arXiv subjects

Carlos Rivera

Publications and source records attributed to Carlos Rivera.

5 recordsLinked to original sources

arXiv2022

Persistence of the Brauer-Manin obstruction on cubic surfaces

Let $X$ be a cubic surface over a global field $k$. We prove that a Brauer-Manin obstruction to the existence of $k$-points on $X$ will persist over every extension $L/k$ with degree relatively prime to $3$. In other words, a cubic surface has nonempty Brauer set over $k$ if and only if it has nonempty Brauer set over some extension $L/k$ with $3\nmid[L:k]$. Therefore, the conjecture of Colliot-Thélène and Sansuc on the sufficiency of the Brauer-Manin obstruction for cubic surfaces implies that $X$ has a $k$-rational point if and only if $X$ has a $0$-cycle of degree $1$. This latter statement is a special case of a conjecture of Cassels and Swinnerton-Dyer.

math.NT↗

arXiv2022

The integral trace form as a complete invariant for real $S_n$ number fields

In the past the first named author has studied to what extent the integral trace can characterize a number field beyond what the discriminant does. The cases of cyclic number fields and non-totally real fields are more or less settled, concluding that for such fields the integral trace does not always characterize the field. In this paper we show that the integral trace is a complete invariant for degree $n$, $S_n$ real number number fields that satisfy certain ramification bound. Among the real $S_n$ fields that our results cover, there are those of square free different ideal. Moreover, for such fields we find an explicit description of the isometry group of the integral trace.

math.NT↗

arXiv2020

Teleoperated aerial manipulator and its avatar. Part 1: Communication, system's interconnection, control, and virtual world

The tasks that an aerial manipulator can perform are incredibly diverse. However, nowadays the technology is not completely developed to achieve complex tasks autonomously. That's why we propose a human-in-the-loop system that can control a semi-autonomous aerial manipulator to accomplish these kinds of tasks. Furthermore, motivated by the growing trend of virtual reality systems, together with teleoperation, we develop a system composed of: an aerial manipulator model programmed in PX4 and modeled in Gazebo, a virtual reality immersion with an interactive controller, and the interconnection between the aforementioned systems via the Internet. This research is the first part of a broader project. In this part, we present experiments in the software in the loop simulation. The code of this work is liberated on our GitHub page. Also, a video shows the conducted experiments.

cs.RO↗

arXiv2020

Non-Stationary Stochastic Global Optimization Algorithms

Gomez proposes a formal and systematic approach for characterizing stochastic global optimization algorithms. Using it, Gomez formalizes algorithms with a fixed next-population stochastic method, i.e., algorithms defined as stationary Markov processes. These are the cases of standard versions of hill-climbing, parallel hill-climbing, generational genetic, steady-state genetic, and differential evolution algorithms. This paper continues such a systematic formal approach. First, we generalize the sufficient conditions convergence lemma from stationary to non-stationary Markov processes. Second, we develop Markov kernels for some selection schemes. Finally, we formalize both simulated-annealing and evolutionary-strategies using the systematic formal approach.

math.OC↗

arXiv2011

Effects of electrostatic force on piezoelectric materials under high electric field: Impact on GaN-based nanoscale structures

The determination of the electromechanical properties of materials for a parallel-plate capacitor structure is affected by the electrostatic force between their electrodes. The corrections induced by this electric-field-induced stress are usually assumed to be linked to the quadratic dependence of the strain on the electric field (electrostriction). Here we show by calculations based on thermodynamic grounds for this simple structure that the effect of the electrostatic force on piezoelectric materials can lead to both quadratic and linear corrections through the combination of the piezoelectric coupling and spontaneous polarization. The case of GaN-based capacitor nanoscale structures is presented taking into account the boundary conditions imposed as well as the effect of geometry. The results in this example point to corrections in the piezoelectric and electrostrictive coefficients higher than 0.3 pmV-1 and 2.6x10-22 m2V-2, respectively.

cond-mat.mtrl-sci↗