This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.
A topic of major importance to engineers and physicists, the theory of distributions remains a difficult subject for the non-mathematician. This version of the theory presents a more natural approach.
Assessments and Conservation of Biological Diversity from Coral Reefs to the Deep Sea: Uncovering Buried Treasures and the Value of the Benthos examines marine benthic habitats around the world that are linked by their physical location at the bottom of the oceans. The book approaches deep sea marine biodiversity with perspectives on genetics, microbiology and evolution, weaving a narrative of vital expert linkages with the goal of protecting something that most people cannot witness or experience. It provides a full assessment of biological diversity within benthic habitats, from coral reefs to plankton and fish species, and offers global case studies. It is the ideal resource for marine conservationists and biologists aiming to expand their knowledge and efforts to the rarely seen, yet equally important, realms of the ocean and respective benthic species. As these deep-sea ecosystems and their species face unprecedented threats of destruction and extinction due to factors including climate change, this book provides the most current knowledge of this undersea world along with solutions for its conservation. Compares and contrasts between shallow and marine habitats to reveal revolutionary connections and continuity Analyzes modern threats and gaps in biological knowledge regarding benthic communities Examines benthic biodiversity through vertical vs. horizontal gradients Poses possible solutions for the conservation of benthic habitats and organisms
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