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We study the isoperimetric problem in the Riemannian products S 1 (r) × Q n c , where Q n c is the n-dimensional simply connected space form of constant sectional curvature c = 0, 1, −1, and r > 0. The problem of classifying stable free boundary hypersurfaces with constant mean curvature between two parallel hyperplanes in R n for n 3 is also treated. c (y)dS n−1 (y) ds. Equations (2)

This paper describes the results of a detailed study relating the performance of undergraduate students admitted to Brazil’s State University of Campinas (Unicamp) from 1994 through 1997 and their socioeconomic and educational background. The study is based on a hierarchical model for the relevant variables involved. The main result is that students coming from disadvantaged backgrounds, in both educational and socioeconomic aspects, have a higher relative performance than their complementary group. We report on an affirmative action programme established at Unicamp for undergraduate admissions, partially motivated by those findings, and present evidence from an initial evaluation showing the programme’s positive impact. Finally, we comment on the effect this study and the Unicamp programme have had on the present debate about affirmative action access policies in Brazilian higher education institutions. by Renato H.L. Pedrosa, J. Norberto W. Dachs, Rafael P. Maia and Cibele Y. Andrade, Benilton S. Carvalho

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We study the effects of temperature, absolute humidity, population density and when country/U.S. state reached 100 cases on early pace of Covid-19 expansion, for all 50 U.S. states and 110 countries with enough data. For U.S. states, weather variables show opposite effects when compared to the case of countries: higher temperature or absolute humidity imply faster early outbreak. The higher the population density or the earlier the date when state reached 100 th case, the faster the pace of outbreak. When all variables are considered, only population density and the timeline variable show statistical significance. Discounting the effect of the timeline variable, we obtain an estimate for the initial growth rate of Covid-19, which can be also used to estimate the basic reproduction number for a region, in terms of population density. This has policy implications regarding how to control the pace of Covid-10 outbreak in a particular area, and we discuss some of them. In the case of countries, for which we did not have demographic information, weather variables lose statistical significance once the timeline variable is added. Relaxing CI requirements, absolute humidity contributes mildly to the reduction of growth rate of cases for the countries studied. Our results suggest that population density should be employed as a control variable and that analysis should have a local character, for subregions and countries separately, in studies involving the dynamics of Covid-19 and similar infectious diseases.