q-cohomologically complete and q-pseudoconvex domains

This dissertation is devoted to the study of the different viewpoints from which an open subset D of a Stein manifold M can be considered, as the geometric concepts of q-completeness and q- pseudoconvexity and the analytic ideas of vanishing of cohomology groups after a certain level and inextendibility of cohomology clas­ses or holomorphic functions. The idea is to generalize to any integer q the well known equivalence between O-complateness and O-cohonological completeness ( see theorem 2.81). A step in this direction, namely that if D is q-complete then it is also q-cohonologically complete, was done in 1962 by Andreotti and Grauert, but the converse implication is still an open problem. Using a rather indirect tool involving certain cohomology classes called "test classes" we can manage to prove that if D is cohomologically q-complete and has C2 boundary then it is q-complete, and this is probably the most interesting result appearing in this thesis ( see theorem 3.3.1) This method however can also be applied to answer certain natural questions about inaxtendibility of cohomology classes, analogous to inextendibility of hoiomorphic functions for domains of holomorphy, and the answer turns out to be not surprising if D has C2 boundary (see theorem 4.1.8) but less intuitive in the general case and counterexamples illustrating this behaviour are discussed in chapter 3. section 4. In particular we describe a particularly interesting applica­tion of the test classes that gives a lower bound on the number of analytic functions needed to define an analytic subvariety just touching D at a point x belonging to its boundary provided the behavi­our of ꝽD near x 13 known (see theorem 4.2.3). All these results can be deduced without knowing the explicit expression for these cohomology classes, but such an expression in terms of Dolbeault cohomology and Cech cohomology is given in the last chapters It can be observed that the test classes are related to the Bochner-Martinelli kernel

Soft Robots for Ocean Exploration and Offshore Operations: A Perspective

The ocean and human activities related to the sea are under increasing pressure due to climate change, widespread pollution, and growth of the offshore energy sector. Data, in under-sampled regions of the ocean and in the offshore patches where the industrial expansion is taking place, are fundamental to manage successfully a sustainable development and to mitigate climate change. Existing technology cannot cope with the vast and harsh environments that need monitoring and sampling the most. The limiting factors are, among others, the spatial scales of the physical domain, the high pressure, and the strong hydrodynamic perturbations, which require vehicles with a combination of persistent autonomy, augmented efficiency, extreme robustness, and advanced control. In light of the most recent developments in soft robotics technologies, we propose that the use of soft robots may aid in addressing the challenges posed by abyssal and wave-dominated environments. Nevertheless, soft robots also allow for fast and low-cost manufacturing, presenting a new potential problem: marine pollution from ubiquitous soft sampling devices. In this study, the technological and scientific gaps are widely discussed, as they represent the driving factors for the development of soft robotics. Offshore industry supports increasing energy demand and the employment of robots on marine assets is growing. Such expansion needs to be sustained by the knowledge of the oceanic environment, where large remote areas are yet to be explored and adequately sampled. We offer our perspective on the development of sustainable soft systems, indicating the characteristics of the existing soft robots that promote underwater maneuverability, locomotion, and sampling. This perspective encourages an interdisciplinary approach to the design of aquatic soft robots and invites a discussion about the industrial and oceanographic needs that call for their application

Empagliflozin in Patients with Chronic Kidney Disease

Background The effects of empagliflozin in patients with chronic kidney disease who are at risk for disease progression are not well understood. The EMPA-KIDNEY trial was designed to assess the effects of treatment with empagliflozin in a broad range of such patients. Methods We enrolled patients with chronic kidney disease who had an estimated glomerular filtration rate (eGFR) of at least 20 but less than 45 ml per minute per 1.73 m(2) of body-surface area, or who had an eGFR of at least 45 but less than 90 ml per minute per 1.73 m(2) with a urinary albumin-to-creatinine ratio (with albumin measured in milligrams and creatinine measured in grams) of at least 200. Patients were randomly assigned to receive empagliflozin (10 mg once daily) or matching placebo. The primary outcome was a composite of progression of kidney disease (defined as end-stage kidney disease, a sustained decrease in eGFR to < 10 ml per minute per 1.73 m(2), a sustained decrease in eGFR of & GE;40% from baseline, or death from renal causes) or death from cardiovascular causes. Results A total of 6609 patients underwent randomization. During a median of 2.0 years of follow-up, progression of kidney disease or death from cardiovascular causes occurred in 432 of 3304 patients (13.1%) in the empagliflozin group and in 558 of 3305 patients (16.9%) in the placebo group (hazard ratio, 0.72; 95% confidence interval [CI], 0.64 to 0.82; P < 0.001). Results were consistent among patients with or without diabetes and across subgroups defined according to eGFR ranges. The rate of hospitalization from any cause was lower in the empagliflozin group than in the placebo group (hazard ratio, 0.86; 95% CI, 0.78 to 0.95; P=0.003), but there were no significant between-group differences with respect to the composite outcome of hospitalization for heart failure or death from cardiovascular causes (which occurred in 4.0% in the empagliflozin group and 4.6% in the placebo group) or death from any cause (in 4.5% and 5.1%, respectively). The rates of serious adverse events were similar in the two groups. Conclusions Among a wide range of patients with chronic kidney disease who were at risk for disease progression, empagliflozin therapy led to a lower risk of progression of kidney disease or death from cardiovascular causes than placebo