Results 1 to 10 of about 1,828 (45)
Euler characteristic reciprocity for chromatic, flow and order polynomials [PDF]
, 2017 The Euler characteristic of a semialgebraic set can be considered as a generalization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define "negative sets" to be the sets with negative Euler characteristics ...
Hasebe, Takahiro +2 more
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On the size of the fibers of spectral maps induced by semialgebraic embeddings [PDF]
, 2015 Let ${\mathcal S}(M)$ be the ring of (continuous) semialgebraic functions on a semialgebraic set $M\subset{\mathbb R}^m$ and ${\mathcal S}^*(M)$ its subring of bounded semialgebraic functions.
Fernando, Jose F.
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Polynomial Bounds for Oscillation of Solutions of Fuchsian Systems [PDF]
, 2009 We study the problem of placing effective upper bounds for the number of zeros of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of ...
Binyamini, Gal, Yakovenko, Sergei
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Matrix Convex Hulls of Free Semialgebraic Sets [PDF]
, 2013 This article resides in the realm of the noncommutative (free) analog of real algebraic geometry - the study of polynomial inequalities and equations over the real numbers - with a focus on matrix convex sets $C$ and their projections $\hat C$.
Helton, J. William +2 more
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Choosing roots of polynomials with symmetries smoothly [PDF]
, 2006 The roots of a smooth curve of hyperbolic polynomials may not in general be parameterized smoothly, even not $C^{1,\alpha}$ for any $\alpha > 0$. A sufficient condition for the existence of a smooth parameterization is that no two of the increasingly ...
Losik, Mark, Rainer, Armin
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On the symmetry breaking phenomenon [PDF]
, 2006 We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems.
Abraham R. +13 more
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On the complements of 3-dimensional convex polyhedra as polynomial images of ${\mathbb R}^3$ [PDF]
, 2014 We prove that the complement ${\mathcal S}:={\mathbb R}^3\setminus{\mathcal K}$ of a 3-dimensional convex polyhedron ${\mathcal K}\subset{\mathbb R}^3$ and its closure $\overline{{\mathcal S}}$ are polynomial images of ${\mathbb R}^3$.
Fernando, José F., Ueno, Carlos
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A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets [PDF]
, 2017 Results of Smale (1957) and Dugundji (1969) allow to compare the homotopy groups of two topological spaces $X$ and $Y$ whenever a map $f:X\to Y$ with strong connectivity conditions on the fibers is given.
Achille, Alessandro +1 more
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Tropical refined curve counting via motivic integration
, 2018 We propose a geometric interpretation of Block and G\"ottsche's refined tropical curve counting invariants in terms of virtual $\chi_{-y}$-specializations of motivic measures of semialgebraic sets in relative Hilbert schemes.
Nicaise, Johannes +2 more
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Semialgebraic Graphs having Countable List-Chromatic Numbers [PDF]
, 2015 The set of semialgebraic graphs having countable list-chromatic numbers is characterized. Some other related sets of graphs having countable list-chromatic numbers also are.Comment: This version has been completely rewritten.
Schmerl, James H.
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