Search results for ""Birkhauser""

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

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This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.

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​This book presents a compact personal biography and a collection of works by Gabriele F. Giuliani - a distinguished condensed matter theorist who made important contributions to our understanding of collective effects in electronic materials. In 2012 he passed away after a long battle with cancer. In addition, the book features scientific contributions from some of Prof. Giuliani's former students and collaborators and a number of personal recollections by friends and colleagues which shed light on the complex, multifaceted personality of a physicist who was also a passionate soccer player and formula Ford pilot.

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Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.

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Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.

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This volume explores, from a mathematical and a philosophical perspective, the virtuous circle connecting logic and rationality. While logic lends its methods, techniques and ideas to the investigation of rationality, the practical problems which arise in modelling rational behaviour, especially in the social sciences, motivate logicians to develop more refined logical formalisms. This is why non classical logics - a unifying theme of this volume - play a fundamental role in the construction of formal models of rationality.

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This book is taken from the lectures given at the ENSAE in March 1998 and at the Scuola Normale Superiore in May 1998. At the beginning of the 70's, the set of mathematical methods of finance were reduced to actuarial calculus. The modern approach uses the stochastic calculus theory and evidences the duality between problems of arbitrage and valorisation and a set of martingale probabilities.

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Since neutrinos interact so weakly with matter, most of their basic properties are still largely unknown. One of the most important issues to be settled concerns their rest mass. We have no idea why neutrinos are so much lighter than their charged lepton partners; no fundamental symmetry in nature requires massless neutrinos. Massive neutrinos are demanded to explain the anomalous counting rate of experiments measuring the solar and the atmospheric neutrino fluxes. The discrepancy between experimental data and theoretical predictions can be accounted for in terms of neutrino oscillations, which would take place only in the case of massive neutrinos. The subject of this thesis is the search for neutrino oscillations in CHOOZ, the first long baseline experiment to explore a neutrino mass region where hints at neutrino oscillations came from the atmospheric neutrino anomaly.

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Neuronal plasticity is the term generally used to describe a great variety of changes in neuronal structure and functions, in particular activity-dependent, prolonged functional changes, accompanied by corresponding biochemical and possibly morphological alterations. The first insights about neuronal plasticity have been obtained on simple forms of life. Today, many areas in the mammalian central nervous system are under investigation, in particular the cortex and the hippocampus. In these areas, neuronal plasticity is considered to be at the basis of learning and memory. The study of brain plasticity in sensory systems has been particularly fruitful, because these systems can be experimentally manipulated in a very precise manner by changes in the sensory imput.

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This volume collects two articles by Christine Laurent-Thiébaut and Jürgen Leiterer which were submitted to, and accepted by the Annali della Scuola Normale Superiore, Classe di Scienze: The q-convex case; the q-concave case. Owing to the character of the systematic exposition of the new scientific results achieved and to the size of the work, the authors agreed to have the two papers published in a separate volume.

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These notes contain lectures on the theory of group representations and its applications to the physics of atoms, molecules and crystals, given at Purdue University, Scuola Normale Superiore (Pisa, Italy) and Universidad Técnica Federico Santa Maria (Valparaiso, Chile) on and off over a period of over 25 years. The topics selected reflect my special interests and their scope is limited by the time available to the students. The style is somewhat concise and will require careful attention on the part of the reader.

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The birth of condensed matter physics in Italy is linked to a small number of very distinguished scientists. Mario Tosi, Professor of Physics of Matter at the Scuola Normale Superiore, is unquestionably among the leading figures, a true founder of the theoretical activity in the country and a true catalyst of novel research directions internationally. This volume collects the proceedings of a symposium held at Scuola Normale Superiore di Pisa, designed to show Mario Tosi's broad, deep influence in very diverse areas of the quantum theory of condensed matter. The topics covered in the volume represent the breadth of his interests and the highlights in the quantum theory of condensed matter: liquids, electronic states in complex structures, quantum degenerate gases, many-body physics.

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Im heutigen Informationszeitalter werden ständig riesige Mengen digitaler Daten über verschiedene Kanäle übertragen. Codierungstheorie und Kryptographie sind Instrumente, um zentrale Probleme der Datenübertragung wie Übertragungsfehler und Datensicherheit zu lösen. Das Buch führt in die aktuellen Methoden der Codierungstheorie und Kryptographie ein und vermittelt notwendige Grundlagen der Algebra und der Algorithmen. Dabei werden LDPC-Codes und der AKS-Algorithmus ausführlich dargestellt. Der Anhang bietet zahlreiche Übungsaufgaben.

