Preserving levels of projective determinacy by tree forcings

We prove that various classical tree forcings -- for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing -- preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes classes are added to thin projective transitive relations by these forcings.Comment: 3 figure

Simple permutations with order 4n+24n + 2. Part I

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez & Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behavior of those periodic points. This paper studies the structure of permutations of mixed order $4n+2$, its properties and a way to describe its genealogy by using Pasting and Reversing.Comment: 17 page

Report on identifying a protocol to elicit flowering in Brachiaria humidicola with photoperiod management

Two Genotypes of Brachiaria humidicola (A and B) were planted on the grounds of CIAT headquarters in Palmira during 2018 – 2019, 10 lamps were placed in the lot to evaluate 6 different photoperiods (1 - 6) with Light in 2 different wavelength range (W.R.) α and β, for this, 17 samples were carried out on the variables height, vigor, chlorophyll content and number of inflorescences; a total of 93 field work were carried out to support the trial, finding that the photoperiod 5 in the W.R. β and 3 photoperiod in the W.R. α for the B genotype show significant differences (p <0.05, Tukey) with respect to the other treatments for height and number of inflorescences, performing the statistical analysis in the SAS software. As to the seed production, it was found that any light stimulus generates greater seed production, despite the conditions under which the crops were made and the method of harvest used. I order to refine the protocol and validate the results in bigger genotype sample another trial with the 2 most efficient treatments was proposed for 2020, focusing on number of inflorescences and seed production

Interview with Dr. Ole Skovmose

Professor emeritus at the Department of Culture and Learning at Aalborg University, Denmark. He develops his research from the perspective of critical mathematics education. He studies the political dimension of mathematical knowledge, and analyses the mechanisms of power as related to bringing mathematics in action. His work contributes to developing central concepts of critical mathematics education (landscapes of investigation, mathematics in action, close-ups of students and the ghetto) without forgetting the per- manent relationship with its practical possibilities. He has published several books, including Towards a Philosophy of Critical Mathematics Education, translated into Spanish, Dialogue and Learning in Mathematics Education (together with Helle Alrø), Traveling Through Education, In Doubt, Critique as Uncertainty, Students’ Foregrounds, and Connecting Humans With Equations (together with Ole Ravn