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

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

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

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

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

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2019, Volume 19, Issue 6, pp. 1223 - 1263

Consider a finite system of non-strict polynomial inequalities with solution set $$S\subseteq \mathbb R^n$$ S ⊆ R n . Its Lasserre relaxation of degree d is a...

52A20 | Positive polynomial | 52A41 | Semidefinitely representable set | Secondary: 12D15 | Mathematics | Moment relaxation | 46L30 | Primary: 13J30 | Linear matrix inequality | Applications of Mathematics | Math Applications in Computer Science | Economics, general | Lasserre relaxation | Spectrahedron | Semidefinite programming | Sum of squares | 14P10 | Linear and Multilinear Algebras, Matrix Theory | 90C26 | Basic closed semialgebraic set | Pure state | Polynomial optimization | Numerical Analysis | 90C22 | Computer Science, general | Approximation theory | Fields, Algebraic | Research | Mathematical research | Mathematical analysis | Polynomials | Hulls (structures) | Linear matrix inequalities | Convexity | Matrix methods | Optimization

52A20 | Positive polynomial | 52A41 | Semidefinitely representable set | Secondary: 12D15 | Mathematics | Moment relaxation | 46L30 | Primary: 13J30 | Linear matrix inequality | Applications of Mathematics | Math Applications in Computer Science | Economics, general | Lasserre relaxation | Spectrahedron | Semidefinite programming | Sum of squares | 14P10 | Linear and Multilinear Algebras, Matrix Theory | 90C26 | Basic closed semialgebraic set | Pure state | Polynomial optimization | Numerical Analysis | 90C22 | Computer Science, general | Approximation theory | Fields, Algebraic | Research | Mathematical research | Mathematical analysis | Polynomials | Hulls (structures) | Linear matrix inequalities | Convexity | Matrix methods | Optimization

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

hyperdeterminants | tensors | 51N35 | Apolarity | real rank | 14P10 | MATHEMATICS | VERONESE | GEOMETRY | Hyperspaces | Cases (containers) | Boundaries | Loci

Journal Article

Mathematical Programming, ISSN 0025-5610, 4/2013, Volume 138, Issue 1, pp. 401 - 445

Given linear matrix inequalities (LMIs) L 1 and L 2 it is natural to ask: (Q1) when does one dominate the other, that is, does $${L_1(X) \succeq 0}$$ imply...

Semidefinite programming | Free positivity | Primary 46L07 | Completely positive | Theoretical, Mathematical and Computational Physics | 14P10 | Mathematics | Real algebraic geometry | Secondary 11E25 | Archimedean quadratic module | 13J30 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Gleichstellensatz | Numerical Analysis | Positivstellensatz | 90C22 | Combinatorics | Linear matrix inequality (LMI) | 46L89 | MATHEMATICS, APPLIED | NONCOMMUTATIVE CHOQUET BOUNDARY | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALGEBRAS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Algebra | Equality | Operators | Equivalence | Mathematical analysis | Mathematical models | Matrices | Linear matrix inequalities | Matrix methods

Semidefinite programming | Free positivity | Primary 46L07 | Completely positive | Theoretical, Mathematical and Computational Physics | 14P10 | Mathematics | Real algebraic geometry | Secondary 11E25 | Archimedean quadratic module | 13J30 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Gleichstellensatz | Numerical Analysis | Positivstellensatz | 90C22 | Combinatorics | Linear matrix inequality (LMI) | 46L89 | MATHEMATICS, APPLIED | NONCOMMUTATIVE CHOQUET BOUNDARY | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALGEBRAS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Algebra | Equality | Operators | Equivalence | Mathematical analysis | Mathematical models | Matrices | Linear matrix inequalities | Matrix methods

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

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

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

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

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

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

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

The article presents a study on a class of polynomial optimization problems over (noncompact) semi-algebraic sets which, by making changes of variables via...

Sum of squares | 14P10 | Mathematics | Theory of Computation | Optimization | 49K99 | 90C30 | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Positivstellensatz | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Polynomials | Algebra | Mathematical analysis

Sum of squares | 14P10 | Mathematics | Theory of Computation | Optimization | 49K99 | 90C30 | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Positivstellensatz | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Polynomials | Algebra | Mathematical analysis

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

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

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

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

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

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

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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