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Academic collection --- Mathematical physics --- Semigroups --- Group theory --- Physical mathematics --- Physics --- Mathematics

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This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development. It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal. By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics.

Operator theory. --- Functional analysis. --- Operator Theory. --- Functional Analysis. --- Semigroups. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Group theory

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This book contains information for specialists in various fields of science. From the point of view of pharmacology, data are reported regarding the effect of echinochrome A and related metabolites from sea urchins on the survival and functional properties of stem cells, which can facilitate ex vivo application of this compound in medicine. For scientists who isolate and establish structures of marine natural compounds, an article devoted to the proof of the microbial origin of a typical metabolite earlier found exclusively from marine invertebrates, 6-epi-monanchorin, may also be of interest. A range of new marine metabolites was discovered from the both marine invertebrates and marine microorganisms, particularly in marine isolates of fungi. Some marine natural products could be applied to treat such diseases as Parkinson’s disease, ischemic stroke, viral infections, and so on. Magnificamide, a new peptide from sea anemones, inhibits porcine and human saliva amylases, showing its probable antidiabetic properties. Application of the genomic approach was discussed in studies on various marine bacteria, producing marine enzymes with unusual specificity. The lectins capable of recognizing glycoforms of different substrates demonstrate the possibility to be used to elaborate new medical diagnostics.

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Addressing a field which, until now, has not been sufficiently investigated, Essentials of Natural Gas Microturbines thoroughly examines several natural gas microturbine technologies suitable not only for distributed generation but also for the automotive industry. An invaluable resource for power systems, electrical, and computer science engineers as well as operations researchers, microturbine operators, policy makers, and other industry professionals, the book: Explains the importance of natural gas microturbines and their use in distributed energy resource (DER) sy

Gas-turbine power-plants. --- Steam power plants.