Related papers: A minimum-energy quadratic curve through three poi…
In this paper, we propose a novel optimization-based trajectory planner that utilizes spherical harmonics to estimate the collision-free solution space around an agent. The space is estimated using a constrained over-determined…
We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…
We discuss a large class of conformally invariant curvature energies for immersed hypersurfaces of dimension 4. The class under study includes various examples that have appeared in the recent literature and which arise from different…
A realistic generalization of the Markov--Dubins problem, which is concerned with finding the shortest planar curve of constrained curvature joining two points with prescribed tangents, is the requirement that the curve passes through a…
In the field of aesthetic design, log-aesthetic curves have a significant role to meet the high industrial requirements. In this paper, we propose a new interactive $G^1$ Hermite interpolation method based on the algorithm of Yoshida et al.…
In one spatial dimension, quantum systems with an attractive three-body contact interaction exhibit a scale anomaly. In this work, we examine the few-body sector for up to six particles. We study those systems with a self-consistent,…
We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a…
In this paper, we define some new associated curves as integral curves of a vector field generated by Frenet vectors of tangent indicatrix of a curve in Euclidean 3-space. We give some relationships between curvatures of these curves. By…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
The enumeration of shortest paths in cubic grid is presented herein, which could have importance in image processing and also in the network sciences. The cubic grid considers three neighborhoods - namely, 6-, 18- and 26-neighborhood…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves defined over a number field k. Since the plane quartic curves are non-hyperelliptic curves of genus 3 we can apply the method developed by…
We propose and test a renormalization procedure which acts in Hilbert space. We test its efficiency on strongly correlated quantum spin systems by working out and analyzing the low-energy spectral properties of frustrated quantum spin…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
Offset curves for planar trajectories are interesting in the generation of tool paths for numerically controlled industrial machines and in trajectory planning methods for autonomous driving systems. Theoretical offset curves may exhibit…
A minimal model for magnetic reconnection and, generally, low-frequency dynamics in low-beta plasmas is proposed. The model combines analytical and computational simplicity with physical realizability: it is a rigorous limit of gyrokinetics…
In this work we present an attractive least-squares fitting procedure to obtain a quartic force field by using energy, gradient and Hessian data arising from electronic wave function calculations on a suitably chosen grid of points. We use…
We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a…