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Mathematische Annalen, ISSN 0025-5831, 10/2017, Volume 369, Issue 1, pp. 387 - 395
We prove a conjecture of Kurdyka stating that every arc-symmetric semialgebraic set is precisely the zero locus of an arc-analytic semialgebraic function. This... 
14P20 | Mathematics, general | Mathematics | 14P99 | 14P10
Journal Article
Mathematische Annalen, ISSN 0025-5831, 06/2018, Volume 371, Issue 1-2, pp. 883 - 959
Linear matrix inequalities (LMIs) play a role in many areas of applications. The set of solutions of an LMI is a spectrahedron. LMIs in (dimension-free) matrix... 
52A05 | 32E30 | 32H02 | Primary 47L25 | 46L07 | Secondary 14P10 | POLYNOMIALS | MATHEMATICS | LINEAR MATRIX INEQUALITY | DETERMINANTAL REPRESENTATIONS | CODIMENSION | NONCOMMUTATIVE RATIONAL FUNCTIONS | THEOREM | FREE HOLOMORPHIC-FUNCTIONS | B(H)(N) | DOMAINS | UNIT BALL | Analysis | Algebra
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2019, Volume 292, Issue 3, pp. 819 - 837
In this paper we consider a problem on whether the number of semialgebraic types appearing in a family of Nash mappings defined on a two-dimensional Nash... 
Mathematics, general | Primary 14P10 | Mathematics | Secondary 32S45 | 57R45 | 32S15 | MATHEMATICS | ZERO | THEOREM | RESOLUTION | FAMILY
Journal Article
Selecta Mathematica, ISSN 1022-1824, 8/2019, Volume 25, Issue 3, pp. 1 - 30
In this work we approach the problem of approximating uniformly continuous semialgebraic maps $$f:S\rightarrow T$$ f:S→T from a compact semialgebraic set S to... 
14P20 | Secondary 14P05 | Primary 14P10 | Approximation of maps between polyhedra | Mathematics, general | Mathematics | 57Q55 | Approximation of semialgebraic maps | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISMS | SPACES | OBSTRUCTIONS | MANIFOLDS | NASH SETS | REAL ALGEBRAIC MORPHISMS | Mathematics - Algebraic Geometry
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 07/2019, Volume 67, Issue 7, pp. 1404 - 1419
In this article, we study forbidden loci and typical ranks of forms with respect to the embeddings of given by the line bundles (2, 2d). We introduce the... 
hyperdeterminants | tensors | 51N35 | Apolarity | real rank | 14P10 | MATHEMATICS | VERONESE | GEOMETRY | Hyperspaces | Cases (containers) | Boundaries | Loci
Journal Article
Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 2018, pp. 1 - 15
AbstractWe present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is... 
2010 Mathematics Subject Classification | 32B2D | 58C25 | 14P10
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 02/2018, Volume 116, Issue 2, pp. 209 - 247
Given a non‐archimedean real closed field with archimedean value group which contains the reals, we establish for the category of semialgebraic sets and... 
06F20 | 03C64 (primary) | 03H05 | 12J25 | 14P10 | 28B15 | 32B20 (secondary) | 28E05 | MATHEMATICS | SUBANALYTIC FUNCTIONS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 2/2018, Volume 370, Issue 1, pp. 39 - 69
Let W be a subset of the set of real points of a real algebraic variety X. We investigate which functions $$f: W \rightarrow \mathbb {R}$$ f : W → R are the... 
Mathematics, general | 14P05 | 26C15 | Mathematics | 14P10 | MATHEMATICS | MAPS | TOPOLOGICAL VECTOR-SPACES | Computer science | Mathematics - Algebraic Geometry
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 05/2018, Volume 167, Issue 7, pp. 1239 - 1309
We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their... 
MATHEMATICS | PREPARATION THEOREM | Algebraic Geometry | Mathematics
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 11/2018, Volume 167, Issue 16, pp. 3115 - 3128
We give rather simple answers to two long-standing questions in real-analytic geometry, on global smoothing of a subanalytic set, and on transformation of a... 
MATHEMATICS
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2018, Volume 46, Issue 5, pp. 1854 - 1858
This article is intended to indicate and discuss some errors in N. Lavi's paper "A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for... 
real algebraic geometry | Primary 14P10 | Secondary 03C64 | Model theory | 12J20 | valuation theory | MATHEMATICS | Algebra | Rational functions | Criteria
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2019, Volume 183, Issue 1, pp. 352 - 363
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 10/2016, Volume 94, Issue 2, pp. 598 - 616
Given a semi‐algebraic set S, we study compactifications of S that arise from embeddings into complete toric varieties. This makes it possible to describe the... 
POLYNOMIALS | MATHEMATICS | SEMIALGEBRAIC SETS | Mathematics - Algebraic Geometry
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 10/2018, Volume 66, Issue 10, pp. 1952 - 1974
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its... 
algebraic boundaries | polytopes | Positive semidefinite rank | 15A23 | spectrahedra | 14P10 | MATHEMATICS | FACTORIZATIONS | LIFTS | NONNEGATIVE RANK | Polytopes | Nesting | Mathematical analysis | Matrix methods
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 03/2016, Volume 65, Issue 1, pp. 131 - 146
To each continuous function f : R -> R there is an associated trace function on n x n real symmetric matrices Tr f. The classical Klein lemma states that f is... 
MATHEMATICS | INEQUALITIES | MOMENT PROBLEM | VARIABLES | HERMITIAN SQUARES | MULTIDIMENSIONAL LINEAR-SYSTEMS | SUMS | 16S10 | 14A22 | 16Z05 | 46L07 | 14P10 | 13J30 | 47Lxx
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2016, Volume 220, Issue 7, pp. 2533 - 2548
The matrix Fejér–Riesz theorem characterizes positive semidefinite matrix polynomials on the real line R. We extend a characterization to arbitrary closed... 
47A56 | 14P10 | 13J30 | POLYNOMIALS | MATHEMATICS | MULTIDIMENSIONAL MOMENT PROBLEM | POSITIVSTELLENSATZE | MATHEMATICS, APPLIED | RINGS | SQUARES | POSITIVITY | SUMS
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 12/2018, Volume 117, Issue 6, pp. 1101 - 1134
Positivstellensätze are fundamental results in real algebraic geometry providing algebraic certificates for positivity of polynomials on semialgebraic sets. In... 
13J30 (primary) | 16W10 | 14P10 (secondary) | 16R30 | MATHEMATICS | POSITIVSTELLENSATZE | SIGNATURES | HERMITIAN-FORMS | RINGS | REAL ALGEBRAIC-GEOMETRY | SQUARES | CONNES EMBEDDING CONJECTURE | SUMS | Mathematics - Rings and Algebras
Journal Article
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, ISSN 0895-4798, 2019, Volume 40, Issue 2, pp. 739 - 773
We prove the existence of an open set of n(1) x n(2) x n(3) tensors of rank r for which popular and efficient algorithms for computing tensor rank... 
ORDER | MATHEMATICS, APPLIED | NUMBER | CPD | canonical polyadic decomposition | Jennrich's algorithm | numerical instability | tensor rank decomposition | IDENTIFIABILITY | UNIQUENESS | Mathematics - Numerical Analysis
Journal Article
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