local rings, Software, source code, etc. for problems pertaining to 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.) Power series rings, Analytic algebras and generalizations, preparation theorems, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, Formal power series rings, Non-Archimedean analysis, Nonlocal and multipoint boundary value problems for ordinary differential equations, Valuations and their generalizations for commutative rings, Valuation rings, Rigid 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.) Foundations of tropical geometry and relations with algebra, Toric varieties, Newton polyhedra, Okounkov bodies, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Valuations and their generalizations for commutative rings, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Homogeneous spaces and 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.) Applications of operator theory in optimization, convex analysis, mathematical programming, economics, Semidefinite programming, Polynomial optimization, Fields related with sums of squares (formally real fields, Pythagorean fields, 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.) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), 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.) Podkorytov, S. S., On the Euler characteristic of a random algebraic hypersurface, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI). J. Math. Sci. (N. Y.), 252 104, 4, 1387\textendash1393 pp., (2001) Real algebraic sets, Topological properties in algebraic geometry, Hypersurfaces and algebraic geometry, Probability theory on algebraic and topological structures
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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.) Safey El~Din, M., Trebuchet, P.: Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry. CoRR arxiv:cs/0610051v2 (2006) Real algebraic sets, Singularities in algebraic geometry, Computational aspects of algebraic surfaces, Computational aspects of higher-dimensional varieties, 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.) Toric varieties, Newton polyhedra, Okounkov bodies, 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.) Lattarulo, M.: The Schottky problem for hyperelliptic real curves. Comm. algebra 31, 1679-1703 (2003) Real algebraic sets, Families, moduli of curves (algebraic), Algebraic moduli of abelian varieties, classification, Torelli problem
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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 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.) Étale and other Grothendieck topologies and (co)homologies, 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.) Topology of real algebraic varieties, Algebraic topology on manifolds and differential topology, Special algebraic curves and curves of low genus, 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.) J. Huisman, M. Lattarulo, Anisotropic hyperelliptic curves and real line arrangements, in preparation. Families, moduli of curves (analytic), Real algebraic sets, Planar arrangements of lines and pseudolines (aspects of discrete geometry), Klein 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.) \(K3\) surfaces and Enriques surfaces, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), 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.) Purbhoo, K., Reality and transversality for Schubert calculus in \(\operatorname{OG}(n, 2 n + 1)\), Math. res. lett., 17, 6, 1041-1046, (2010) Grassmannians, Schubert varieties, flag manifolds, Classical problems, Schubert calculus, 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.) Dubois, D. W.; Recio, T.: Order extensions and real algebraic geometry. Contemporary math. 8 (1981) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, 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.) Effectivity, complexity and computational aspects of algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Toric varieties, Newton polyhedra, Okounkov bodies, Real algebraic sets, Systems biology, networks
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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.), 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.) Families, moduli of curves (algebraic), Singularities of curves, local rings, 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.) D. A. Weinberg and N. J. Willis, ``Singular points of real sextic curves-I,'' Acta Applicandae Mathematicae, vol. 110, no. 2, pp. 805-862, 2010. Singularities of curves, local rings, 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.) Dress, A; Wenzel, W, Algebraic, tropical, and fuzzy geometry, Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry, 52, 431-461, (2011) Varieties and morphisms, Fuzzy algebraic structures, Valuations and their generalizations for commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials
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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.: On the Pierce--Birkhoff conjecture over ordered fields. Rocky Mt. J. Math. 19(3), 651--668 (1989) Semialgebraic sets and related spaces, Real algebraic sets, Approximation by polynomials, Ordered rings, algebras, 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.) Alekseevskii, A. V.; Natanzon, S. M., The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces, Izv. Math., 72, 627-646, (2008) Topological quantum field theories (aspects of differential topology), Graph theory, Klein surfaces, 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.) Knop, F., Über bewertungen, welche unter einer reduktiven gruppe invariant sind, Math. Ann., 295, 333-363, (1993) Group actions on varieties or schemes (quotients), 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.) Plane and space curves, Real algebraic sets, Convex sets in \(2\) dimensions (including convex 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: 10.5802/afst.1260 Valuations and their generalizations for commutative rings, Valuation rings, 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.) Vector bundles on curves and their moduli, 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.) E. Shustin, A tropical approach to enumerative geometry. \textit{Algebra i Analiz}\textbf{17} (2005), 170-214. Translated