Related papers: Testing the Existence of a Supporting Plane
In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in…
One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
An algorithm to compute the six distances between particles of a planar Four-Body central configuration is presented according to the following schema. An orthocentric tetrahedron is computed as a function of given masses. Each mass is…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
We solve the Milne, constant-source and albedo problems for isotropic scattering in a two-dimensional "Flatland" half-space via the Wiener-Hopf method. The Flatland $H$-function is derived and benchmark values and some identities unique to…
We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
The Kerr theorem is revisited as part of the twistor program in six dimensions. The relationship between pure spinors and integrable 3-planes is investigated. The real condition for Lorentzian spacetimes is seen to induce a projective…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We…
Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
This work proposes a coverage controller that enables an aerial team of distributed autonomous agents to collaboratively generate non-myopic coverage plans over a rolling finite horizon, aiming to cover specific points on the surface area…
In this paper, we propose a cost-effective strategy for heterogeneous UAV swarm systems for cooperative aerial inspection. Unlike previous swarm inspection works, the proposed method does not rely on precise prior knowledge of the…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
The introduction of automated flight control and management systems have made possible aircraft designs that sacrifice arodynamic stability in order to incorporate stealth technology intro their shape, operate more efficiently, and are…
This article focuses on the occurrence of 3-point configurations in subsets of $\mathbb{R}^d$ of sufficient thickness. We prove that a compact set $A\subset \mathbb{R}^d$ contains a similar copy of any linear $3$-point configuration (such…
Lipton's reduction theory provides an intuitive and simple way for deducing the non-interference properties of concurrent programs, but it is difficult to directly apply the technique to verify linearizability of sophisticated fine-grained…