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This book contains a collection of exercises designed to support and complement the theoretical exposition of standard topics for a first-year course in linear algebra and geometry at the university level.In this context, this exercise book naturally complements the text: F. Bottacin, "Linear Algebra and Geometry," Esculapio, Bologna, which will be referred to for the necessary theoretical concepts.In presenting solutions to the proposed exercises, my primary goal is to teach how to approach and solve problems. For this reason, in many cases, theoretical considerations have been included, and different solution methods have been proposed for the same type of exercise. The reader will thus be able to evaluate, on a case-by-case basis, the advantages and disadvantages of each method

In the last two decades, Italian neurological research has experienced significant development, making a substantial contribution to the global cultural growth of Neurology. This Manual has been authored by neurologists from Sapienza University of Rome, who are experts in various fields of Neurology. Special attention has been given to diagnostic, clinical, and therapeutic aspects of different neurological disorders, including recent scientific advancements. The volume comprises 33 chapters covering topics in Neurology, Neuroradiology, and Neurosurgery, including a chapter on Neurorehabilitation, one on Pediatric Neurology, and one on Principles of Psychiatry. The Manual serves as a valuable tool for medical students, including those pursuing healthcare professions, as well as Neurology residents. It dedicates ample space to symptoms of potential neurological origin encountered in general clinical practice and the neurological conditions that clinicians must be familiar with.

This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the physical behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.

The main aim of this book is to analyze the mathematical fundamentals and the main features of the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. Furthermore, another interesting aim of the present book is to shown that from the two numerical techniques mentioned above it is possible to derive two different approaches such as the Strong and Weak Finite Element Methods (SFEM and WFEM), that will be used to solve various structural problems and arbitrarily shaped structures. A general approach to the Differential Quadrature is proposed. The weighting coefficients for different basis functions and grid distributions are determined. Furthermore, the expressions of the principal approximating polynomials and grid distributions, available in the literature, are shown. Besides the classic orthogonal polynomials, a new class of basis functions, which depend on the radial distance between the discretization points, is presented. They are known as Radial Basis Functions (or RBFs). The general expressions for the derivative evaluation can be utilized in the local form to reduce the computational cost. From this concept the Local Generalized Differential Quadrature (LGDQ) method is derived. The Generalized Integral Quadrature (GIQ) technique can be used employing several basis functions, without any restriction on the point distributions for the given definition domain. To better underline these concepts some classical numerical integration schemes are reported, such as the trapezoidal rule or the Simpson method. An alternative approach based on Taylor series is also illustrated to approximate integrals. This technique is named as Generalized Taylor-based Integral Quadrature (GTIQ) method. The major structural theories for the analysis of the mechanical behavior of various structures are presented in depth in the book. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. Generally speaking, two formulations of the same system of governing equations can be developed, which are respectively the strong and weak (or variational) formulations. Once the governing equations that rule a generic structural problem are obtained, together with the corresponding boundary conditions, a differential system is written. In particular, the Strong Formulation (SF) of the governing equations is obtained. The differentiability requirement, instead, is reduced through a weighted integral statement if the corresponding Weak Formulation (WF) of the governing equations is developed. Thus, an equivalent integral formulation is derived, starting directly from the previous one. In particular, the formulation in hand is obtained by introducing a Lagrangian approximation of the degrees of freedom of the problem. The need of studying arbitrarily shaped domains or characterized by mechanical and geometrical discontinuities leads to the development of new numerical approaches that divide the structure in finite elements. Then, the strong form or the weak form of the fundamental equations are solved inside each element. The fundamental aspects of this technique, which the author defined respectively Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are presented in the book.

