Results 1 to 10 of about 1,868 (82)
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
core +2 more sources
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
core +2 more sources
Convex computation of the region of attraction of polynomial control systems [PDF]
, 2012 We address the long-standing problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints.
Henrion, Didier, Korda, Milan
core +8 more sources
Computing the homology of basic semialgebraic sets in weak exponential time [PDF]
, 2018 We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time.
Bürgisser, Peter +2 more
core +5 more sources
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
core +2 more sources
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.
core +1 more source
Algebraically constructible functions [PDF]
, 1996 An algebraic version of Kashiwara and Schapira's calculus of constructible functions is used to describe local topological properties of real algebraic sets, including Akbulut and King's numerical conditions for a stratified set of dimension three to be ...
McCrory, Clint, Parusinski, Adam
core +4 more sources
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
core +2 more sources
Operads, configuration spaces and quantization [PDF]
, 2011 We review several well-known operads of compactified configuration spaces and construct several new such operads, C, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of A-infinity ...
Merkulov, S. A.
core +3 more sources
An inverse mapping theorem for blow-Nash maps on singular spaces
, 2015 A semialgebraic map $f:X\to Y$ between two real algebraic sets is called blow-Nash if it can be made Nash (i.e. semialgebraic and real analytic) by composing with finitely many blowings-up with non-singular centers.
Campesato, Jean-Baptiste
core +3 more sources