共查询到20条相似文献,搜索用时 15 毫秒
1.
J. Huisman 《Indagationes Mathematicae》2003,14(2):197-205
We improve Clifford's Inequality for real algebraic curves. As an application we improve Harnack's Inequality for real space curves having a certain number of pseudo-lines. Another application involves the number of ovals that a real space curve can have. 相似文献
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V. A. Krasnov 《Mathematical Notes》1998,64(3):347-350
Real theta characteristics of a real algebraic curve are studied. The numbers of even and odd real theta characteristics are
calculated. These numbers depend on the topological characteristics of the curve only.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 403–106, September, 1998. 相似文献
3.
Ricardo Uribe-Vargas 《Bulletin of the Brazilian Mathematical Society》2005,36(3):285-307
The focal curve of an immersed smooth curve γ : θ ↦ γ (θ), in Euclidean space ℝm+1, consists of the centres of its osculating hyperspheres. This curve may be parametrised in terms of the Frenet frame of γ (t, n1, . . . , nm), as Cγ (θ) = (γ +c1n1+ c2n2 + • • • + cmnm)(θ), where the coefficients c1, . . . , cm-1 are smooth functions that we call the focal curvatures of γ . We discovered a remarkable formula relating the Euclidean curvatures κi , i = 1, . . . ,m, of γ with its focal curvatures. We show that the focal curvatures satisfy a system of Frenet equations (not vectorial, but scalar!).
We use the properties of the focal curvatures in order to give, for ℓ = 1, . . . ,m, necessary and sufficient conditions for the radius of the osculating ℓ-dimensional sphere to be critical. We also give necessary
and sufficient conditions for a point of γ to be a vertex. Finally, we show explicitly the relations of the Frenet frame and the Euclidean curvatures of γ with the Frenet frame and the Euclidean curvatures of its focal curve Cγ. 相似文献
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We present a method for constructing shape-preserving C
3 interpolants in R
3. The resulting curve is obtained by adding a polynomial perturbation of high degree to a curve which is shape-preserving but not sufficiently smooth. The degree of the perturbed curve is selected in order to maintain the shape properties of the basic curve. 相似文献
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We study monomial curves, toric ideals and monomial algebras associated to 4-generated pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of these toric ideals, give a characterization for these monomial algebras to have strongly indispensable minimal graded free resolutions. We also characterize when the tangent cones of these monomial curves at the origin are Cohen–Macaulay. 相似文献
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Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves, a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found. Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper. 相似文献
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Masanori Asakura 《Inventiones Mathematicae》2002,149(3):661-685
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In this paper we study some problems in Hessian topology. We prove that certain real plane curves satisfy the requirements of the Hessian curve of a differential function. The real plane curves we consider are those with k outer ovals and also those which only have one nest of depth k, with \({k \in \mathbb{N}}\) . 相似文献
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B. G. Konopelchenko L. Martínez Alonso E. Medina 《Theoretical and Mathematical Physics》2007,151(3):820-830
Based on the Lenard relations, we completely classify integrable deformations of general algebraic curves. We construct the
general solution of the Lenard relation from the invariance condition with respect to an element of the Galois group of the
curve. We give some examples and also some associated conservation laws.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 458–469, June, 2007. 相似文献
17.
Z. Ran 《Israel Journal of Mathematics》2001,122(1):359-369
We consider the locus of smooth rational curves of given degree in a given projective space, which are incident to a generic
collection of linear spaces. When this locus is finite (resp. 1-dimensional) we give a recursive procedure to compute its
degree (resp. geometric genus). The method is based on the elementary geometry of ruled surfaces. 相似文献
18.
Alexandra Shlapentokh 《Archive for Mathematical Logic》2009,48(1):77-114
We show that elliptic curves whose Mordell–Weil groups are finitely generated over some infinite extensions of , can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite
extensions of rational numbers.
相似文献
19.
Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let
. Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces. 相似文献
20.
Hisao Yoshihara 《Proceedings of the American Mathematical Society》1996,124(5):1371-1375
We consider the degree of irrationality of some algebraic surface . Firstly we give an estimate of for a surface with a structure of a fiber space. Secondly we prove the existence of a nonsingular curve of genus 3 on for a certain elliptic curve with complex multiplications. As a corollary, we obtain that .