On the lower semicontinuous envelope of functionals defined on polyhedral chains

In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by $H \colon \mathbb{R} \to \left[ 0,\infty \right)$ an even, subadditive, and lower semicontinuous function with $H(0)=0$, and by $\Phi_H$ the functional induced by $H$ on polyhedral $m$-chains, namely \Phi_{H}(P) := \sum_{i=1}^{N} H(\theta_{i}) \mathcal{H}^{m}(\sigma_{i}), \quad\mbox{for every }P=\sum_{i=1}^{N} \theta_{i} [[ \sigma_{i} ]] \in\mathbf{P}_m(\mathbb{R}^n), we prove that the lower semicontinuous envelope of $\Phi_H$ coincides on rectifiable $m$-currents with the $H$-mass \mathbb{M}_{H}(R) := \int_E H(\theta(x)) \, d\mathcal{H}^m(x) \quad \mbox{ for every } R= [[ E,\tau,\theta ]] \in \mathbf{R}_{m}(\mathbb{R}^{n}). Comment: 14 page

From ancient Assyria to European stages and screens

UID/HIS/04666/2019 Copyright Year 2020“Adieu, Assyria! / I loved thee well”. These were the last words of king Sardanapalus, the last king of Assyria, according to Lord Byron. Throughout the centuries, Europe was confronted with the tragic story of Mesopotamia’s last monarch, a king more effeminate than a woman, a lascivious and idle man, a governor who loathed all expressions of militarism and war. But this story was no more than it proposed to be: a story, not history. Sardanapalus was not even real! The Greeks conceived him; artists, play writers, and cineastes preserved him. Through the imaginative minds of early Modern and Modern historians, artists and dramaturgs, Sardanapalus’ legend endured well into the 20th-century in several different media. Even after the first excavations in Assyria, and the exhumation of its historical archives, where no king by the name of Sardanapalus was recorded, fantasy continued to surpass history.authorsversionpublishe

Cardio classics revisited – focus on the role of candesartan

Angiotensin II receptor blockers (ARBs) are antihypertensive agents with considerable evidence of efficacy and safety for the reduction of cardiovascular (CV) disease risk in numerous patient populations across the CV continuum. There are several agents within this class, all of which have contributed to various degrees, to this evidence base. The evidence with ARBs continues to accumulate, with ongoing trials investigating their role in additional patient populations, potentially expanding their efficacy across a broad spectrum of CV disease states. Cardiovascular disease (CVD) is a leading cause of death around the world, accounting for approximately 29.2% of total global deaths. Of all the deaths attributed to CVD, approximately 43% are due to ischemic heart disease, 33% to cerebrovascular disease, and 23% to hypertensive and other heart conditions. CVD has been represented as a “CV continuum”. This continuum concept can be used to describe CVD in general or in specific vascular beds (eg, coronary artery disease or cerebrovascular disease). This review article will discuss the results of the landmark ARB candesartan clinical trials published over the past decade. The evidence presented spans the entire CV continuum, including the effects of ARBs in at-risk patients, stroke, myocardial infarction (MI), and heart failure (HF), as well as a brief discussion of ongoing trials