Liouville-Riemann-Roch theorems on Abelian coverings / / Minh Kha, Peter Kuchment

• Record Nr.: UNISA996466549803316
• Autore: Kha Minh
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-67428-2
• Edizione: [1st ed. 2021.]
• Descrizione fisica: 1 online resource (XII, 96 p. 2 illus., 1 illus. in color.)
• Collana: Lecture Notes in Mathematics ; ; Volume 2245
• Disciplina: 515.353
• Soggetti: Differential equations, Elliptic; Riemann-Roch theorems
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Preliminaries -- The Main Results -- Proofs of the Main Results -- Specific Examples of Liouville-Riemann-Roch Theorems -- Auxiliary Statements and Proofs of Technical Lemmas -- Final Remarks and Conclusions.
• Sommario/riassunto: This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity. The classical Riemann–Roch theorem and its generalizations to elliptic equations on bounded domains and compact manifolds, due to Maz’ya, Plameneskii, Nadirashvilli, Gromov and Shubin, account for the contribution to the index due to a divisor of zeros and singularities. On the other hand, the Liouville theorems of Avellaneda, Lin, Li, Moser, Struwe, Kuchment and Pinchover provide the index of periodic elliptic equations on abelian coverings of compact manifolds with polynomial growth at infinity, i.e. in the presence of a "divisor" at infinity. A natural question is whether one can combine the Riemann–Roch and Liouville type results. This monograph shows that this can indeed be done, however the answers are more intricate than one might initially expect. Namely, the interaction between the finite divisor and the point at infinity is non-trivial. The text is targeted towards researchers in PDEs, geometric analysis, and mathematical physics.

Debating dispositions [[electronic resource] ] : issues in metaphysics, epistemology, and philosophy of mind / / edited by Gregor Damschen, Robert Schnepf, and Karsten R. Stüber

• Record Nr.: UNINA9910780735303321
• Pubbl/distr/stampa: Berlin ; ; New York, : Walter de Gruyter, 2009
• ISBN: 1-282-71415-5; 9786612714153; 3-11-021182-3
• Descrizione fisica: 1 online resource (362 p.)
• Classificazione: CC 1100
• Altri autori (Persone): DamschenGregor; SchnepfRobert; StüberKarsten
• Disciplina: 111
• Soggetti: Disposition (Philosophy); Philosophy
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Frontmatter -- Table of Contents -- I. The Discovery of Dispositions: Ancient Foundations -- Knowledge and Virtue as Dispositions in Plato's Theaetetus / Gonzalez, Francisco J. -- Aristotle's Theory of Dispositions From the Principle of Movement to the Unmoved Mover / Jansen, Ludger -- Dispositions in Greek Historiography / Meissner, Burkhard -- II. The Debate about Dispositions from the Beginning of Modern Sciences to the 20th century -- The Dispositions of Descartesc / Machamer, Peter -- Explicable Explainers: the Problem of Mental Dispositions in Spinoza's Ethics / Renz, Ursula -- Harmonizing Modern Physics with Aristotelian Metaphysics. Leibniz's Theory of Force / Liske, Michael-Thomas -- From Ordinary Language to the Metaphysics of Dispositions - Gilbert Ryle on Disposition Talk and Dispositions / Scholz, Oliver R. -- III. Contemporary Philosophical Analyses of Dispositions -- Hic Rhodos, Hic Salta: From Reductionist Semantics to a Realist Ontology of Forceful Dispositions / Schrenk, Markus -- Ascribing Dispositions / Mumford, Stephan -- Dispositional Pluralism / McKitrick, Jennifer -- Dispositions and Their Intentions / Borghini, ; Andrea -- IV. The Role of Dispositions in Scientific and Philosophical Contexts -- Dispositions in Physics / Hüttemann, Andreas -- The Role of Dispositions in Historical Explanations / Schnepf, Robert -- Empathy, Mental Dispositions, and the Physicalist Challenge / Stueber, Karsten -- Dispositional Knowledge-How versus Propositional Knowledge-That / Damschen, Gregor -- Epistemic Virtues and Cognitive Dispositions / Henderson, David / Horgan, Terry -- The Epistemic Function of Virtuous Dispositions / Brendel, Elke -- Backmatter
• Sommario/riassunto: Ordinary language and scientific discourse are filled with linguistic expressions for dispositional properties such as "soluble," "elastic," "reliable," and "humorous." We characterize objects in all domains - physical objects as well as human persons - with the help of dispositional expressions. Hence, the concept of a disposition has historically and systematically played a central role in different areas of philosophy ranging from metaphysics to ethics. The contributions of this volume analyze the ancient foundations of the discussion about disposition, examine the problem of disposition within the context of the foundation of modern science, and analyze this dispute up to the 20th century. Furthermore, articles explore the contemporary theories of dispositions.; Sowohl die Alltags- als auch die Wissenschaftssprache sind reich an Dispositionsausdrücken wie "löslich", "elastisch", "zuverlässig" und "humorvoll". Wir charakterisieren Objekte aus allen Gegenstandsbereichen, sowohl physische Gegenstände als auch menschliche Personen, mit Hilfe von dispositionellen Ausdrücken. Der Begriff der Disposition hat deshalb in der Philosophie in historischer und in systematischer Hinsicht immer eine entscheidende Rolle gespielt. Der Band präsentiert die reichhaltigen philosophischen Auseinandersetzungen um die Existenz, die Natur und die Rolle der Dispositionen von der Antike bis zum 20. Jh. und diskutiert aktuelle Theorien der Dispositionen in der Metaphysik, Erkenntnistheorie und Philosophie des Geistes.