Plane Curves(平面曲线)研究综述
Plane Curves 平面曲线 - We investigate the problem of classifying pencils of plane curves of degree d up to projective equivalence. [1] Applications also include a non-iterative construction of the uniform parametrization for an important class of plane curves, which is used in a convergence study of the time-stepping procedure implemented in the previous work by Nitsche and Steen [J. [2] The chapter is devoted to the study of plane curves from the point of view of differential geometry. [3] The plane curves of constant equiaffine curvature with fractional-order are classified. [4] The same technique applies to enumeration of real plane cuspidal curves: we show that, for any fixed $r\ge 1$ and $d\ge 2r+3$, there exists a generic real $2r$-dimensional linear family of plane curves of degree $d$ in which the number of real $r$-cuspidal curves is asymptotically comparable with the total number of complex $r$-cuspidal curves in the family, as $d\to \infty $. [5] The objective of this paper is to define one class of plane curves with arc-length parametrization. [6] This paper introduces a geometric generalization of signed distance fields for plane curves. [7] The article reveals a set of quantitative indicators that sufficiently and completely characterize the visual smoothness and clarity of the central projections of elementary spatial and plane curves. [8] (1998) for plane curves with M being the composition of a dilatation and a rotation. [9] In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. [10] We illustrate this with a variety of examples: (chaotic) time series, plane curves, space filling curves, knots and strange attractors. [11] We focus on quadrics and plane curves of low degree (i. [12] As a by-product we recover a theorem of du Plessis-Wall on the global Tjurina number of plane curves and some other related results. [13] The idea of envelope of a family of plane curves is an elementary notion in differential geometry. [14] We compute the equation of the mirror $M$ of the orbifold ball quotient $(X,M)$ and by taking the quotient by an involution, we obtain an orbifold ball quotient surface with mirror birational to an interesting configuration of plane curves of degrees $1,2$ and $3$. [15] In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. [16] A surface is formed on the basis of the framework, linear elements of which are plane curves, which are defined analytically or structurally. [17] We investigate the relationship of primitivoids and pedals of plane curves. [18] Over the past forty years many papers have studied logarithmic sheaves associated to reduced divisors, in particular logarithmic bundles associated to plane curves. [19] In this paper, for the orthogonal group G = O(2) and special orthogonal group G = O+(2) global G-invariants of plane paths and plane curves in two-dimensional Euclidean space E2 are studied. [20] The computation of the dimension of linear systems of plane curves through a bunch of given multiple points is one of the most classic issues in algebraic geometry. [21] ABSTRACT We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. [22] The first complexity analysis of the \pv~Algorithm is due to Burr, Gao and Tsigaridas who proved a \mathcalO \big(2^τ d^4 łog d \big) worst-case cost bound for degree d plane curves with maximum coefficient bit-size~τ. [23] We use the intersection theory of plane curves to show that this number is 2n− 3. [24] Using results of Greuel and Knorrer this yields a characterization of plane curves of finite Cohen--Macaulay type in terms of trace ideals. [25] Implicitization usually focuses on plane curves and (hyper)surfaces, in other words, varieties of codimension 1. [26] It is based on the winding number of plane curves, that is related to the number of zeros of a polynomial in a plane region. [27] This is an improvement over existing algorithms which could only compute the periods of plane curves. [28]我们研究了将 d 次平面曲线的铅笔分类到射影等价的问题。 [1] 应用还包括对一类重要平面曲线的均匀参数化的非迭代构造，该构造用于 Nitsche 和 Steen 先前工作中实施的时间步长过程的收敛性研究 [J. [2] 本章致力于从微分几何的角度研究平面曲线。 [3] 对分数阶等等仿曲率的平面曲线进行分类。 [4] 相同的技术适用于实平面尖曲线的枚举：我们证明，对于任何固定的 $r\ge 1$ 和 $d\ge 2r+3$，存在一个通用的实平面曲线的 $2r$ 维线性族度为 $d$，其中实际 $r$-尖牙曲线的数量与家庭中复杂 $r$-尖牙曲线的总数渐近可比，如 $d\to\infty$。 [5] 本文的目的是定义一类具有弧长参数化的平面曲线。 [6] 本文介绍了平面曲线的有符号距离场的几何推广。 [7] 文章揭示了一组量化指标，充分、完整地表征了基本空间曲线和平面曲线的中心投影的视觉平滑度和清晰度。 [8] (1998) 对于平面曲线，M 是膨胀和旋转的组合。 [9] 为了做到这一点，我们将注意力限制在平面曲线的特殊情况上，即平滑曲线在更高维度上的投影。 [10] 我们用各种例子来说明这一点：（混沌）时间序列、平面曲线、空间填充曲线、节点和奇怪的吸引子。 [11] 我们专注于低度数的二次曲线和平面曲线（i. [12] 作为副产品，我们恢复了关于全局 Tjurina 平面曲线数的 du Plessis-Wall 定理和一些其他相关结果。 [13] 平面曲线族的包络概念是微分几何中的一个基本概念。 [14] 我们计算了orbifold 球商$(X,M)$ 的镜像$M$ 的方程，并通过对合取商，我们获得了一个orbifold 球商表面，其镜像双有理化到度数平面曲线的有趣配置1.2 美元和 3 美元。 [15] 在形状匹配和对象分类的弹性形状分析方法中，平面曲线表示为无限维黎曼流形中的点，其中形状相异性通过测地线距离测量。 [16] 一个表面是在框架的基础上形成的，其线性元素是平面曲线，它们是通过解析或结构定义的。 [17] 我们研究了原始空隙和平面曲线的踏板之间的关系。 [18] 在过去的四十年中，许多论文研究了与约数除数相关的对数滑轮，特别是与平面曲线相关的对数束。 [19] 本文针对正交群G=O(2)和特殊正交群G=O+(2)研究了二维欧几里得空间E2中平面路径和平面曲线的全局G-不变量。 [20] 通过一组给定的多点计算平面曲线线性系统的维数是代数几何中最经典的问题之一。 [21] 摘要 我们研究将欧几里得平面上的函数映射到其在平面曲线上的积分族的积分变换，即平面曲线的函数。 [22] \pv~算法的第一个复杂性分析归功于 Burr、Gao 和 Tsigaridas，他们证明了具有最大系数的 d 次平面曲线的 \mathcalO \big(2^τ d^4 łog d \big) 最坏情况成本界比特大小~τ。 [23] 我们使用平面曲线的相交理论来证明这个数是 2n-3。 [24] 使用 Greuel 和 Knorrer 的结果，这产生了根据迹理想的有限 Cohen-Macaulay 类型的平面曲线的表征。 [25] 隐式通常侧重于平面曲线和（超）曲面，换句话说，就是余维数 1 的变体。 [26] 它基于平面曲线的绕组数，与平面区域内多项式的零点数有关。 [27] 这是对只能计算平面曲线周期的现有算法的改进。 [28]
Smooth Plane Curves 平滑平面曲线
A number of quasi-Galois points for smooth plane curves of degree d are studied. [1] We study the asymptotic proportion of smooth plane curves over a finite field $\mathbb{F}_q$ which are tangent to every line defined over $\mathbb{F}_q$. [2] For a fixed integer $$d\ge 4$$ , the list of groups that appear as automorphism groups of smooth plane curves whose degree is d is unknown, except for $$d=4$$ or 5. [3] We consider the parameter space $\mathcal U_d$ of smooth plane curves of degree $d$. [4] We characterize twists possessing such models and use such characterization to improve, for the particular case of smooth plane curves, the algorithm to compute twists of non-hyperelliptic curves wrote recently down by the third author. [5] We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. [6]研究了d次平滑平面曲线的若干拟伽罗瓦点。 [1] 我们研究了有限域 $\mathbb{F}_q$ 上平滑平面曲线的渐近比例，这些曲线与定义在 $\mathbb{F}_q$ 上的每条线相切。 [2] 对于固定整数 $$d\ge 4$$ ，作为度数为 d 的平滑平面曲线的自同构群出现的群的列表是未知的，除了 $$d=4$$ 或 5。 [3] 我们考虑度为$d$ 的平滑平面曲线的参数空间$\mathcal U_d$。 [4] 我们对具有此类模型的扭曲进行了表征，并使用此类表征来改进对于平滑平面曲线的特定情况，第三作者最近写下的计算非超椭圆曲线扭曲的算法。 [5] 我们给出了两种算法来计算任何场上任何度数的平滑平面曲线的线性行列式表示。 [6]
Tropical Plane Curves 热带平面曲线
As an application of this classification, we prove new obstructions to graphs arising as skeleta of tropical plane curves. [1] Tropical plane curves are one of the building blocks in the study of tropical algebraic geometry. [2] We study tropically planar graphs, which are the graphs that appear in smooth tropical plane curves. [3] Our model arises from considerations on tropical plane curves, which are zeros of random tropical polynomials in two variables. [4]作为这种分类的一个应用，我们证明了作为热带平面曲线骨架的图形的新障碍。 [1] 热带平面曲线是热带代数几何研究的基石之一。 [2] 我们研究热带平面图，即出现在平滑热带平面曲线中的图。 [3] 我们的模型源于对热带平面曲线的考虑，热带平面曲线是两个变量中随机热带多项式的零点。 [4]
Closed Plane Curves
