相关论文: A note on geodesics on ellipsoid

The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…

We prove a lower bound for the topological complexity, in the sense of Smale, of the problem of finding a flex point on a cubic plane curve. The key is to bound the Schwarz genus of a cover associated to this problem. We also show that our…

We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle…

This note contains some observations on abelian convexity theorems. Convexity along an orbit is established in a very general setting using Kempf-Ness functions. This is applied to give short proofs of the Atiyah-Guillemin-Sternberg theorem…

A new algorithm for the efficient numerical approximation of weakly singular integrals over convex polytopes is introduced. Such integrals appear in the Galerkin discretizations of integral equations and nonlocal partial differential…

We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean space via Gauss map. In this way, the result for Bernstein…

Weierstrass elliptic and related functions have been recently shown to enable analytical explicit solutions to classical problems in astrodynamics. These include the constant radial acceleration problem, the Stark problem and the two-fixed…

The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is,…

We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the…

On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude…

We prove that, generically, magnetic geodesics on surfaces will turn away from points with lightlike tangent planes, and we motivate our result with numerical solutions for closed magnetic geodesics.

Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards.…

In this paper we study geodesic mappings of $n$-dimensional surfaces of revolution. From the general theory of geodesic mappings of equidistant spaces we specialize to surfaces of revolution and apply the obtained formulas to the case of…

We show how the basic idea of parabolic Jacobi relaxation can be modified to obtain a new class of hyperbolic relaxation schemes that are suitable for the solution of elliptic equations. Some of the analytic and numerical properties of…

Orbit determination (OD) from three position vectors is one of the classical problems in astrodynamics. Early contributions to this problem were made by J. Willard Gibbs in the late 1800s and OD of this type is known today as ``Gibbs…

We study the theta decomposition of Jacobi forms of nonintegral lattice index for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications.

The paper is devoted to investigating a Cauchy problem for nonlinear elliptic PDEs in the abstract Hilbert space. The problem is hardly solved by computation since it is severely ill-posed in the sense of Hadamard. We shall use a modified…

We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…

The Jacobian elliptic functions are generalized to functions including the generalized trigonometric functions. The paper deals with the basis property of the sequence of generalized Jacobian elliptic functions in any Lebesgue space. In…