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Calculation of industrial robot trajectory in frame composite production

Mlýnek, Jaroslav, Martinec, Tomáš, Petrů, Michal (2017)

Programs and Algorithms of Numerical Mathematics

This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide...

Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang, Shanyu Ji (2002)

Annales de l’institut Fourier

For a strongly pseudoconvex domain $D \subset ℂ^{n + 1}$ defined by a real polynomial of degree $k_{0}$ , we prove that the Lie group $Aut (D)$ can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle $Y$ of $\partial D$ , and that the sum of its Betti numbers is bounded by a certain constant $C_{n, k_{0}}$ depending only on $n$ and $k_{0}$ . In case $D$ is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...

Central Orderings in Fields of Real Meromorphic Function Germs.

Jesús M. Ruiz (1984)

Manuscripta mathematica

Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities

M. Baran, W. Pleśniak (2000)

Studia Mathematica

We show that in the class of compact sets K in $ℝ^{n}$ with an analytic parametrization of order m, the sets with Zariski dimension m are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for tangential derivatives of (the traces of) polynomials on K.

Characterization of smooth, compact algebraic curves in ℝ²

L. Bos, N. Levenberg, B. Taylor (1995)

Banach Center Publications

Classification of obstructions for separation of semialgebraic sets in dimension 3.

F. Acquistapace, F. Broglia, C. Andradas (1997)

Revista Matemática de la Universidad Complutense de Madrid

Applying general results on separation of semialgebraic sets and spaces of orderings, we produce a catalogue of all possible geometric obstructions for separation of 3-dimensional semialgebraic sets and give some hints on how separation can be made decidable.

Clifford’s Theorem for real algebraic curves

Jean-Philippe Monnier (2010)

Annales de l’institut Fourier

We establish, for smooth projective real curves, an analogue of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

Closure Theorem for Partially Semialgebraic Sets

María-Angeles Zurro (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

In 1988 it was proved by the first author that the closure of a partially semialgebraic set is partially semialgebraic. The essential tool used in that proof was the regular separation property. Here we give another proof without using this tool, based on the semianalytic L-cone theorem (Theorem 2), a semianalytic analog of the Cartan-Remmert-Stein lemma with parameters.

Codimension 1 subvarieties $ℳ_{g}$ and real gonality of real curves

Edoardo Ballico (2003)

Czechoslovak Mathematical Journal

Let $ℳ_{g}$ be the moduli space of smooth complex projective curves of genus $g$ . Here we prove that the subset of $ℳ_{g}$ formed by all curves for which some Brill-Noether locus has dimension larger than the expected one has codimension at least two in $ℳ_{g}$ . As an application we show that if $X \in ℳ_{g}$ is defined over $ℝ$ , then there exists a low degree pencil $u X \to ℙ^{1}$ defined over $ℝ$ .

Codimension two transcendental submanifolds of projective space

Wojciech Kucharz, Santiago R. Simanca (2010)

Annales de l’institut Fourier

We provide a simple characterization of codimension two submanifolds of $ℙ^{n} (ℝ)$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n \geq 6$ . If the codimension two submanifold is a nonsingular algebraic subset of $ℙ^{n} (ℝ)$ whose Zariski closure in $ℙ^{n} (ℂ)$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in $ℙ^{n} (ℝ)$ .

Cohomologie de Galois et cohomologie des variétés algébriques réelles ; applications aux surfaces rationnelles

R. Silhol (1987)

Bulletin de la Société Mathématique de France

Coloring triangles and rectangles

Jindřich Zapletal (2023)

Commentationes Mathematicae Universitatis Carolinae

It is consistent that ZF + DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles on $ℝ^{2}$ does not.

Compactification via le spectre réel d’espaces des classes de représentation dans SO $(n, 1)$

Taoufik Bouzoubaa (1994)

Annales de l'institut Fourier

Soit $Γ$ un groupe de type fini non élémentaire. On note $D^{n} (Γ)$ l’ensemble des structures hyperboliques de dimension $n$ sur $Γ$ . $D^{n} (Γ)$ peut se réaliser comme fermé dans un espace semi-algébrique qui admet une compactification naturelle par le spectre réel. On note ${\overline{D^{n} (Γ)}}^{sp}$ le compactifié via le $\underline{spectre}$ réel de $D^{n} (Γ)$ . L’objet de cet article est de décrire les points ajoutés dans ${\overline{D^{n} (Γ)}}^{sp}$ . La compactification obtenue de cette manière permet d’interpréter “les points frontières” comme des représentations de $Γ$ dans ${SO}_{F}^{+} (n, 1)$ où $F (\supset ℝ)$ est un corps réel...

Compactifications de l'espace de modules de Hilbert-Blumenthal

M. Rapoport (1978)

Compositio Mathematica

Compactifications of moduli spaces in real algebraic geometry.

R. Silhol (1992)

Inventiones mathematicae

Complete decomposability of quotients by complex conjugation for real complete intersection surfaces.

S. M. Finashin (1997)

Revista Matemática de la Universidad Complutense de Madrid

Complex arrangements and derivations.

Knöller, F.W. (1997)

General Mathematics

Complex orientation formulas for $M$ -curves of degree $4 d + 1$ with 4 nests

S.Yu. Orevkov (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

On démontre la formule d’orientations complexes pour les $M$ -courbes dans ${ℝ P}^{2}$ de degré $4 d + 1$ ayant $4$ nids. Cette formule généralise celle pour les $M$ -courbes à nid profond. C’est un pas vers la classification des $M$ -courbes de degré $9$ .

Complexifications of nonnegatively curved manifolds

Burt Totaro (2003)

Journal of the European Mathematical Society

Complexity of intersections of real quadrics and topology of symmetric determinantal varieties

Antonio Lerario (2016)

Journal of the European Mathematical Society

Currently displaying 1 – 20 of 38

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