This paper deals with the 1 / κ α -type area-preserving nonlocal flow of smooth convex closed plane curves for all constant α > 0. [1] We consider a problem of realizability of Gauss diagrams by closed plane curves where the plane curves have only double points of transversal self-intersection. [2] We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants J ± and St behave under the generalized connected sums. [3]本文处理所有常数 α > 0 的光滑凸闭合平面曲线的 1 / κ α 型保面积非局部流动。 [1] 我们考虑通过封闭平面曲线实现高斯图的问题，其中平面曲线只有两个横向自交点。 [2] 我们定义了通用闭合平面曲线的广义连通和，推广了 Arnold 定义的奇异和，并完整描述了 Arnold 不变量 J ± 和 St 在广义连通和下的行为。 [3]
Certain Plane Curves
We investigate algorithms for encoding of one-point algebraic geometry (AG) codes over certain plane curves called我们研究了在称为 <inline-formula> <tex-math notation="LaTeX">$C_{ab}$ </tex-math></inline 的某些平面曲线上对单点代数几何 (AG) 代码进行编码的算法-formula> 曲线，以及用于反转编码映射的算法，我们称之为“unencoding”。 [1] 然后 Bauer、Malara、Szpond 和 Szemberg 研究了意想不到的超曲面，接着是 Harbourne、Migliore、Nagel 和 Teitler，他们引入了 BMSS 对偶性的概念，并表明它在某些情况下是成立的（例如某些平面曲线，在更高维度上，对于某些锥体）。 [2]
Algebraic Plane Curves
this constraint on the relative positions of the graphs of four real polynomials, the author tries to understand all such constraints, then to place the problem in the more general context of singularities of real algebraic plane curves, that is, curves defined implicitly by equations of the form F(x,y) = 0 for some real polynomial F. [1] The goal of this paper is to measure the non-convexity of compact and smooth connected components of real algebraic plane curves. [2]这种对四个实数多项式图的相对位置的约束，作者试图理解所有这些约束，然后将问题放在更一般的实数平面曲线奇异性的上下文中，即由方程隐含定义的曲线一些实数多项式 F 的形式 F(x,y) = 0。 [1] 本文的目标是测量实代数平面曲线的紧致平滑连通分量的非凸性。 [2]
Quartic Plane Curves
As a novel contribution, we propose quartic plane curves to represent the confidence regions of the loci of conic sections. [1] Sensing zone of a single transmitter-receiver couple in such systems is defined by Cassini ovals, a family of quartic plane curves with unique properties. [2]作为一个新颖的贡献，我们提出了四次平面曲线来表示圆锥截面轨迹的置信区域。 [1] 这种系统中单个发射器-接收器对的传感区域由卡西尼椭圆定义，这是一组具有独特属性的四次平面曲线。 [2]
plane curves behavior
This question involves the traces’s family of plane curves behavior, whose initial trace of the curve is given by a circle of radius k and the whose others, intuitively, approach to a square with side measuring 2k. [1] This question involves the traces’s family of plane curves behavior, whose initial trace of the curve is given by a circle of radius k and the whose others, intuitively, approach to a square with side measuring 2k. [2]这个问题涉及迹线的平面曲线行为族，其曲线的初始迹线由半径为 k 的圆给出，其其他迹线直观地接近边长为 2k 的正方形。 [1] 这个问题涉及迹线的平面曲线行为族，其曲线的初始迹线由半径为 k 的圆给出，其其他迹线直观地接近边长为 2k 的正方形。 [2]
plane curves whose
For a fixed integer $$d\ge 4$$ , the list of groups that appear as automorphism groups of smooth plane curves whose degree is d is unknown, except for $$d=4$$ or 5. [1] ABSTRACT We analyze the variation around the mean of the distribution of the number of rational points on non-hyperelliptic genus 3 curves over finite fields, by extrapolating from results on the distribution of traces of Frobenius for plane curves whose degree is small with respect to the cardinality of their finite base field. [2]对于固定整数 $$d\ge 4$$ ，作为度数为 d 的平滑平面曲线的自同构群出现的群的列表是未知的，除了 $$d=4$$ 或 5。 [1] 摘要 我们通过从 Frobenius 迹分布的结果外推非超椭圆属 3 曲线上的有理点数分布在有限域上的平均值的变化它们的有限基域的基数。 [2]
plane curves obtained 获得的平面曲线
The reliability of the devised setup is verified by finite element simulation and by reproducing in-plane curves obtained via an anti-buckling fixture. [1] In recent work, Annette Werner and the author initiated the study of degenerations of plane curves obtained by Mustafin varieties by means of arithmetic geometry. [2]所设计装置的可靠性通过有限元模拟和再现通过抗屈曲夹具获得的平面内曲线来验证。 [1] 在最近的工作中，Annette Werner 和作者发起了用算术几何的方法对 Mustafin 簇获得的平面曲线的退化进行了研究。 [2]