Results 21 to 30 of about 1,867 (83)
On spectral types of semialgebraic sets [PDF]
, 2013 In this work we prove that a semialgebraic set $M\subset{\mathbb R}^m$ is determined (up to a semialgebraic homeomorphism) by its ring ${\mathcal S}(M)$ of (continuous) semialgebraic functions while its ring ${\mathcal S}^*(M)$ of (continuous) bounded ...
Fernando, José F., Gamboa, J. M.
core
Certification of Real Inequalities -- Templates and Sums of Squares
, 2014 We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic operations as well as some transcendental functions like $\cos$, $\arctan$,
Allamigeon, Xavier +3 more
core +3 more sources
On the one‐dimensional polynomial, regular, and regulous images of closed balls and spheres
Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.Abstract We present a full geometric characterization of the one‐dimensional (semialgebraic) images S$S$ of either n$n$‐dimensional closed balls B¯n⊂Rn$\overline{{\mathcal {B}}}_n\subset {\mathbb {R}}^n$ or n$n$‐dimensional spheres Sn⊂Rn+1${\mathbb {S}}^n\subset {\mathbb {R}}^{n+1}$ under polynomial, regular, and regulous maps for some n⩾1$n\geqslant 1$
José F. Fernando
wiley +1 more source
A Jordan–Chevalley decomposition beyond algebraic groups
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We prove a decomposition of definable groups in o‐minimal structures generalizing the Jordan–Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G$G$ is a semidirect product of its maximal normal definable torsion‐free subgroup N(G)$\mathcal {N}(G)$ and a definable subgroup P$P$, unique up to ...
Annalisa Conversano
wiley +1 more source
, 2003 Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a
Abud M +22 more
core +3 more sources
On Rainbow Turán Densities of Trees
Random Structures &Algorithms, Volume 66, Issue 3, May 2025.ABSTRACT For a given collection 𝒢=(G1,…,Gk) of graphs on a common vertex set V$$ V $$, which we call a graph system, a graph H$$ H $$ on a vertex set V(H)⊆V$$ V(H)\subseteq V $$ is called a rainbow subgraph of 𝒢 if there exists an injective function ψ:E(H)→[k]$$ \psi :E(H)\to \left[k\right] $$ such that e∈Gψ(e)$$ e\in {G}_{\psi (e)} $$ for each e∈E(H)$$
Seonghyuk Im +3 more
wiley +1 more source
Outer Lipschitz classification of normal pairs of Hölder triangles
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract A normal pair of Hölder triangles is the union of two normally embedded Hölder triangles satisfying some natural conditions on the tangency orders of their boundary arcs. It is a special case of a surface germ, a germ at the origin of a two‐dimensional closed semialgebraic (or, more general, definable in a polynomially bounded o‐minimal ...
Lev Birbrair, Andrei Gabrielov
wiley +1 more source
The Moment Problem for Continuous Positive Semidefinite Linear functionals
, 2012 Let $\tau$ be a locally convex topology on the countable dimensional polynomial $\reals$-algebra $\rx:=\reals[X_1,...,X_n]$. Let $K$ be a closed subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated quadratic module in $\rx$. We
C. Berg +12 more
core +1 more source
New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
wiley +1 more source
Data‐driven methods for quantitative imaging
GAMM-Mitteilungen, Volume 48, Issue 1, March 2025.Abstract In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as quantitative magnetic resonance imaging (qMRI), where quantitative maps of biophysical parameters can characterize ...
Guozhi Dong +5 more
wiley +1 more source