Global homotopy theory

This book introduces a new context for global homotopy theory, i.e., equivariant homotopy theory with universal symmetries. Many important equivariant theories naturally exist not just for a particular group, but in a uniform way for all groups in a specific class. Prominent examples are equivariant stable homotopy, equivariant $K$-theory or equivariant bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e., the adjective `global' refers to simultaneous and compatible actions of all compact Lie groups. We give a self-contained treatment of unstable and stable global homotopy theory, modeled by orthogonal spaces respectively orthogonal spectra under global equivalences. Specific topics include the global stable homotopy category, operations on equivariant homotopy groups, global model structures, and ultra-commutative multiplications. The book includes many explicit examples and detailed calculations

Representation Theory of Finite Dimensional Algebras

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Homological mirror symmetry for invertible curve singularities

The central theme of this thesis is homological mirror symmetry for curve singularities defined by invertible polynomials. The main results are contained in Chapters 3, 4, and 5. Chapter 3 is based on joint work with Jack Smith, and establishes homological Berglund--Hübsch mirror symmetry for invertible polynomials in two variables by matching generating collections on both sides. Along the way, we show that the category of graded matrix factorisations has a tilting object, confirming a conjecture of Lekili and Ueda in the case of curves. In Chapter 4, we build on the results of Chapter 3 to establish a derived equivalence between the Fukaya category of the Milnor fibre and the derived category of perfect complexes on the proposed mirror. The strategy of proof builds on that of Lekili and Ueda, and uses a moduli of $A_\infty$-structures argument. A key step in the proof of this result is to reconstruct the Milnor fibres by a gluing procedure. In Chapter 5, we prove homological mirror symmetry for a framework which generalises that of invertible curve singularities. Namely, the B--model is taken to be a chain or ring of weighted projective lines joined nodally such that each irreducible component is allowed to have non-trivial generic stabiliser, and the A--model is built using the gluing construction of Chapter 4. As a special case, this completely resolves a conjecture of Lekili and Ueda on invertible polynomials in complex dimension one. This also re-establishes the results of Chapter 4 by different methods and generalises the results of Lekili and Polishchuk. As a corollary, we prove some derives equivalences between categories of sheaves on the B--models by studying when the corresponding A--models are graded symplectomorphic

Liver Biopsy

Liver biopsy is recommended as the gold standard method to determine diagnosis, fibrosis staging, prognosis and therapeutic indications in patients with chronic liver disease. However, liver biopsy is an invasive procedure with a risk of complications which can be serious. This book provides the management of the complications in liver biopsy. Additionally, this book provides also the references for the new technology of liver biopsy including the non-invasive elastography, imaging methods and blood panels which could be the alternatives to liver biopsy. The non-invasive methods, especially the elastography, which is the new procedure in hot topics, which were frequently reported in these years. In this book, the professionals of elastography show the mechanism, availability and how to use this technology in a clinical field of elastography. The comprehension of elastography could be a great help for better dealing and for understanding of liver biopsy

Dictionary of Invertebrate Zoology

An exhaustive dictionary of over 13,000 terms relating to invertebrate zoology, including etymologies, word derivations and taxonomic classification. Entries cover parasitology, nematology, marine invertebrates, insects, and anatomy, biology, and reproductive processes for the following phyla: Acanthocephala Annelida Arthropoda Brachiopoda Bryozoa Chaetognatha Cnidaria Ctenophora Echinodermata Echiura Entoprocta Gastrotricha Gnathostomulida Kinorhyncha Loricifera Mesozoa Mollusca Nemata Nematomorpha Nemertea Onychophora Pentastoma Phoronida Placozoa Platyhelminthes Pogonophora Porifera Priapula Rotifera Sipuncula Tardigrada.https://digitalcommons.unl.edu/zeabook/1061/thumbnail.jp