Compactness results in Symplectic Field Theory

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [M Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307--347] as well as compactness theorems in Floer homology theory, [A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775--813 and Morse theory for Lagrangian intersections, J. Diff. Geom. 28 (1988) 513--547], and in contact geometry, [H Hofer, Pseudo-holomorphic curves and Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 307--347 and H Hofer, K Wysocki and E Zehnder, Foliations of the Tight Three Sphere, Annals of Mathematics, 157 (2003) 125--255].Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper25.abs.htm

Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles

Quasi-periodic cocycles with a diophantine frequency and with values in SL(2,R) are shown to be almost reducible as long as they are close enough to a constant, in the topology of k times differentiable functions, with k great enough. Almost reducibility is obtained by analytic approximation after a loss of differentiability which only depends on the frequency and on the constant part. As in the analytic case, if their fibered rotation number is diophantine or rational with respect to the frequency, such cocycles are in fact reducible. This extends Eliasson's theorem on Schr\"odinger cocycles to the differentiable case

Virtual water highway: water use efficiency in global food trade

International audienceAmid an increasing water scarcity in many parts of the world, virtual water trade as both a policy instrument and practical means to balance the regional, national and global water budget has received much attention in recent years. Built upon the knowledge of virtual water accounting in the literature, this study examines the efficiency of the resource use embodied in the global virtual water trade from the perspectives of exporting and importing countries. Different characteristics between "green" and "blue" virtual water corresponding to rainfed and irrigated agriculture are elaborated. The investigation reveals that the virtual water flows primarily from countries of high water productivity to countries of low water productivity, generating a global saving of water resources. Meanwhile, the domination of green virtual water in the total virtual water trade constitutes low opportunity costs and environmental impacts as opposed to blue virtual water. The results suggest efficiency gains in the global food trade in terms of water resource utilization. The study raises awareness of negative impacts of increasing reliance on irrigation for food production in many countries, including food exporting countries. The findings of the study call for a greater emphasis on rainfed agriculture to improve global food security and environmental sustainability

Synchronization in pairs of opto-thermally driven mechanically coupled micro-oscillators

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning. We also show that the experimentally measured frequency fluctuations of the system reduce with an increase in coupling strength.Comment: 8 pages, 7 figure

Measurement of electron screening in muonic lead

Energies of the transitions between high-lying (n≥6) states of muonic lead were accurately determined. The results are interpreted as a ∼2% test of the electron screening. The agreement between experiment and theory is good if it is assumed that the refilling of the electron K shell is fast. The present results furthermore severely restrict possible ionization of the electron L shell

Stabilizing sodium hypochlorite at high pH: effects on soft tissue and dentin

NaOH-stabilized NaOCl solutions have a higher alkaline capacity and are thus more proteolytic than standard counterparts

Effect of calcium-channel blockers on calcium—phosphate metabolism in patients with end-stage renal disease

Background After EDTA-induced hypocalcaemia, healthy volunteers treated with diltiazem display more severe hyperparathyroidism than subjects on felodipine studied under identical conditions. Therefore patients with end-stage renal disease (ESRD) and severe secondary hyperparathyroidism might be particularly sensitive to this side-effect. Methods To test this hypothesis, seven patients with ESRD on chronic haemodialysis (3 women and 4 men) with serum levels of intact PTH ranging from 204 to 675 pg/ml were studied both before and during the first 180 min of haemodialysis against a dialysate with low calcium concentration (0.75 mmol/1, n=6 and 1 mmol/1, n=1) under the following three experimental conditions: control, felodipine (10 mg/day) and diltiazem (120 mg b.i.d.). Results At onset of dialysis, plasma phosphorus level was higher on diltiazem (2.03±0.08 mM) than on felodipine (1.64±0.10, P<0.02), and on the latter it was lower than in control condition (1.88±0.16, P<0.02). As a probable consequence, blood ionized calcium concentration was lower on diltiazem (1.14 mM±0.02, mean±SEM) than on felodipine (1.2±0.03, P<0.05) or in control condition (1.17±0.01, NS). There was a trend for intact PTH to be higher on diltiazem (324±47 pg/ml) than on felodipine (246±55) or in control condition (305±49) and 1,25-dihydroxyvitamin D was higher indeed on diltiazem (6.70±0.92 pg/ml) than on felodipine (4.75±0.91, P<0.02) or control (3.87±0.62, P<0.05). Area under the curve PTH over the first 60 min of dialysis was higher by 16±7% on diltiazem than on felodipine (P<0.05). Conclusions While on diltiazem rather than on felodipine, patients with ESRD display higher plasma phosphorus levels, and slightly aggravate the degree of severity of hyperparathyroidism recorded during haemodialysis against low-calcium dialysate. The longterm effect of this new observation remains to be evaluate

Analyses of impacts of China's international trade on its water resources and uses

This study provides an insight into the impact of China's international trade of goods and services on its water resources and uses. Virtual water flows associated with China's international trade are quantified in an input-output framework. The analysis is scaled down to the sectoral and provincial levels to trace the origins and destinations of virtual water flows associated with the international trade. The results show that China is a net virtual water exporter of 4.8 &amp;times; 10&lt;sup&gt;10&lt;/sup&gt; m&lt;sup&gt;3&lt;/sup&gt; yr&lt;sup&gt;&amp;minus;1&lt;/sup&gt;, accounting for 2.1% of its renewable water resources and 8.6% of the total water use. Water scarce regions tend to have higher percentages of virtual water export relative to their water resources and water uses. In the water scarce Huang-Huai-Hai region, the net virtual water export accounts for 8.0% of the region's water resources and 11.3% of its water uses. For individual sectors, major net virtual water exporters are those where agriculture provides raw materials in the initial process of the production chain. The results suggest that China's economic gains from being a world "manufacture factory" have come at a high cost to its water resources