This book comprehends basic and advanced theoretical tools for the analysis of structure and operation of power electrical machines. The principal machine typologies are discussed: single and three phase transformer, induction machine, and synchronous machine. The first chapter resumes important notions of electromagnetism, oriented to the study of electrical machines: starting from the properties of Maxwell's equations in matter (in particular in magnetic materials), electric and magnetic integral laws and their application to practical electric and magnetic circuits are explained. In the subsequent chapters the electrical machines are analyzed in first from a physical point of view, and then suitable models, equations, and equivalent circuits are derived from the fundamental principles. The AC operation is deepened, by using both time-domain and frequency domain equations and equivalent circuits, since this is the main operating modality.The text is mainly targeted to students enrolled in a Master degree in Electrical Engineering, and is designed to be used for a one- or two-semester course in electrical machines. The prerequisites for effective use of the text are the courses of mathematical analysis, physics, and circuit theory.

Differential equations play a relevant role in many disciplines and provide powerful tools for analysis and modeling in applied sciences. The book contains several classical and modern methods for the study of ordinary and partial differential equations.

The aim of the book is to provide a comprehensive and unified description of high-intensity short laser pulses and their applications at the simplest level compatible with a correct physical understanding. The idea is to provide an intuitive picture of the phenomena under consideration with simple mathematical description useful for a better understanding. The book is based on the teaching experience of the graduate course of the Politecnico di Milano "HIGH INTENSITY LASERS FOR NUCLEAR AND PHYSICAL APPLICATIONS I + II" and is particularly addressed to graduate students with a background in electromagnetism; is mostly suitable for master students in Nuclear Engineering, in Engineering Physics, and in Physics and It's recommended also to students in material sciences (or similar) and to PhD students. The text organization is due to help to follow the lessons in the classroomand to be used for self-study by students.

This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.

This is the 13th edition of a book written for students and specialists who are interested in developing a fundamental understanding of pathology and treatment of hematologic diseases. The amount of knowledge required by hematologists to identify the best course of treatment for a patient in this field is changing rapidly and has fueled an explosion of new drugs that target pathways virtually unknown a decade ago. We are now also entering an era of effective immunotherapy for a variety of hematologic malignancies, but the long term outcomes and toxicities of these treatment approaches are still unknown. This first edition in English is a significant novelty in the history of this work. Its underlying goals, however, remain the same of the first Italian edition: to help students and specialists understand the basis, treatment and management of hematologic diseases.

The book discusses in details the main hardware and firmware fundamentals about micro- controllers. The goal is to present all the concepts necessary to understand and design an embedded system based on microcontrollers.The book discusses on: Binary logic and arithmetic; Embedded-systems basics; Low-end 8-bit microcontrollers by Microchip and STMicroelectronics; On-chip memories, Input/Output ports, peripherals; Assembly instruction sets; EasyPIC evaluation board by MikroElektronika; High-end 32-bit cores by ARM-Cortex; STM32F4 microprocessor by STMicroelectronics; Nucleo board for STM32F4 by STMicroelectronics; Custom developed board.The book is not targeted for just either low-end or high-end microcontrollers. Instead, the book fully describes both, moving from the basics of microcontroller systems, to 8-bit devices and then to the 32-bit ones.In fact, the book targets well-renowned, commercially-available microcontrollers by the microelectronic leaders in the field. As for low-end 8-bit microcontrollers, the book reviews the widely-spread and well-assessed devices by Microchip (the PIC16 family) and by STMicroelectronics (the ST6 family). Instead, as for high-end 32-bit microcontrollers, the book presents the leading-edge M3 and M4 cores by ARM-Cortex and its implementation by STMicroelectronics (the STM32F4 series).The Book is very modular and most Chapters can be used as stand-alone mini text books (e.g., Chapter 3 - "8-bit microcontrollers", Chapter 5 - "ARM-Cortex architectures", Chapter 6 - "STM32 microcontroller"). Moreover, Chapter 4 and Chapter 7 provide a very useful insight to electronic circuits employing microcontrollers and on-board components, by means of the EasyPIC v7 board by Mikroelektronika (for PIC microcontrollers) and Nucleo board by STmicroelectronics (for the STM32 ARM-Cortex M4 microcontrollers).

