相关论文: Preferred Parameterisations on Homogeneous Curves

In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…

In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are…

Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area…

The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct…

We study the order of lengths of closed geodesics on hyperbolic surfaces. Our first main result is that the order of lengths of curves determine a point in Teichm\"uller space. In an opposite direction, we identify classes of curves whose…

We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex…

Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…

We construct the Lagrangian Floer homotopy type, in the exact setting, as a spectrum parameterized over the moduli space of Maslov data. Our primary motivation for this construction is to provide stronger lower bounds for (possibly…

We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic…

We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the collection of all such mappings (in the…

In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…

In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in…

We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.

Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…

For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…

The paper studies homogenization problem for a non-autonomous parabolic equation with a large random rapidly oscillating potential in the case of one dimensional spatial variable. We show that if the potential is a statistically homogeneous…

We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…

The parameter-uniform convergence of a fitted operator method for a singularly perturbed differential equation is normally available only for uniform meshes. Here we establish the parameter-uniform convergence of a fitted operator method on…

An investigation of morphisms that coincide topologically is used to generalize to all characteristics and partly reprove Tamagawa's theorem on the Grothendieck conjecture in anabelian geometry for affine hyperbolic curves. The theorem now…