73 research outputs found
Topology of 2D and 3D Rational Curves
In this paper we present algorithms for computing the topology of planar and
space rational curves defined by a parametrization. The algorithms given here
work directly with the parametrization of the curve, and do not require to
compute or use the implicit equation of the curve (in the case of planar
curves) or of any projection (in the case of space curves). Moreover, these
algorithms have been implemented in Maple; the examples considered and the
timings obtained show good performance skills.Comment: 26 pages, 19 figure
VALIDATION INTERNE DE LA METHODE DE DOSAGE DU PLOMB DANS LES PRODUITS DE LA PECHE PAR SPECTROPHOTOMETRIE DâABSORPTION ATOMIQUE EN FOUR A GRAPHITE (ASS-FG)
La validation intra laboratoire dâune mĂ©thode dâanalyse est dĂ©finie comme lâaction de soumettre une mĂ©thode dâanalyse Ă une Ă©tude statistique intra laboratoire, fondĂ©e sur un protocole normalisĂ© et/ou reconnu, et apportant la preuve que dans son domaine dâapplication, la mĂ©thode dâanalyse satisfait Ă des critĂšres de performance prĂ©Ă©tablis. Dans notre Ă©tude, nous avons utilisĂ© la norme marocaine NM 08.0.056 2007 pour valider en interne la mĂ©thode de dosage du Plomb dans les produits de la pĂȘche, en respectant les exigences spĂ©cifiques applicables Ă la spectrophotomĂ©trie dâAbsorption Atomique en Four Ă graphite (SAA-FG) Ă©ditĂ©es dans AOAC 2002, 999.10. La validation a Ă©tĂ© rĂ©alisĂ©e selon les quatre plans dâexpĂ©riences (types: A,B,C et D); le plan dâexpĂ©rience de type «A» pour caractĂ©riser la linĂ©aritĂ©, ainsi que les limites de dĂ©tection et de quantification de la courbe dâĂ©talonnage, le plan de type «B» pour le contrĂŽle des effets de matrice (spĂ©cificitĂ©) de la mĂ©thode, le plan de type «C» pour estimer la fidĂ©litĂ© (rĂ©pĂ©tabilitĂ© interne), la justesse et Ă©ventuellement la rĂ©pĂ©tabilitĂ© interne; et le plan de type «D» (optionnel) qui servira Ă calculer la reproductibilitĂ© interne. nous avons obtenus donc un domaine de linĂ©aritĂ© validĂ© (3-30ÎŒg/l), un modĂšle de rĂ©gression acceptable, la limite de dĂ©tection est de lâordre de 0,0015 ppb, la limite de quantification est de 0,005 ppb, la mĂ©thode est spĂ©cifique avec absence dâinterfĂ©rences, juste par rapport aux matĂ©riaux de rĂ©fĂ©rence et fidĂšle
A Szemeredi-Trotter type theorem in
We show that points and two-dimensional algebraic surfaces in
can have at most
incidences, provided that the
algebraic surfaces behave like pseudoflats with degrees of freedom, and
that . As a special case, we obtain a
Szemer\'edi-Trotter type theorem for 2--planes in , provided
and the planes intersect transversely. As a further special case, we
obtain a Szemer\'edi-Trotter type theorem for complex lines in
with no restrictions on and (this theorem was originally proved by
T\'oth using a different method). As a third special case, we obtain a
Szemer\'edi-Trotter type theorem for complex unit circles in . We
obtain our results by combining several tools, including a two-level analogue
of the discrete polynomial partitioning theorem and the crossing lemma.Comment: 50 pages. V3: final version. To appear in Discrete and Computational
Geometr
Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve
International audienceLet CP â©Q be a smooth real analytic curve embedded in R 3 , defined as the solutions of real analytic equations of the form P (x, y, z) = Q(x, y, z) = 0 or P (x, y, z) = âP âz = 0. Our main objective is to describe its projection C onto the (x, y)-plane. In general, the curve C is not a regular submanifold of R 2 and describing it requires to isolate the points of its singularity locus ÎŁ. After describing the types of singularities that can arise under some assumptions on P and Q, we present a new method to isolate the points of ÎŁ. We experimented our method on pairs of independent random polynomials (P, Q) and on pairs of random polynomials of the form (P, âP âz) and got promising results
A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications
International audienceEffective quantifier elimination procedures for first-order theories provide a powerful tool for genericallysolving a wide range of problems based on logical specifications. In contrast to general first-order provers, quantifierelimination procedures are based on a fixed set of admissible logical symbolswith an implicitly fixed semantics. Thisadmits the use of sub-algorithms from symbolic computation. We are going to focus on quantifier elimination forthe reals and its applications giving examples from geometry, verification, and the life sciences. Beyond quantifierelimination we are going to discuss recent results with a subtropical procedure for an existential fragment of thereals. This incomplete decision procedure has been successfully applied to the analysis of reaction systems inchemistry and in the life sciences
An Elementary Approach to Subresultants Theory
In this paper we give an elementary approach to univariate polynomial subresultants theory. Most of the known results of subresultants are recovered, some with more precision, without using Euclidean divisions or existence of roots for univariate polynomials. The main contributions of this paper are not new results on subresultants, but rather extensions of the main results over integral rings to arbitrary commutative rings
An Improved Upper Complexity Bound for the Topology Computation of a Real Algebraic Plane Curve
The computation of the topological shape of a real algebraic plane curve is usually driven by the study of the behavior of the curve around its critical points (which includes also the singular points). In this paper we present a new algorithm computing the topological shape of a real algebraic plane curve whose complexity is better than the best algorithms known. This is due to the avoiding, through a sufficiently good change of coordinates, of real root computations on polynomials with coefficients in a simple real algebraic extension of to deal with the critical points of the considered curve. In fact, one of the main features of this algorithm is that its complexity is dominated by the characterization of the real roots of the discriminant of the polynomial defining the considered curve
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