Related papers: Solving the Gibbs Problem with Algebraic Projectiv…
We provide an algorithmic approach to the construction of point transformations for scalar ordinary differential equations that admit three-dimensional symmetry algebras which lead to their respective canonical forms.
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
Orbital semilattices are introduced as bounded semilattices that are, in addition, equipped with an outer multiplication (a semigroup action) and diagonals (a concept borrowed from cylindric algebra), where each semilattice element has a…
Applying symmetry reduction to a class of $\mathrm{SL}(2,\mathbb R)$-invariant third-order ODEs, we obtain Abel equations whose general solution can be parametrised by hypergeometric functions. Particular case of this construction provides…
In this paper, we present a deterministic algorithm to find a strong generic position for an algebraic space curve. We modify our existing algorithm for computing the topology of an algebraic space curve and analyze the bit complexity of…
We present a novel numerical method for solving ODEs while preserving polynomial first integrals. The method is based on introducing multiple quadratic auxiliary variables to reformulate the ODE as an equivalent but higher-dimensional ODE…
We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
We present a deformation of the Okubic Albert algebra introduced by Elduque whose rank-1 idempotent elements are in biunivocal correspondence with points of the Okubic projective plane, thus extending to Okubic algebras the correspondence…
We present the results of our investigation on the use of the two-body integrals to compute preliminary orbits by linking too short arcs of observations of celestial bodies. This work introduces a significant improvement with respect to the…
We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…
In celestial mechanics, proper orbits related to missions are obtained by solving two-point boundary value problems. Since a selection method of initial value affects the convergence of the solution, developing an effective method to find…
In orbital mechanics, Gauss's method for orbit determination (OD) is a popular, minimal assumption solution for obtaining the initial state estimate of a passing resident space object (RSO). Since much of the cislunar domain relies on…
The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…
Motivated by the necessity to find exact solutions with the elliptic Weierstrass function of the Einstein's equations (see gr-qc/0105022),the present paper develops further the proposed approach in hep-th/0107231, concerning the s.c. cubic…
Three point mass gravitational lens equation is a two-dimensional vector equation that can be embedded in a tenth order analytic polynomial equation of one complex variable, and we can solve the one variable equation on the source…
We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…
We study the orchard problem on cubic surfaces. We classify possibly reducible cubic surfaces $X\subseteq \mathbb{P}^3(\C)$ with smooth components on which there exist families of finite sets (of unbounded size) with quadratically many…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
In this paper we introduce a new classification algorithm called Optimization of Distributions Differences (ODD). The algorithm aims to find a transformation from the feature space to a new space where the instances in the same class are as…