This book presents the outcomes of the 2017 International Conference on Applications and Techniques in Cyber Security and Intelligence, which focused on all aspects of techniques and applications in cyber and electronic security and intelligence research. The conference provides a forum for presenting and discussing innovative ideas, cutting-edge research findings, and novel techniques, methods and applications on all aspects of cyber and electronic security and intelligence.

International Conference on Applications and Techniques in Cyber Security and Intelligence: Applications and Techniques in Cyber Security and ... in Intelligent Systems and Computing, 580)

Computers & Technology

Computer Science

Edizioni della Normale

This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered on the occasion of the International Congress of Mathematicians in 1900 in Paris: - 19th problem: are the solutions to regular problems in the Calculus of Variations always necessarily analytic? - 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as is in regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; finally, harmonic maps and minimal graphs in codimension 1 and greater than 1.

An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs (Publications of the Scuola Normale Superiore / Lecture Notes (Scuola Normale Superiore))

Science & Math

Luca Martinazzi Mariano Giaquinta

Mathematics

This volume collects the lecture notes of an introductory course on the theory of many-body systems, held at the Scuola Normale Superiore di Pisa. It is mainly addressed to fourth and fifth-year undergraduates and to first-year graduates in physics and chemistry. The book is also suitable for researchers in the field wanting to gain a general introductory overview on its modern focal points. Starting from a set of notes first prepared in 1994, which were mainly focused on conduction electrons in metals and semiconductors, these lecture notes are now being reprinted with some major changes and additions in order to provide the reader with an overview of recent developments in the understanding of low-dimensional electron fluids and of confined quantum gases made from bosonic and fermionic atoms and molecules. The book is divided into seven chapters and includes 18 appendices on specialized topics. The introductory chapter illustrates some of the longstanding problems in many-body physics. Chapters 2, 3 and 4 are mainly devoted to topics concerning electron fluids. A formal presentation of the theory of Green's functions and linear response functions for fermions in chapter 2 is followed by a chapter on electron liquids in the normal state and by a further chapter on the magnetism of conduction electrons and strongly correlated electron fluids. Chapter 5 turns to the formal theory of Green's functions and linear response functions for bosons. And finally, Chapters 6 and 7 are on trapped boson gases and on confined fermion gases and gaseous boson-fermion mixtures.

Many-body physics in condensed matter systems (Publications of the Scuola Normale Superiore, 4)

Polini, Marco

Tosi, Mario

Earth Sciences

On the work of Givental relative to mirror symmetry (Publications of the Scuola Normale Superiore)

Bini, Gilberto

De Concini, Conrado

Polito, Marzia

Mathematical theory of discrete time decision processes, also known as stochastic control, is based on two major ideas: backward induction and conditioning. It has a large number of applications in almost all branches of the natural sciences. The aim of these notes is to give a self-contained introduction to this theory and its applications. Our intention was to give a global and mathematically precise picture of the subject and present well motivated examples. We cover systems with complete or partial information as well as with complete or partial observation. We have tried to present in a unified way several topics such as dynamic programming equations, stopping problems, stabilization, Kalman-Bucy filter, linear regulator, adaptive control and option pricing. The notes discuss a large variety of models rather than concentrate on general existence theorems.

Chance and decision. Stochastic control in discrete time (Publications of the Scuola Normale Superiore)

Zabczyk, Jerzy

This is a collection of the following articles: F. Strocchi, Classification of solutions of non-linear hyperbolic equations and non-linear elliptic problems, E.H. Zarantonello, Conical spectral theory, E. De Giorgi, Generalized limits in calculus of variations, G. Dal Maso and L. Modica, A general theory of variational functionals.

Topics in functional analysis 1980-81 (Publications of the Scuola Normale Superiore)

Strocchi, Franco

Dal Maso, Gianni

De Giorgi, Ennio

Zarantonello, Eduardo H.

Modica, Luciano

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.

Spectral properties of Schroedinger operators and scattering theory (Publications of the Scuola Normale Superiore)

Agmon, Shmuel

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.

Exterior differential calculus and applications to economic theory (Publications of the Scuola Normale Superiore)

Ekeland, Ivar

These notes are based on six Fermi Lectures held at the Scuola Normale Superiore in Pisa in March and April 1981. The topics treated depend on basic concepts of classical mechanics, elementary geometry, complex analysis as well as spectral theory and are meant for mathematicians and theoretical physicists alike. These lectures weave together a number of threads from various fields of mathematics impinging on the subject of inverse spectral theory. I did not try to give an overview over this fast moving subject but rather tie various aspects together by one guiding theme: the construction of all potentials for the one-dimensional Schrödinger equation which gives rise to finite band potentials, which is done by reducing it to solving a system of differential equations. In fact, we will see that the problem of finding all almost periodic potentials having finitely many intervals as its spectrum is equivalent to the study of the geodesics on an ellipsoid. To make this connection clear we have carried together several facts from classical mechanics and from spectral theory and we give a self-contained exposition of the construction of these finite band potentials.

Integrable Hamiltonian systems and spectral theory (Publications of the Scuola Normale Superiore)

Moser, Jürgen

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.

Symmetry in nature: Volume II: A volume in honour of Luigi A. Radicati di Bronzolo (Publications of the Scuola Normale Superiore)

Physics

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