Publications of the Scuola Normale Superiore – serie
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62 produkter
242 kr
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The achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties. The attention given in this article to methods beyond standard mean-field approaches should make it a useful reference point for future advances in these areas.
253 kr
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The notes are based on lectures on stochastic processes given at Scuola Normale Superiore in 1999 and 2000. Some new material was added and only selected, less standard results were presented. We did not include several applications to statistical mechanics and mathematical finance, covered in the lectures, as we hope to write part two of the notes devoted to applications of stochastic processes in modelling. The main themes of the notes are constructions of stochastic processes. We present different approaches to the existence question proposed by Kolmogorov, Wiener, Ito and Prohorov. Special attention is also paid to Levy processes. The lectures are basically self-contained and rely only on elementary measure theory and functional analysis. They might be used for more advanced courses on stochastic processes.
221 kr
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This is a written version of the Cattedra Galileiana lectures, presented in 2002 at the Scuola Normale in Pisa. The objective is to combine an orientation to credit-risk modeling (emphasizing the valuation of corporate debt and credit derivatives) with an introduction to the analytical tractability and richness of affine state processes. This is not a general survey of either topic, but rather is designed to introduce researchers with some background in mathematics to a useful set of modeling techniques and an interesting set of applications.
Probabilistic methods of investigating interior smoothness of harmonic functions associated with degenerate elliptic operators
Häftad, Engelska, 2004
167 kr
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The lectures concentrate on some old and new relations between quasiderivatives of solutions to Ito stochastic equations and interior smoothness of harmonic functions associated with degenerate elliptic equations. Recent progress in the case of constant coefficients is discussed in full detail.
328 kr
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These Lecture Notes are based on a course given in June 2001 at the Cattedra Galileiana of Scuola Normale Superiore di Pisa. The course consisted of a short introduction into the basic concepts of Mathematical Finance, focusing on the notion of “no arbitrage”, and subsequently applying these concepts to portfolio optimization. To avoid technical difficulties I mainly dealt with the situation where the underlying probability space is finite and only sketched the difficulties arising in the general case. We then pass to the scheme of utility optimisation for general semi-martingale models. Some topics of this course are not standard: for example, in the treatment of the general existence theorem for the optimal portfolio, we give a direct proof which is not relying on duality theory. Similarly, the treatment of the asymptotic elasticity of utility functions and a related counter-example are original to these notes.
135 kr
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In the present thesis we develop new strategies concerning the use of lanthanide cations as spectroscopic probes for the study of molecular structures in solution. A widespread interest for lanthanides is mainly centered in two large fields: organic synthesis and clinical practice. Systems containing lanthanides enjoy a very favorable situation, since these ions feature high coordination numbers, which assure rich binding chemistry, and at the same time they possess the right spectroscopic properties to monitor it. The present thesis develops the potentialities of electronic spectroscopy of lanthanide systems in solution. We point out and overcome the drawbacks which have mainly hampered this kind of study so far, namely: a sensivity problem, an instrumental problem and a calibration problem.
146 kr
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These are the informal notes of two seminars held at the Università di Roma “La Sapienza”, and at the Scuola Normale Superiore in Pisa in spring and autumn 1997. We discuss in detail the content of the parts of a paper by Givental dealing with mirror symmetry for projective complete intersections.
274 kr
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This set of lecture notes is the outcome of a lecture series, given in April 2000 by the author while holding the “Cattedra Galileiana” at Scuola Normale Superiore in Pisa. The purpose of the lectures was to give an overview of some recent work concerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market.
274 kr
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We consider in Rn a differential operator P(D), P a polynomial, with constant coefficients. Let U be an open set in Rn and A(U) be the space of real analytic functions on U. We consider the equation P(D)u=f, for f in A(U) and look for a solution in A(U). Hormander proved a necessary and sufficient condition for the solution to exist in the case U is convex. From this theorem one derives the fact that if a cone W admits a Phragmen-Lindeloff principle then at each of its non-zero real points the real part of W is pure dimensional of dimension n-1. The Phragmen-Lindeloff principle is reduced to the classical one in C. In this paper we consider a general Hilbert complex of differential operators with constant coefficients in Rn and we give, for U convex, the necessary and sufficient conditions for the vanishing of the H1 groups in terms of the generalization of Phragmen-Lindeloff principle.
200 kr
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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.
