Discrete-Time Fractional Variational Problems

We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when $h$ tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.Comment: Submitted 24/Nov/2009; Revised 16/Mar/2010; Accepted 3/May/2010; for publication in Signal Processing

An experience with Desmos in the study of the quadratic function

In this paper we present a didactic experience in the subject of Mathematics carried out in a distance learning context, on the topic Quadratic Function, using the digital and free platform Desmos. The use of this tool was determinant for the teaching and learning of quadratic function since its teaching took place in distance education, due to the pandemic situation. In a pandemic context, the use of tools to gauge student learning was a necessity, but practices such as the one described in this paper should be incorporated into a normal classroom environment, promoting discovery through graphical and algebraic manipulation.publishe

An optimization method for the best fractional order to estimate real data analysis

In this paper we consider fractional differential equations, with dependence on a Caputo fractional derivative of real order. Using real experimental data of Blood Alcohol Level we obtain a system of fractional differential equations that model the problem. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data as well as other related parameters. We prove that it describes better the dynamics than the classical one

The weird governance of fact-checking: from watchdogs to content moderators

In this work, we chart the multiple conflicts between stakeholders in the pursuit of a common standard for fact-checking outside Western Industrialized Educated Rich and Educated (WEIRD) countries, a problem that sits at the center of the institutional mission of fact-checkers as watchdogs of politicians and enforcers of content moderation. We apply reflexive thematic analysis to a set of interviews with 37 fact-checking experts from 35 organizations in 27 countries to catalogue the methods employed by fact-checkers and the pressures they contend with in non-WEIRD countries. In contrast to the one-size-fits-all approach to community guidelines implemented by social platforms worldwide, our results show that the asymmetric relationship with platform companies compels fact-checkers to adjust their methods and strategies to account for the political and cultural dimensions driving mis- and disinformation in their local contexts. Our findings detail three ways through which social platforms impinge on the scope, values, and institutional mission of non-WEIRD fact-checking organizations. As we argue, the platformization of non-WEIRD fact-checkers entails a convoluted process in which social media platforms gradually nudge fact-checkers into becoming part of the content moderation industry, a shift that runs counter to the democracy-building values underpinning the fact-checking movement. We conclude with a discussion of our findings and recommendations for content moderation both in WEIRD and non-WEIRD contexts

The use of essential oils to protect rice from storage fungi

Rice (Oryza sativa) is the main food of half of the population of our planet. The growth of fungi closely associated to the eventual occurrence of mycotoxins can be responsible for serious economic losses and public health risks. Knowledge about the origin of the growth of toxigenic fungi is a prerequisite to the establishment of mycotoxin control programs. Socio-economical and environmental factors led to an extreme reduction of rice availability, while the estimated rice production losses increased in all continents what increases the importance to develop new harmless strategies for the control of fungi affecting stored rice. Natural products from plant origin were screened for the control of main pernicious fungi.In this work we have collected rice samples from different origins (national and imported) and these samples were analysed for fungal infection. Several fungi taxa were isolated: Absidia, Alternaria, Aspergillus, Bipolaris, Botrytis, Chaetomium, Curvularia, Cunninghamela, Epicoccum, Fusarium, Geotrichum, Helicoma, Nigrospora, Penicillium, Pyricularia, Rhizopus, Scytalidium, Stemphylium, Sordaria, Trichoconiella, Trichoderma, Trichothecium and Ulocladium. Some of the fungi isolated are potentially mycotoxigenic. We also studied a way to control the growth of some of these fungi using plant extracts and essential oils from Syzyginum aromaticum and Laurus nobilis. Promising results were obtained.Keywords: Rice, Cereals, Fungi, Bio-pesticides, Plant extracts