in \textit{St}. \textit{Petersburg Math}. \textit{J}. \textbf{17} (2006), 343-375. MR2159589 Zbl 1100.14046 Real algebraic sets, Enumerative problems (combinatorial problems) in algebraic geometry, Families, moduli of curves (analytic), Toric varieties, Newton polyhedra, Okounkov 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.) Assaf Hasson and Alf Onshuus, Unstable structures definable in o-minimal theories, Selecta Math. (N.S.) 16 (2010), no. 1, 121 -- 143. Classification theory, stability, and related concepts in model theory, Model theory of ordered structures; o-minimality, Applications of model 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.) Valuations and their generalizations for commutative rings, Toric varieties, Newton polyhedra, Okounkov 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.) M.J. de la Puente , Riemann surfaces of a ring and compactifications of semi-algebraic sets , Doctoral Dissertation, Stanford 1988 [14] M.J. de la Puente , Specializations and a local homomorphism theorem for real Riemann surfaces of rings , Pac. J. Math. 176 ( 1996 ), 427 - 442 Article | MR 1435000 | Zbl 0868.13004 Valuations and their generalizations for commutative rings, Ordered rings, Relevant commutative algebra, Valued fields, Ordered fields, Basic properties of first-order languages and structures
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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, Erdős problems and related topics of discrete 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.) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Topological properties 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.) Plane and space curves, Commutative semigroups, Valuations and their generalizations for commutative rings, Software, source code, etc. for problems pertaining to group 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.) Gilmer, P., Topology of Real Algebraic Varieties and Related Topics, 173, Real algebraic curves and link cobordism II, 73-84, (1996), American Mathematical Society, Providence, RI Real-analytic and Nash 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.) Other groups and their modular and automorphic forms (several variables), 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.) 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.) Nash functions and manifolds, Real algebraic sets, Real-analytic and Nash manifolds, Relevant commutative algebra, Real-analytic manifolds, real-analytic 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.) Barone, S; Basu, S, On a real analog of Bezout inequality and the number of connected components of sign conditions, Proc. Lond. Math. Soc., 112, 115-145, (2016) Effectivity, complexity and computational aspects of algebraic geometry, Real algebraic sets, Erdős problems and related topics of discrete geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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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.) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Real algebraic sets, Topology of real algebraic varieties, Real algebra, Plane and space curves, Plane and solid geometry (educational 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.) V. V. Nikulin, ''On the Brauer group of real algebraic surfaces,'' in:Algebraic Geometry and Its Applications, Yaroslavl (1992), pp. 114--136. 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.) D. Henrion, J. B. Lasserre, and C. Savorgnan, \textit{Approximate volume and integration for basic semialgebraic sets}, SIAM Rev., 51 (2009), pp. 722--743, . 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.) M. Marshall : Minimal generation of basic sets in the real spectrum of a commutative ring, in Contemporary Math., to appear Real algebraic sets, Real and complex fields, 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.) Nakazato, H., Quartic curves associated to 4 by 4 matrices, Sci. Rep. Hirosaki Univ., 43, 209-221, (1986) Special algebraic curves and curves of low genus, Norms of matrices, numerical range, applications of functional analysis to matrix 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.) H.C. Mork, R. Piene, Polars of real singular plane curves, in Algorithms in Algebraic Geometry, based on the workshop, Minneapolis, MN, USA, September 18--22, 2006, ed. by A. Dickenstein et al., The IMA Volumes in Mathematics and Its Applications, vol. 146 (Springer, New York, 2008), pp. 99--115. Plane and space curves, Hypersurfaces and 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.) J. A. de Loera and F. J. Wicklin,On the need of convexity in patchworking, Advances in Applied Mathematics20 (1998), 188--219. Topology of real algebraic varieties, Arithmetic ground fields for 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.) C. Scheiderer, Sums of squares on real algebraic surfaces. \textit{Manuscripta Math}. \textbf{119} (2006), 395-410. MR2223624 Zbl 1120.14047 Real algebraic sets, Sums of squares and representations by other particular quadratic forms, Real 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.) Henrion, D.; Infusino, M.; Kuhlmann, S.; Vinnikov, V., Real algebraic geometry with a view toward moment problems and optimization, Oberwolfach Rep., 14, 771-862, (2017) Collections of abstracts of lectures, Proceedings of conferences of miscellaneous specific interest, 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, Computational aspects of algebraic surfaces, Numerical methods involving duality, Point processes (e.g., Poisson, Cox, Hawkes processes), Random measures, Semidefinite programming, Algebraic methods, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, 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.) B. Bertrand, L. López de Medrano, and J.-J. Risler, \textit{On the total curvature of tropical hypersurfaces}, in Algebraic and Combinatorial Aspects of Tropical Geometry, Contemp. Math. 589, Amer. Math. Soc., Providence, RI, 2013, pp. 21--43. Real algebraic sets, Lattice polytopes in convex geometry (including relations with commutative algebra 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.) W. Kucharz, Approximation by continuous rational maps into spheres, J. Eur. Math. Soc. (JEMS) 16 (2014), 1555-1569. 