The Projective Pedal of an Eq\"uiaffine Immersion

Given a codimension $1$ immersion $f$ together with an eq\"uiaffine tranversal vector field $\xi$, its projective pedal is a codimension $2$ immersion obtained as the centroaffine dual of the lifting of the pair $(f,\xi)$. In this paper we discuss the properties of the projective pedal, the most significant being that its asymptotic lines correspond to the curvature lines of the original immersion. As a consequence, we prove that Loewner's conjecture for asymptotic lines at inflection points of surfaces in $4$-space is equivalent to Loewner's conjecture for curvature lines at umbilical points of surfaces in $3$-space with an eq\"uiaffine transversal vector field.Comment: 11 pages. The earlier versions of this article was divided in the new version and article Arxiv: 2008.0476

Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.Comment: 5 pages, 5 figure

Prethermalization Production of Dark Matter

At the end of inflation, the inflaton field decays into an initially nonthermal population of relativistic particles which eventually thermalize. We consider the production of dark matter from this relativistic plasma, focusing on the prethermal phase. We find that for a production cross section $\sigma(E)\sim E^n$ with $n> 2$, the present dark matter abundance is produced during the prethermal phase of its progenitors. For $n\le 2$, entropy production during reheating makes the nonthermal contribution to the present dark matter abundance subdominant compared to that produced thermally. As specific examples, we verify that the nonthermal contribution is irrelevant for gravitino production in low scale supersymmetric models ($n=0$) and is dominant for gravitino production in high scale supersymmetry models ($n=6$).Comment: 12 pages, 4 figure

A histórica distinção entre ética pública e ética privada e sua incidência na construção do conceito dos direitos fundamentais : a contribuição de Christian Thomasius = The historical distinction between public ethic and private ethic and its influence in constructing the concept of fundamental rights : the contribution of Christian Thomasius

Distingue ética pública de ética privada, expondo a contribuição e influência do jurista e filósofo alemão Christian Thomasius e trata do “processo de formação do ideal dos direito fundamentais, assim como na construção do atual conceito dos mesmos”. Discorre acerca da formulação do Direito natural racionalista e do iluminismo. Tece comentários sobre a separação das questões de direito das questões de moral e sobre “a luta pela humanização do Direito penal e seu procedimento, para apartar as questões de moral privada do direito”

Monitoring Asthma in Childhood: Still a Challenge

Asthma monitoring should be focused on patient outcomes and goals. Using clinical practice tools allows the clinicians to detect problems such as bad adherence to maintenance therapy, comorbidities, or other external reason for a poorly controlled asthma. To succeed in the process of asthma control, doctors need the participation of the family. Because such educational task requires good agreement between patient environment and doctor, it might be difficult to achieve. However, it is worth to implement because the benefit is a life without symptoms of asthma with a minimum medication