A Resolvent Approach to Metastability

We provide a necessary and sufficient condition for the metastability of a Markov chain, expressed in terms of a property of the solutions of the resolvent equation. As an application of this result, we prove the metastability of reversible, critical zero-range processes starting from a configuration

In and out and out again: The travails of Brazil as a security provider in Africa

The story of Brazil as a contemporary security actor in Africa can prove a peculiar one. Marked by quick gains and an equally quick recognition over a short period of time, it has also been followed by an equally quick turnaround which has led, as of 2020, to a visible disengagement on the ground. We explore the main travails in this domain, which have compromised much of the gains previously obtained throughout the continent. The chapter begins with a general balance of the progress achieved between 2003 and 2016, followed by the highlights of the recent downturn. We then analyze a specific sub-area, namely, the inroads carried out at the defence industry level, in order to showcase the promises and contradictions often associated to what the country has offered across the Atlantic. We conclude by presenting some opportunities for a new pickup of Brazilian interest in the middle and long run

Floração de espécies apícolas no Pantanal baseada em informações de herbário e literatura.

O objetivo desse estudo foi descrever e avaliar a influência do porte das plantas apícolas do Pantanal na ocorrência de floração ao longo do ano. As informações das espécies apícolas foram organizadas a partir da compilação de dados de literatura e do acervo do herbário CPAP, anotando-se o período de floração, porte de crescimento (herbáceo, arbustivo, arbóreo ou trepadeira), sendo que as palmeiras foram consideradas como de porte arbóreo, e a ocorrência ou não em área inundável (espécies aquáticas ou anfíbias e terrestres).bitstream/CPAP-2010/57290/1/BP91.pd

Micelle Forms in Lyotropic Nematics and Cholesterics

Nematic and cholesteric lyotropic liquid crystals (lyomesophases based on micelles) with positive and negative diamagnetic aniiSotropy wexe studied by polaxizing microscopy. The textures of nematics oriented in a magnetic field confirm the disc- · like and rodlike structure of the lyomesophases. The textures of cholesterics show a characteristic helical structure where the pitch of the helix depends on the composition and temperature

Micelle Forms in Lyotropic Nematics and Cholesterics

Nematic and cholesteric lyotropic liquid crystals (lyomesophases based on micelles) with positive and negative diamagnetic aniiSotropy wexe studied by polaxizing microscopy. The textures of nematics oriented in a magnetic field confirm the disc- · like and rodlike structure of the lyomesophases. The textures of cholesterics show a characteristic helical structure where the pitch of the helix depends on the composition and temperature

On complexity and convergence of high-order coordinate descent algorithms

Coordinate descent methods with high-order regularized models for box-constrained minimization are introduced. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with respect to all the variables simultaneously is $O(\varepsilon^{-(p+1)})$. Numerical examples involving multidimensional scaling problems are presented. The numerical performance of the methods is enhanced by means of coordinate-descent strategies for choosing initial points