Search results for ""birkhauser""

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.

Read more less

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.

Read more less

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).

Read more less

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.

Read more less

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.

Read more less

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.

Read more less

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.

Read more less

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.

Read more less

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.

Read more less

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.

Read more less

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.

Read more less

Das Lehrbuch diskutiert gängige Fragen der Analysis und linearen Algebra und verwendet für die rechnergestützten Antworten die Software Matlab und Mathematica. Es stellt mathematische Standard-Algorithmen im Detail vor und zeigt deren Umsetzung in die Programme. Zusätzlich erläutert es, wie deren Funktionen Probleme lösen. Die Inhalte sind nach Datentypen (Polynome, reelle Funktionen, Matrizen) gegliedert. Im Vordergrund: die Objekte am Rechner, Grundoperationen an diesen Objekten und typische Fragen. Mit Algorithmen in Pseudocode. Plus zum Download: Programme für Mathematica und Matlab, alle Beispiele, Grafiken, interaktive Elemente.

Read more less

In seinem Kopf stellte er die mathematische Welt auf den Kopf. Er berechnete Flüssigkeitsströmungen, das Trägheitsmoment, entwickelte die Variationsrechnung und die moderne Zahlentheorie. Als Wissenschaftler steht er auf einer Stufe mit Newton und Einstein. Konstrukteure in aller Welt arbeiten tagtäglich mit seinen Formeln – egal ob es um den Schiffsrumpf der "Alinghi" geht oder um die Schwingungen des "Viaduc de Millau", der Welt höchster Autobahnbrücke. Dabei war er ein Mensch, der bürgerliche Behaglichkeit und Ruhe liebte. Nicht ganz einfach zur Gründungszeit von St. Petersburg inmitten russischer Kaisermorde oder im Berlin zur Zeit der schlesischen Kriege. Und erst recht nicht inmitten einer grossen Kinderschar. Der Comic von Elena Pini (Graphik) und Alice und Andreas K. Heyne (Text) zeichnet das Leben des genialen Baslers nach, der vor 300 Jahren geboren wurde, mit zwanzig Jahren seine Heimatstadt verliess – und nie wieder zurückkehrte.

Read more less

Der Band enthält einen Teil der Abhandlungen Eulers zur Störungstheorie. Er ist der zweite von drei diesem Thema gewidmeten Bänden. Gegenstand der Untersuchungen ist die Beschreibung der Bewegung eines Himmelskörpers um ein Zentralgestirn unter Berücksichtigung der von weiteren Himmelskörpern auf ihn wirkenden Gravitationskräfte. Als Beispiel sei die gravitative Wirkung der Venus auf die Erdbahn erwähnt.Von grosser praktischer Bedeutung, insbesondere für die Navigation auf See, war die Untersuchung des Einflusses der Sonne auf die Mondbewegung. Mit diesem Thema beschäftigte Euler sich zeit seines Lebens.

Read more less

This timely book explores crises as an inevitable part of modern society, which causes ramifications not only for organisations, but also for a diverse range of stakeholders. Addressing the need for organisations to be guided by a stakeholder-oriented approach throughout all phases of the crisis communication process, the author draws upon various business disciplines and covers the management of issues, risk, reputation and relationships. Covering all stages of crisis communication, from pre-crisis to post-crisis, stakeholder engagement is analysed through a series of case studies, with a particular focus on the role of social media. Scholars of corporate communications and business strategy will find this new book undoubtedly useful, and it will be of particular interest to those involved in crisis communication and management.

Read more less

Why do polished stones look wet? How does the Twin Paradox work? What if Jupiter were a star? How can we be sure that pi never repeats? How does a quantum computer break encryption? Discover the answers to these, and other profound physics questions! This fascinating book presents a collection of articles based on conversations and correspondences between the author and complete strangers about physics and math. The author, a researcher in mathematical physics, responds to dozens of questions posed by inquiring minds from all over the world, ranging from the everyday to the profound. Rather than unnecessarily complex explanations mired in mysterious terminology and symbols, the reader is presented with the reasoning, experiments, and mathematics in a casual, conversational, and often comical style. Neither over-simplified nor over-technical, the lucid and entertaining writing will guide the reader from each innocent question to a better understanding of the weird and beautiful universe around us. Advance praise for Do Colors Exist?: “Every high school science teacher should have a copy of this book. The individual articles offer enrichment to those students who wish to go beyond a typical ‘dry curriculum’. The articles are very fun. I probably laughed out loud every 2-3 minutes. This is not easy to do. In fact, my children are interested in the book because they heard me laughing so much.” – Ken Ono, Emory University

Read more less

The cities of Rome and Las Vegas commonly sit at opposite ends of what architecture represents: whereas the former capital of the Roman Empire is perceived as ancient, proper and eternal, Sin City is described as flashy, vulgar and fake. Yet, both find themselves historically and contemporarilyat the intersection of power and play.Released fifty years after Denise Scott Brown and Robert Venturi's now canonical Learning FromLas Vegas (1972), the images in this book capture the atmosphere of both cities from the sky to the ground, revealing unexpected similarities and rediscovering Las Vegas' extravaganza on the streets of Rome. Iwan Baan's photographs contrast and subvert common perceptions of authenticity and artificiality and ultimately question such bipolar distinctions. In their dialogue, the photographs follow Scott Brown and Venturi's plea to first look, understand and only then judge.

