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Kolmogorov and Markov Type Inequalities on Certain Algebraic Varieties
In this paper we introduce a generalization to compact subsets of certain algebraic varieties of the classical Markov inequality on the derivatives...
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Approximation of maps into spheres by regulous maps
Let X be a compact real algebraic set of dimension n . We prove that every Euclidean continuous map from X into the unit n -sphere can be approximated...
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Continuous rational maps into the unit 2-sphere
Investigated are continuous rational maps from a compact nonsingular real algebraic set into unit spheres. Special attention is devoted to such maps...
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Real ideal and the duality of semidefinite programming for polynomial optimization
We study the ideal generated by polynomials vanishing on a semialgebraic set and give elementary proofs for some equivalent conditions for reality of...
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Virtual Poincaré polynomial of the link of a real algebraic variety
The link of an affine real algebraic variety at a point is defined to be the intersection of the variety with a small sphere centred at the point....
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Welschinger invariants of real Del Pezzo surfaces of degree ≥ 3
We give a recursive formula for purely real Welschinger invariants of real Del Pezzo surfaces of degree K 2 ≥ 3, where in the case of surfaces of...
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Algebraicity of cycles on smooth manifolds
According to the Nash–Tognoli theorem, each compact smooth manifold M is diffeomorphic to a nonsingular real algebraic set, called an algebraic model...
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Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces
For a real square-free multivariate polynomial F , we treat the general problem of finding real solutions of the equation F =0, provided that the real...
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Positivstellensätze for real function algebras
We look for algebraic certificates of positivity for functions which are not necessarily polynomial functions. Similar questions were examined...
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Hermitian Symmetric Polynomials and CR Complexity
Properties of Hermitian forms are used to investigate several natural questions from CR geometry. To each Hermitian symmetric polynomial we assign a...
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Invariant CR Map**s
This paper concerns CR map**s between hyperquadrics. We emphasize the case when the domain is a sphere and the maps are invariant under a finite...
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Sums of squares on reducible real curves
We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring....
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Singular Points of Real Sextic Curves I
A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by...
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A List of Challenges for Real Algebraic Plane Curve Visualization Software
Recently, the visualization of implicitly given algebraic curves and surfaces has become an area of active research. Most of the approaches either...