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Progress in Commutative Algebra 1. Combinatorics and Homology

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Book Series: De Gruyter Proceedings in Mathematics ISBN: 9783110250404 Year: Pages: 372 DOI: 10.1515/9783110250404 Language: English
Publisher: De Gruyter Grant: Knowledge Unlatched - 102374
Subject: Mathematics
Added to DOAB on : 2019-04-25 11:21:03
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This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological art

New Mineral Species and Their Crystal Structures

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ISBN: 9783038976882 Year: Pages: 204 DOI: 10.3390/books978-3-03897-689-9 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General)
Added to DOAB on : 2019-04-05 11:07:22
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One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory.

Keywords

ariegilatite --- nabimusaite group --- new mineral --- crystal structure --- intercalated hexagonal antiperovskite --- CO3-group --- Raman --- pyrometamorphic rocks --- Hatrurim Complex --- tiberiobardiite --- chalcophyllite group --- copper --- silicate --- sulfate --- Cretaio --- Tuscany --- Italy --- oyonite --- lillianite homologous series --- sulfosalt --- copper --- antimony --- arsenic --- Oyon district --- Lima department --- Peru --- fiemmeite --- new oxalate mineral --- Val di Fiemme --- Trentino --- Italy --- sharyginite --- new mineral --- crystal structure --- Raman spectroscopy --- Bellerberg volcano --- Germany --- kurchatovite --- clinokurchatovite --- crystal structure --- borate --- polymorphism --- polytypism --- structural complexity --- structural combinatorics --- configurational entropy --- least-action principle --- barioferrite --- crystal structure --- single-crystal investigation --- Raman --- Hatrurim Complex --- Rusinovite --- Raman spectroscopy --- pyrometamorphism --- stacking faults --- Shadil-Khokh volcano --- Bellerberg volcano --- aurihydrargyrumite --- Au6Hg5 phase --- gold --- placer --- self-electrorefining --- Ehime --- Japan --- cerromojonite --- selenium --- copper --- lead --- mercury --- bismuth --- sou?ekite --- bournonite group --- El Dragón --- Bolivia --- nöggerathite-(Ce) --- new mineral --- zirconolite --- laachite --- sanidinite --- crystal structure --- alkaline volcanic rock --- Laacher See --- Eifel --- parafiniukite --- apatite supergroup --- hedyphane group --- manganese --- calcium --- phosphorus --- Szklary pegmatite --- Lower Silesia --- Poland --- thermaerogenite --- cuprospinel --- gahnite --- magnesioferrite --- CuAl2O4 --- CuFe2O4 --- copper oxide --- new mineral --- spinel supergroup --- fumarole sublimate --- Tolbachik volcano --- Kamchatka --- verneite --- new mineral --- crystal structure --- Hekla --- Vesuvius --- Eldfell --- aluminofluoride

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