相关论文: Testing the Existence of a Supporting Plane
The concurrence vectors are proposed by employing the fundamental representation of $A_n$ Lie algebra, which provides a clear criterion to evaluate the entanglement of bipartite system of arbitrary dimension for both pure and mixed states.…
Given a set $S$ of $n$ line segments in the plane, we say that a region $\mathcal{R}\subseteq \mathbb{R}^2$ is a {\em stabber} for $S$ if $\mathcal{R}$ contains exactly one endpoint of each segment of $S$. In this paper we provide optimal…
Huang, McKinnon, and Satriano conjectured that if $v \in \mathbb{R}^n$ has distinct coordinates and $n \geq 3$, then a hyperplane through the origin other than $\sum_i x_i = 0$ contains at most $2\lfloor n/2 \rfloor (n-2)!$ of the vectors…
A control system verification framework is presented for unmanned aerial vehicles using theorem proving. The framework's aim is to set out a procedure for proving that the mathematically designed control system of the aircraft satisfies…
In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
Small multi-rotor unmanned aerial vehicles (UAVs), mainly quadcopters, are nowadays ubiquitous in research on aerial autonomy, including serving as scaled-down models for much larger aircraft such as vertical-take-off-and-lift vehicles for…
The purpose of this paper is twofold. In the first part we concentrate on hyperplane sections of algebraic schemes, and present results for determining when Gr\"obner bases pass to the quotient and when they can be lifted. The main…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
J. J. Sylvester's four-point problem asks for the probability that four points chosen uniformly at random in the plane have a triangle as their convex hull. Using a combinatorial classification of points in the plane due to Goodman and…
Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few…
Obstacle avoidance is an essential topic in the field of autonomous drone research. When choosing an avoidance algorithm, many different options are available, each with their advantages and disadvantages. As there is currently no consensus…
The cutting plane approach to optimal matchings has been discussed by several authors over the past decades (e.g., Padberg and Rao '82, Grotschel and Holland '85, Lovasz and Plummer '86, Trick '87, Fischetti and Lodi '07) and its…
We show a new simple algorithm that solves the model-checking problem for recursion schemes: check whether the tree generated by a given higher-order recursion scheme is accepted by a given alternating parity automaton. The algorithm…
This article considers a cooperative vehicle routing problem for an intelligence, surveillance, and reconnaissance mission in the presence of communication constraints between the vehicles. The proposed framework uses a ground vehicle and…
This work proposes a receding horizon coverage control approach which allows multiple autonomous aerial agents to work cooperatively in order cover the total surface area of a 3D object of interest. The cooperative coverage problem which is…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present…
We consider the following problem: Let $\mathcal{L}$ be an arrangement of $n$ lines in $\mathbb{R}^3$ colored red, green, and blue. Does there exist a vertical plane $P$ such that a line on $P$ simultaneously bisects all three classes of…