Read more less

Die Villa Savoye ist eine Ikone der modernen Architektur. Wer aber waren Eugénie und Pierre Savoye, die das Haus bauen ließen? Warum beauftragten sie Le Corbusier? Und wie lebten sie?Der Enkel Jean-Marc Savoye erzählt die Geschichte der Villa und der Bewohner anhand von Dokumenten und Familienerinnerungen. Jean-Philippe Delhomme illustriert die Baustelle, den Alltag, die Kriegszeit, die Nutzung als Scheune und die Rettung vor dem Abriss.

Read more less

This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers.In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of continuous and discrete spectrum, multiple scales in space and time, and the ill-posedness of these problems.This volume collects a series of lectures which introduce into the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.

Read more less

The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key importance – schedule delays, inconvenience, customer dissatisfaction, and loss of prestige and even weakening of national security are common examples of results that are caused by unreliability of systems and individuals. The book begins with an introduction to C0-semigroup theory. Then, after a brief history of reliability theory, methods that study the well-posedness, the asymptotic behaviors of solutions and reliability indices for varied reliability models are presented. Finally, further research problems are explored.Functional Analysis Methods for Reliability Models is an excellent reference for graduate students and researchers in operations research, applied mathematics and systems engineering.

Read more less

Sound protection may even play an important role at the design stage of a project, because the orientation of a building and its plan layout may influence it. Important factors to be taken into account are noise impacting on the building from the outside and noise generated by people and technical equipment inside the building. Basics Sound Insulation conveys to the reader a thorough understanding of sound protection requirements in the design and construction of a building. To start with, the basics of acoustics are explained, including basic terms of physics, how sound is generated and propagated, and how sound is perceived. This is followed by an explanation of how sound emissions are assessed and what sound-reducing and design options are available to the designer.

Read more less

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer­ sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo­ pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.

Read more less

* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training

Read more less

Villa Savoye is an icon of modern architecture. But who were Eugénie and Pierre Savoye, who had the house built between 1928 and 1930? Why did they commission Le Corbusier? And how did they live in the country house they dubbed "Villa les Heures Claires"? Their grandson Jean-Marc Savoye tells the story of the villa and its residents using rare documents and family memories. In his pictures, illustrator Jean-Philippe Delhomme – long fascinated by the building – brings to life the construction site, everyday life, the war period, its use as a barn, and its rescue from demolition. In 1965, Le Corbusier lived to see Villa Savoye declared a monument; in 2016 it earned a spot on the UNESCO World Heritage list and now welcomes 40,000 visitors each year.

Read more less

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.​

Read more less

This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates.In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.

Read more less

This book describes the searches that lead to the discovery of a Higgs boson performed at CMS, one of the two main experiments at the CERN LHC. After an overview of the theory and of the CMS experiment, all search channels are described, with emphasis on the ones with the best sensitivity. The statistical methodology used to analyse and the outcomes of the searches and the discovery results are then presented in detail.

Read more less

This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.

Read more less

This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

Read more less

The book deals with some questions related to the boundary problem in complex geometry and CR geometry. After a brief introduction summarizing the main results on the extension of CR functions, it is shown in chapters 2 and 3 that, employing the classical Harvey-Lawson theorem and under suitable conditions, the boundary problem for non-compact maximally complex real submanifolds of Cn, n=3 is solvable. In chapter 4, the regularity of Levi flat hypersurfaces Cn (n=3) with assigned boundaries is studied in the graph case, in relation to the existence theorem proved by Dolbeault, Tomassini and Zaitsev. Finally, in the last two chapters the structure properties of non-compact Levi-flat submanifolds of Cn are discussed; in particular, using the theory of the analytic multifunctions, a Liouville theorem for Levi flat submanifolds of Cn is proved.

Read more less

In this thesis I study the untwisted affine quantum algebras and their specialization at a primitive l-th root of unity. In particular my goal is the complete description of the center, when l is odd. The center of the specialization of the quantum algebra at odd roots of unity is already known in the finite case, that is for finite dimensional semisimple Lie algebras. In this thesis I prove that analogous results hold in the affine untwisted case.

Read more less

Electron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simpe metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides a general framework which can account for both.

Read more less

The subject of the present thesis is a study on bipolaron formation in heavily doped and polar materials. The study is applied to the physics of superconducting compounds with high transition temperature. In particular this thesis addresses the problem of the formation and superconducting properties of real space electron (hole) pairs in these systems and their dependence on the carrier density. The pairing mechanism results from the dynamical cooperation of photonic and electronic degrees of freedom which characterize the heavily doped polar material. We call these pairs biplasmapolarons (BBP) because they can be thought as quasi-particles composed by two electrons (holes) and their cloud of virtual photons and plasmons. In the present work we extend the theory to the calculation of both BPP binding energy and effective mass and we discuss the features of the effective electron-electron interaction.

Read more less

The main goal of these lectures is to get students acquainted with a glossary of nonlinear physics. I try to present the material of the lectures (delivered at SNS Pisa in April -- June 1999) in such a way that the students do not need to use additional literature during the first reading. The lectures focus on the following arguments: discussion of nonlinear problems in classical physics; the use of the multiple time scale expansion method to solve problems of nonlinear oscillations; description of nonlinear wave steepening and shock wave formation using the Lagrange variables; solution of nonlinear elliptic equations considering the Liouville equation; soliton solutions of the Korteweg de Vries, Sine-Gordon and Nonlinear Schrödinger equations; the use of the Backlund transformation; self-similarity of nonlinear systems.

Read more less