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Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Over the past three decades studies investigating heritage speaker (HS) linguistic competencies have shown, time and again that, despite being L1 or 2L1 native speakers of their home language(s), HS outcomes display variation across a wide spectrum of differences as compared to each other, other types of bilinguals as well as their monolingual peers. Studies have traditionally used—mostly behavioral—methodologies rooted in adjacent established fields (e.g., L1 acquisition, adult L2 acquisition) offering, in addition to documenting and describing HS performance, important insights for linguistic theory and challenges related to (home/minority) language maintenance, contact, policy and more. A birds-eye view makes it clear that the methodologies one uses to tap into HSs’ linguistic knowledge areas, if not more, are important than the phenomena under investigation, especially in light of how their unique experiences with their heritage and other languages are present across a continuum.
The World Malaria Report 2015assesses global malaria disease trends and changes in the coverage and financing of malaria control programs between 2000 and 2015. It also summarizes progress towards international targets, and provides regional and country profiles that summarize trends in each WHO region and each country with malaria. The report is produced with the help of WHO regional and country offices, ministries of health in endemic countries, and a broad range of other partners. The data presented are assembled from the 96 countries and territories with ongoing malaria transmission, and a further five countries that have recently eliminated malaria. Most data are those reported for 2014 and 2015, although in some cases projections have been made into 2015, to assess progress towards targets for 2015.
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A comprehensive, encyclopedic guide to the authors, works, and topics crucial to the literature of Central and South America and the Caribbean, the Encyclopedia of Latin American Literature includes over 400 entries written by experts in the field of Latin American studies. Most entries are of 1500 words but the encyclopedia also includes survey articles of up to 10,000 words on the literature of individual countries, of the colonial period, and of ethnic minorities, including the Hispanic communities in the United States. Besides presenting and illuminating the traditional canon, the encyclopedia also stresses the contribution made by women authors and by contemporary writers. Outstanding Reference Source Outstanding Reference Book
This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.
A comprehensive, encyclopedic guide to the authors, works, and topics crucial to the literature of Central and South America and the Caribbean, the Encyclopedia of Latin American Literature includes over 400 entries written by experts in the field of Latin American studies. Most entries are of 1500 words but the encyclopedia also includes survey articles of up to 10,000 words on the literature of individual countries, of the colonial period, and of ethnic minorities, including the Hispanic communities in the United States. Besides presenting and illuminating the traditional canon, the encyclopedia also stresses the contribution made by women authors and by contemporary writers. Outstanding Reference Source Outstanding Reference Book