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The origins of the word problem are in group theory, decidability and complexity. But through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry. This book contains accounts of many recent developments in Geometric Group Theory and shows the interaction between the word problem and geometry continues to be a central theme. It contains many figures, numerous exercises and open questions.

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Across Ground comprises two new books by the Swiss-born, San-Francisco-based photographer Lukas Felzmann, who for nearly thirty years has been making poetic images that explore the intersection of nature and culture in California's landscape. Developed in tandem between 2017and 2024, the two volumes take us on an allusive journey through the Golden State's fifty-eight counties, revealing seemingly liminal zones located in between cities, national parks and landmarks. Using a large format view camera, Felzmann follows the border of the continent to the edges of small towns to create a conceptual atlas of the Californian hinterland.In Across Felzmann roams the territory freely, collecting signs of human activity in the natural environment, from foothills to felled cypress trees, in windows and reflections, across floodplains and focal planes. Across is not only a journey across land, but also across time and the processof photography, which Felzmann treats like a sculptural activity anch

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Honoring the fiftieth anniversary of the death of Louis Kahn in March 1974, this facsimile edition exquisitely reproduces the notebook in which the renowned American architect sketched and wrote during his travels in the last year of his life.Anchored by a magnificent set of drawings illustrating the final design of the Franklin D. Roosevelt Four Freedoms Park in New York City (1973/74, posthumously completed in 2012), Louis Kahn's Last Notebook provides an intimate glimpse into the architect's mind and design process. These private sketches and poetic reflections reveal Kahn's spiritual understanding of architecture as inclusiveof our total environment and shed new light on the architect's influential philosophy for designing, building and conceiving architecture.The facsimile pays close attention to the material qualities of the original notebook, replicating its delicate, transparent paper. Made widely available for the first time, the publication includes transcriptions of Kahn's h

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The long-awaited fifth volume on The Complete Works of Herzog & de Meuron presents the sixty projects completed between 2002 and 2004 with characteristic attention to detail. These include buildings that have already become contemporary architectural icons, such as the National Stadium in Beijing and the Elbphilharmonie in Hamburg, but also projects which, though never realized, have influenced the architectural discourse. These include the residential tower for the Schatzalp Hotel, which overlooks Davos and inspired a new generation of Alpine architecture. In the period covered by this volume, urban planing was a major focus of Herzog & de Meuron's work. International acclaim fueled by booming construction led to numerous commissions in China (the Jindong New Development Area), and in Europe: master plans for Jerez de la Frontera in Spain, and the Olympic Games in London opened up entire urban regions to future development.

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The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.​

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This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

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This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.

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This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

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This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.

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This case-based text provides treatment approaches to common and uncommon movement disorders. The first two parts of the book are devoted to the wide spectrum of motor and non-motor problems encountered in caring for people with Parkinson’s disease, as well as Parkinsonian syndromes. Next are parts with chapters addressing essential and other tremor disorders followed by management of the various dystonic syndromes and other hyperkinetic disorders including chorea, tics, and myoclonus. Other disorders covered are drug-induced movement disorders, psychogenic movement disorders, Wilson’s disease, hemifacial spasm and more. Authored by experts globally, this practical guide will help physicians, other healthcare professionals and trainees care for patients with a wide spectrum of movement disorder related problems.

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This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler's equations in general.

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This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

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This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.

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The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.

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In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier’ theorem on existence of optimal transport maps and of Caffarelli’s Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero.

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This book introduces some methods for the determination of the three-dimensional geometry of molecules in solution and the occurrence of dynamical processes (interaction with the solvent, rearrangements in the molecular geometry, interactions with other molecules) in several ytterbium complexes. An especial attention has been deserved to the study of some important catalysts that were recently developed in the scientific research. The determination of molecular geometry and dynamics in solution, even if it is generally a hard task, is often a crucial step to understand and rationalize the catalytic mechanism, as well to design new catalysts. The proposed methods are applied here to several systems, even chiral, and are founded on a detailed analysis of the paramagnetic and optical properties of the ytterbium ion, and combining several instrumental techniques (mainly Nuclear Magnetic Resonance and Circular Dichroism).

