Introductory Notes On Valuation Rings And Function Fields In One Variable


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Introductory Notes on Valuation Rings and Function Fields in One Variable


Introductory Notes on Valuation Rings and Function Fields in One Variable

Author: Renata Scognamillo

language: en

Publisher: Springer

Release Date: 2014-07-01


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The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert’s Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons.

Lectures on Elliptic Partial Differential Equations


Lectures on Elliptic Partial Differential Equations

Author: Luigi Ambrosio

language: en

Publisher: Springer

Release Date: 2019-01-10


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The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

Transcriptome Analysis


Transcriptome Analysis

Author: Alessandro Cellerino

language: en

Publisher: Springer

Release Date: 2018-06-14


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The goal of this book is to be an accessible guide for undergraduate and graduate students to the new field of data-driven biology. Next-generation sequencing technologies have put genome-scale analysis of gene expression into the standard toolbox of experimental biologists. Yet, biological interpretation of high-dimensional data is made difficult by the lack of a common language between experimental and data scientists. By combining theory with practical examples of how specific tools were used to obtain novel insights in biology, particularly in the neurosciences, the book intends to teach students how to design, analyse, and extract biological knowledge from transcriptome sequencing experiments. Undergraduate and graduate students in biomedical and quantitative sciences will benefit from this text as well as academics untrained in the subject.