114 kr
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These are the written notes of Fermi's Lectures supported by the Accademia Nazionale dei Lincei and given at the Scuola Normale Superiore of Pisa during March-April 1973. We propose to discuss here certain spectral properties of Schrödinger operators H=-D+V(x) (D the Laplacian and V a potential) which have application to scattering theory. We consider an operator H with potential V of class SR. We show that the positive point spectrum of H is a discrete set in R+. Eigenfunctions which correspond to positive eigenvalues are shown to decay rapidly. This property is shown to hold also for generalized eigenfunctions. We then establish the limiting absorbing principle, which is a basic tool in our study.
190 kr
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The present article is based on the Fermi Lectures I gave in May, 1985, at Scuola Normale Superiore, Pisa, in which I discussed various methods for solving the Cauchy problem for abstract nonlinear differential equations of evolution type. Here I present a detailed exposition of one of these methods, which deals with “elliptic-hyperbolic” equations in the abstract form and which has applications, among other things, to mixed initial-boundary value problems for certain nonlinear partial differential equations, such as elastodynamic and Schrödinger equations.
200 kr
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During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.
Symmetry in nature
Volume II: A volume in honour of Luigi A. Radicati di Bronzolo
Häftad, Engelska, 1989
253 kr
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The papers published here have been written by friends, former students and colleagues of Luigi Radicati di Bronzolo on the occasion of his 70th birthday to express the affection and deep esteem he induced in them with his considerateness, intelligence, knowledge and culture. The papers appear in two volumes; on the basis of their titles it is easy to recognize that they may be grouped according to the following subjects: 1) Atomic, molecular and nuclear physics; 2) Astrophysics; 3) Elementary particles; 4) Mathematics; 5) Physical and biological ordered and disordered states; 6) Principles of quantum mechanics and of field theory.
167 kr
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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.
200 kr
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In the academic year 1994/95 I lectured on semigroups in the Scuola Normale Superiore and in the Politecnico di Torino. The purpose of the lectures was to present to an audience of graduate students a self-contained introduction to the theory of strongly continuous semigroups of linear operators acting on a Banach space. The main trust was concentrated on laying down the basic geometrical aspects of the theory as a background for applications to concrete problems in the analysis of differential operators.
167 kr
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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. Grid methods are the tool of the trade for the solution of ordinary and partial differential equations and consequently they represent a “must” for anyone dealing with computational science. With grid methods, a major distinction is made between methods which do not require matrix algebra and those which do.
167 kr
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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.
167 kr
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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 Schrodinger equations; the use of the Backlund transformation; self-similarity of nonlinear systems.
Ground state properties and excitation spectrum of correlated electron systems
Häftad, Engelska, 1999
167 kr
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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.
study on the activity-dependent expression of neurotrophic factors in the rat visual system
Häftad, Engelska, 1997
167 kr
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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.
Biochemical and spetroscopic characterization of cp20, a protein involved in synaptic plasticity mechanism
Häftad, Engelska, 1998
114 kr
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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.
114 kr
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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.
study on nerve growth factor (NGF) receptor expression in the rat visual cortex: possible sites and mechanisms of NGF action in cortical plasticity
Häftad, Engelska, 2004
114 kr
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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.
Search for neutrinos from stellar gravitational collapse with the MACRO experiment at Gran Sasso
Häftad, Engelska, 1996
114 kr
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Low energy neutrino astrophysics studies the evolutionary life of the stars via the neutrinos emitted during the quiescent phase (solar neutrinos) and during the explosive death of big mass stars (supernova neutrinos). The neutrino mean free path in matter is about twenty orders of magnitude greater than that of light; therefore neutrinos reaching us can be produced also in deep and high-density levels of stars. Since massless neutrinos are unaffected by their travel in the interstellar space, their energies and arrival directions carry information on the star history. The subject of this thesis is the search for neutrino bursts from galactic stellar gravitational collapses performed in the MACRO experiment, a large area modular detector, operating since autumn 1989.
Untwisted affine quantum algebras: the highest coefficient of det H_\eta and the center at odd roots of 1
Häftad, Engelska, 1996
114 kr
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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.
Search for neutrino oscillations in a long baseline experiment at the CHOOZ nuclear reactors
Häftad, Engelska, 1999
114 kr
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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.
160 kr
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The newly estabilished Centro di Ricerca Matematica “Ennio De Giorgi” began its activities hosting a Research Trimester on Dynamical Systems, from February 4th through April 26th, 2002. In the two volumes some of the contributions have been collected. The contributions are in the following different fields: Holomorphic dynamics and foliations, Hamiltonian dynamics, Small divisor problems, Celestial mechanics, Ergodic theory and randomly perturbed systems, Periodic orbits and zeta functions, Topology and dynamics, Partially hyperbolic and non-uniformly hyperbolic systems, Bifurcation theory and related topics, Dynamics on non archimedean fields.
221 kr
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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.
167 kr
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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.