scholarly journals LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future

2012 ◽  
pp. 325-349 ◽  
Author(s):  
Victor Vinnikov
Keyword(s):  
Semialgebraic Sets ◽  
Algebraic Hypersurfaces

A Module-theoretic Characterization of Algebraic Hypersurfaces

2018 ◽  
Vol 61 (1) ◽  
pp. 166-173
Author(s):  
Cleto B. Miranda-Neto
Keyword(s):  
Algebraic Variety ◽  
Characteristic Zero ◽  
Vector Fields ◽  
Exterior Power ◽  
Algebraic Hypersurfaces ◽  
Theoretic Characterization

AbstractIn this note we prove the following surprising characterization: if X ⊂ is an (embedded, non-empty, proper) algebraic variety deûned over a field k of characteristic zero, then X is a hypersurface if and only if the module of logarithmic vector fields of X is a reflexive -module. As a consequence of this result, we derive that if is a free -module, which is shown to be equivalent to the freeness of the t-th exterior power of for some (in fact, any) t ≤ n, then necessarily X is a Saito free divisor.

ON THE IRREDUCIBLE COMPONENTS OF A SEMIALGEBRAIC SET

2012 ◽  
Vol 23 (04) ◽  
pp. 1250031 ◽  
Author(s):  
JOSÉ F. FERNANDO ◽  
J. M. GAMBOA
Keyword(s):  
Integral Domain ◽  
Hilbert Problem ◽  
Semialgebraic Sets ◽  
Semialgebraic Set ◽  
Irreducible Components ◽  
Real Geometry ◽  
Nash Manifold ◽  
Substitution Theorem ◽  
Satisfactory Theory ◽  
17Th Hilbert Problem

In this work we define a semialgebraic set S ⊂ ℝn to be irreducible if the noetherian ring [Formula: see text] of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring [Formula: see text]: Substitution Theorem, Positivstellensätze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, we give full characterizations of the families of semialgebraic sets for which these classical results are true.

scholarly journals Singular Points of Complex Algebraic Hypersurfaces

2018 ◽  
Vol 11 (6) ◽  
pp. 670-679
Author(s):  
Antipova Irina A. ◽  
◽  
Mikhalkin Evgeny N. ◽  
Tsikh Avgust K. ◽  
◽  
...  
Keyword(s):  
Singular Points ◽  
Algebraic Hypersurfaces

scholarly journals Equivalent reliability polynomials modeling EAS and their geometries

2015 ◽  
Vol 53 (1) ◽  
pp. 177-195 ◽  
Author(s):  
Zahir Abdul Haddi Hassan ◽  
Constantin Udriște
Keyword(s):  
Graph Theory ◽  
Reliability Analysis ◽  
Geometric Modeling ◽  
Intrinsic Properties ◽  
Matlab Software ◽  
Reliability Models ◽  
Algebraic Hypersurfaces ◽  
Theory Technique ◽  
Made In

AbstractIn this paper we shall introduce two equivalent techniques in order to evaluate reliability analysis of electrical aircrafts systems (EAS): (i) graph theory technique, and (ii) simplifying diffeomorphism technique. Geometric modeling of reliability models is based on algebraic hypersurfaces, whose intrinsic properties are able to select those models which are relevant for applications. The basic idea is to cover the reliability hypersurfaces by exponentially decay curves. Most of the calculations made in this paper have used Maple and Matlab software.

A measure for semialgebraic sets related to Boolean complexity

1989 ◽  
Vol 283 (2) ◽  
pp. 203-209 ◽  
Author(s):  
Gilbert Stengle
Keyword(s):  
Semialgebraic Sets

When is a Distribution of Signs Locally Completable?

1994 ◽  
Vol 46 (3) ◽  
pp. 449-473 ◽  
Author(s):  
F. Acquistapace ◽  
F. Broglia ◽  
E. Fortuna
Keyword(s):  
Algebraic Curve ◽  
Algebraic Surface ◽  
Regular Function ◽  
Connected Components ◽  
Semialgebraic Sets ◽  
Sign Distribution

AbstractLet V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.

scholarly journals Doubling chains on complements of algebraic hypersurfaces

2020 ◽  
Vol 140 (2) ◽  
pp. 617-636
Author(s):  
Omer Friedland ◽  
Yosef Yomdin
Keyword(s):  
Algebraic Hypersurfaces
Sign in / Sign up

Export Citation Format

Share Document