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.) Real algebraic sets, Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.), Real algebra, 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.) [PSS] A. Pillay, P. Scowcroft and C. Steinhorn,Between groups and rings, Rocky Mountain J.9 (1989), 871--885. Semialgebraic sets and related spaces, Quantifier elimination, model completeness, and related topics, 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.) Broglia, F.; Pernazza, L.: An Artin--lang property for germs of C\(\infty \)functions. J. reine angew. Math. 548, 129-147 (2002) Real-analytic manifolds, real-analytic spaces, Real algebraic sets, Real-analytic and semi-analytic 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.) Toric varieties, Newton polyhedra, Okounkov bodies, Fibrations, degenerations in algebraic geometry, 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.) Polynomials in real and complex fields: location of zeros (algebraic theorems), Real algebraic sets, 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.) Cutkosky, S. D.: Simultaneous resolution of singularities. Proc. amer. Math. soc. 128, 1905-1910 (2000) Global theory and resolution of singularities (algebro-geometric aspects), Valuations and their generalizations for commutative rings, 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.) Elhitti, S.: Perron transforms. Comm. algebra 42, 2003-2045 (2014) Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Singularities of curves, local 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.) Real algebraic sets, Topological lattices
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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.) Q. Guo, M. Safey El Din, and L. Zhi, \textit{Computing rational solutions of linear matrix inequalities}, in Proceedings of ISSAC, Boston, 2013. Symbolic computation and algebraic computation, Real algebraic sets, Linear inequalities of matrices, Matrices over special rings (quaternions, finite fields, etc.), 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.) D'Angelo, J. P.; Lebl, J., Hermitian symmetric polynomials and CR complexity, J. Geom. Anal., 21, 3, 599-619, (2011) Embeddings of CR manifolds, Hermitian, skew-Hermitian, and related matrices, Proper holomorphic mappings, finiteness 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.) Families, moduli of curves (analytic), Real algebraic sets, Differentials on Riemann 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.) Mahé, L.: On the separation of connected components by étale cohomology,K-Theory 9 (1995), 545-549. Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), 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.) 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.) Hà, HV; Ho, TM, Positive polynomials on nondegenerate basic semi-algebraic sets, Adv. Geom., 16, 497-510, (2016) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Moment problems, Polynomials in general fields (irreducibility, 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.) Divisors, linear systems, invertible sheaves, 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.) Eigenwillig, A., Kerber, M., Wolpert, N., 2007. Fast and exact geometric analysis of real algebraic plane curves. In: C.W. Brown (Ed.), Proc. ACM Int. Symp. on Symbolic \& Algebraic Comput., Waterloo, Canada, pp. 151--158 Computational aspects of algebraic curves, 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.) Boucksom, S.; De Fernex, T.; Favre, C.; Urbinati, S., \textit{valuation spaces and multiplier ideals on singular varieties}, Recent advances in algebraic geometry, 29-51, (2015), Cambridge University Press, Cambridge Multiplier ideals, 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.) C.-T. Le, Nonnegative Morse polynomial functions and polynomial optimization, Positivity 20 (2016), no. 2, 483--498. Real algebraic sets, Semialgebraic sets and related spaces, Real algebra, 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.) Z.~Izhakian, M.~Knebusch, and L.~Rowen, Supertropical semirings and supervaluations, \emph{J. Pure and Appl.~Alg.}, 215(10):2431--2463, 2011 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.) CAMPBELL LA, The asymptotic variety of a Pinchuk map as a polynomial curve, Appl Math Lett 24 pp 62-- (2011) Jacobian problem, 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.) Napoletani, D.: A power function approach to kouchnirenko's conjecture, Contemp. math. 286, 99-106 (2001) 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.) Plane and space curves, Curves in Euclidean and related spaces, Real algebraic sets, Projective techniques in algebraic geometry, Classical problems, Schubert calculus
| 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, Special algebraic curves and curves of low genus, Dynamical systems and ergodic 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.) Combinatorial aspects of matroids and geometric lattices, Real algebraic sets, Convex sets in \(n\) dimensions (including convex hypersurfaces), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Nonlinear programming, Semidefinite programming, 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.) C. Scheiderer, \textit{Semidefinite representation for convex hulls of real algebraic curves}, SIAM J. Appl. Algebra Geom., 2 (2018), pp. 1--25, . 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.) Nabutovsky, Smoothing of real algebraic hypersurfaces by rigid isotopies, Ann. Inst. Fourier, (Grenoble) 41 (1) pp 11-- (1991) Real algebraic sets, Triangulating manifolds, Isotopy in differential topology, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, 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.) Dubois, D. W.: Ordered fields and real algebraic geometry. AMS contemporary mathematics 8 (1982) Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to field theory, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Valued fields, 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. Haran and M. Jarden,The absolute Galois group of a pseudo padically closed field, Journal für die reine und angewandte Mathematik Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, Separable extensions, Galois theory, Limits, profinite groups
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