Some controllability results for the 2D Kolmogorov equation

In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the right-hand side of the equation, located on a subdomain, that acts linearly on the state. In the first case, it is the complementary of a strip with axis x and in the second one, it is a strip with axis x. The proof relies on two ingredients. The first one is an explicit decay rate for the Fourier components of the solution in the free system. The second one is an explicit bound for the cost of the null controllability of the heat equation with potential that the Fourier components solve. This bound is derived by means of a new Carleman inequality. © 2009 Elsevier Masson SAS. All rights reserved

Large Time Asymptotics for Partially Dissipative Hyperbolic Systems

This work is concerned with (n-component) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t → ∞. Using the Fourier transform, we examine the role that control theoretical tools, such as the classical Kalman rank condition, play. We build Lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable. In this way we extend the previous analysis by Shizuta and Kawashima under the so-called algebraic condition (SK). In particular, we show the existence of systems exhibiting more complex behavior than the one that the (SK) condition allows. We also discuss links between this analysis and previous literature in the context of damped wave equations, hypoellipticity and hypocoercivity. To conclude, we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws. Our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover

Growth of Sobolev norms and controllability of Schr\"odinger equation

In this paper we obtain a stabilization result for the Schr\"odinger equation under generic assumptions on the potential. Then we consider the Schr\"odinger equation with a potential which has a random time-dependent amplitude. We show that if the distribution of the amplitude is sufficiently non-degenerate, then any trajectory of system is almost surely non-bounded in Sobolev spaces

Results from campaign in the Channel-North Sea and Belgian Coastal Zone – RV <i>Simon Stevin</i>

Objective: The purpose of this study is to determine the relationship between iron storage and overall well-being in female college athletes. This was done to determine a cost-effective screening method for iron deficiency. Design: Retrospective Cohort Subjects and Settings: All subjects were 117 Division I Female Athletes at James Madison University. Subjects were ages 17-22 from different teams(Cross Country, Track & Field, Basketball, Field Hockey, Lacrosse, Volleyball, Golf, Swimming & Diving, Soccer, and Softball). We excluded 1 subject based on a medical diagnosis. Some subjects had more than one data entry based on their year at JMU. Main Outcome Measure: Data was recorded for individuals who have in the past received blood draws testing for ferritin levels and have completed a Henriques 10-Item Well-being Questionnaire(H10WB) within a year of the blood draw. Results: Correlations resulted in no significant relationship between ferritin levels and H10WB total scores with a 1-tailed p-value of .071. There was some significance seen with responses to individual questions within the questionnaire and ferritin(p=.02 and p= .032). Conclusion: Since there was very little significance found for this relationship we can conclude that the symptoms of changes in athlete’s overall well-being status are not present in those with iron deficiency. Research does support a relationship between these symptoms with iron deficiency anemia therefore, these results could represent that those symptoms are not experienced with iron deficiency. This suggests the increased need to find a screening tool for healthcare providers to use to determine an iron deficiency without requiring blood draws from everyone. This would allow professionals to determine this deficiency before it becomes anemia and these symptoms develop

Report on identification of keystone species and processes across regional seas. DEVOTES FP7 Project

WP6, Deliverable 6.1, DEVOTES ProjectIn managing for marine biodiversity, it is worth recognising that, whilst every species contributes to biodiversity, each contribution is not of equal importance. Some have important effects and interactions, both primary and secondary, on other components in the community and therefore by their presence or absence directly affect the biodiversity of the community as a whole. Keystone species have been defined as species that have a disproportionate effect on their environment relative to their abundance. As such, keystone species might be of particular relevance for the marine biodiversity characterisation within the assessment of Good Environmental Status (GEnS), for the Marine Strategy Framework Directive (MSFD).The DEVOTES Keystone Catalogue and associated deliverable document is a review of potential keystone species of the different European marine habitats. The catalogue has 844 individual entries, which includes 210 distinct species and 19 groups classified by major habitat in the Baltic Sea, North East Atlantic, Mediterranean, Black Sea (EU Regional Seas) and Norwegian Sea (Non-­‐EU Sea). The catalogue and the report make use/cite 164 and 204 sources respectively. The keystones in the catalogue are indicated by models, by use as indicators, by published work (e.g. on traits and interactions with other species), and by expert opinion based on understanding of systems and roles of species/groups. A total of 74 species were considered to act as keystone predators, 79 as keystone engineers, 66 as keystone habitat forming species, while a few were thought of having multiple roles in their marine ecosystems. Benthic invertebrates accounted for 50% of the reported keystone species/groups, while macroalgae contributed 17% and fish12%. Angiosperms were consistently put forward as keystone habitat forming and engineering species in all areas. A significant number of keystones were invasive alien species.Only one keystone, the bivalve Mya arenaria, was common to all four EU regional seas. The Mediterranean Sea had the largest number of potential keystones (56% of the entries) with the least in the Norwegian Sea. There were very few keystones in deep waters (Bathyal-­‐Abyssal, 200+ m), with most reported in sublittoral shallow and shelf seabeds or for pelagic species in marine waters with few in reduced/variable salinity waters. The gaps in coverage and expertise in the catalogue are analysed at the habitat and sea level, within the MSFD biodiversity component groups and in light of knowledge and outputs from ecosystem models (Ecopath with Ecosim).The understanding of keystones is discussed as to when a species may be a dominant or keystone with respect to the definition term concerning ‘disproportionate abundance’, how important are the ‘disproportionate effects’ in relation to habitat formers and engineers, what separates a key predator and key prey for mid-­‐trophic range species and how context dependency makes a species a keystone. Keystone alien invasive species are reviewed and the use of keystone species model outputs investigated. In the penultimate sections of the review the current level of protection on keystone species and the possibilities for a keystone operational metric and their use in management and in GEnS assessments for the MSFD are discussed. The final section highlights the one keystone species and its interactions not covered in the catalogue but with the greatest impact on almost all marine ecosystems, Homo sapiens

Heat equation on the Heisenberg group: Observability and applications

We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain (−1,1)×T×T taking as observation regions slices of the form ω = (a,b) × T × T, with −1 0 but both observability and Lipschitz stability hold true after a positive minimal time, which depends on the distance between ω and the boundary. Our proof follows a mixed strategy which combines the approach by Lebeau and Robbiano, which relies on Fourier decomposition, with Carleman inequalities for the heat equations that are solved by the Fourier modes. We extend the analysis to the unbounded domain (−1, 1) × T × R