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Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.

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The experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. This thesis presents an overview of theoretical and experimental facts on ultra-cold atomic gases. A Green's function scheme is examined, and the book also applies a novel spin-density-functional approach to the study of Fermi gases inside one-dimensional optical lattices.

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These notes contain my lectures on light scattering by matter presented at the Scuola Normale Superiore, Pisa during May and June 1995. I have deleted some of the topics discussed then and added a few related to my recent work. The notes are not to be regarded as exhaustive but rather as a selection of topics. In particular I have discussed, as examples, the theoretical basis for the interpretation of experiment on light scattering by photons in alpha-quartz and by electronic excitations in boron-doped diamond.

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The study of shape optimization problems is a very wide field, both classical, as the isoperimetric problem and Newton problem of the best aerodynamical shape show, and modern, for all the recent results obtained in the last two, three decades. The fascinating feature is that the competing objects are shapes, i.e. domains of Rn, instead of functions, as usually occurs in problems of calculus of variations. This constraint often produces additional difficulties that lead to a lack of existence of a solution and the introduction of suitable relaxed formulations of the problem. However, in a few cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restriction on the class of competing domains. This volume collects the lecture notes of two courses given in the academic year 2000/01 by the authors at the University of Pisa and at the Scuola Normale Superiore respectively. The courses were mainly addressed to Ph. D. students and required a background in the topics in functional analysis that are usually taught in undergraduate courses.

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Sensory experience can dynamically modify both the anatomy and function of the brain. In particular, neurons can modify their connections in response to enviromental stimuli. This process, generally referred to as “neuronal plasticity”, is the basis of learning and memory processes in the brain. Which are the bases of neuronal plasticity? That is, how can environmental factors and sensory experience modify the connections between neurons? Neurotrophic factors of the Nerve Growth Factor (NGF) family are known to finely regulate the development and maintenance of synaptic connections in the PNS. The results obtained by the group of Maffei firstly suggested the hypothesis that neurotrophic factors could play a key role in the plasticity of the mammalian visual system. The purpose of this thesis is to give a general overview about the recent advances in the field of neurotrophine-regulated plasticity of the mammalian visual system.

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Cp20 is a neuronal protein involved in the molecular mechanisms of synaptic plasticity. Cp20 was first identified in the CNS of the marine snail Hermissenda, which can be trained to learn an association between visual and vestibular stimuli in a Pavlovian conditioning procedure. Upon learning, cp20 is phosphorylated in a few defined neurons of Hermissenda, and inhibits the Ca2+-dependent K+ channels. This results in an increase in membrane resistence and therefore a hyperexcitability of the neuronal pathway. Similar biochemical mechanisms have been proposed to underlie memory in higher species, such as rabbit and rat. Cp20 was isolated from squid optic lobes by a 5-step purification. The protein was cloned, fused with an oligohistidine tail, and expressed in Esterichia coli. The activation of PKC, the enzyme responsible for cp20 phosphorylation, was also studied by an in vivo imaging system.

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These volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. The second part deals with various types of particle methods, both deterministic and stochastic, used in modern applications of computer simulations in physics and related disciplines.

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This volume contains 17 mathematical works by Johann Bernoulli, written between 1680 – when he was only 13 years old and studied mathematics with his brother Jacob – and 1732, when he was 65 years old. Five of the works are handwritten manuscripts, and another three belong to the Anekdota, which he published in the fourth volume of his Opera Omnia. The book features also seven works by other authors: John Craig, Jacob Hermann, Gottfried Wilhelm Leibniz, and Ehrenfried Walther von Tschirnhaus. Another work included in this book was co-written by Johann Bernoulli and Samuel Klingenstjerna. The texts presented here are divided into two parts: the first consists of a substantial untitled paper (Ms. 27) that contains, in a sequence numbered by the author, 120 propositions on various subjects that Bernoulli explored over a very long period of time, namely from 1685 to the first decades of the 18th century. In turn, the second part is composed of a series of articles and manuscripts devoted to problems on the rectification and transformation of curves, on geodesics, and on spherical epicycloids. In addition to information on the rapid advances in mathematics during this period, the volume also shares fascinating insights into the connections between the mathematicians.

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