The title, "Laminated Composite Doubly-Curved Shell Structures. Differential and Integral Quadrature. Strong Form Finite Elements" illustrates the theme treated and the prospective followed during the composition of the present work. The aim of this manuscript is to analyze the static and dynamic behavior of thick and moderately thick composite shells through the application of the Differential Quadrature (DQ) method. The book is divided into two volumes wherein the principal higher order structural theories are illustrated in detail and the mechanical behavior of doubly-curved structures are presented by several static and dynamic numerical applications. In particular, the first volume is mainly theoretical, whereas the second one is mainly related to the numerical DQ technique and its applications in the structural field. The numerical results reported in the present volume are compared to the one available in the literature, but also to the ones obtained through several codes based on the Finite Element Method (FEM). Furthermore, an advanced version of the DQ method, termed Strong Formulation Finite Element Method (SFEM), is presented. The SFEM solves the differential equations inside each element in the strong form and implements the mapping technique typical of the FEM.

Nuclear medicine is a medical imaging specialty involving the use of radioactive compounds for diagnostic and therapeutic purposes. As a medical branch, it is considered part of Diagnostic Imaging, but differs substantially from Radiology with respect to the source of the radiation made visible by the diagnostic devices. Nuclear medicine adopts also some types of radioactive emissions for therapeutic purposes, allowing the employment of the metabolic properties of the radiopharmaceuticals for the cure of certain clinical conditions and malignant diseases. Nuclear medicine is a relatively recent discipline and owes its origins to the discovery of natural radioactivity and the development of the first instruments for medical diagnostics. From the introduction of the first gamma camera of Anger, the technology has greatly improved. The evolution has led to the development of SPECT and PET technology and in the recent years to the introduction of hybrid tomographs allowing the combination in one session of both functional and morphological images. The purpose of this textbook is to illustrate synthetically the principals of nuclear medicine diagnostics, with reference both to the technical part and main clinical indications. The booklet is addressed primarily to the degree courses for technologists, but can be reasonably used in other courses and medical training programs where there is necessity for relatively simple, yet complete and clinically relevant concepts of nuclear medicine discipline. As a complement, the manuscript will end with a dedicated section summarizing some concepts of nuclear medicine therapy.

The retail space is now recognized as the place where the enterprise enacts an important step in the process of value creation, not only from the economic point of view, but also regarding the relational processes it establishes with its users. The supply system of the enterprise is increasingly linked to the consistency of information, symbolic and sense assets. The organization of space, material and immaterial, leads to the creation of specific atmospheres in which displaying all the products means highlighting their main symbolic value. Through a skillful knowledge of the structures of perception, interpretation and motivation which underlie the mode of experiencing space - coupled with the ability of design to define its shape and significance - the visual merchandising project is able to lead the public through the brand's new narrative experiences.

Photonics originated as a research discipline during the 1960s, with the invention and production of the first lasers. The development of these optical sources was followed in the 1970s by the large-scale deployment of optical fibers, as a medium for information transmission by means of light beams. In the years that followed, scientific research and constant technological development fostered a revolution in the telecommunications field. The association of photonics with other disciplines opened new horizons, unimaginable just a few decades ago. This volume, as it contains material intended for prospective telecommunications and electronic engineers who are going to professionally design optics-based devices and subsystems, it also presents the basic notions to approach further disciplines with which photonics may pro tably interact.

The aim of this book is to provide the basic concepts concerning the mathematical finance which is unescapable to understand the way modern financial markets operate.

Deep comprehension of applied sciences requires a solid knowledge of Mathematical Analysis. For most of high level scientific research, the good understanding of Functional Analysis and weak solutions to differential equations is essential. This book aims to deal with the main topics that are necessary to achieve such a knowledge. Still, this is the goal of many other texts in advanced analysis; and then, what would be a good reason to read or to consult this book? In order to answer this question, let us introduce the three Authors. Alberto Ferrero got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Universit`a del Piemonte Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano. Maurizio Zanotti got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano.The three Authors, for the variety of their skills, decided to join their expertises to write this book. One of the reasons that should encourage its reading is that the presentation turns out to be a reasonable compromise among the essential mathematical rigor, the importance of the applications and the clearness, which is necessary to make the reference work pleasant to the readers, even to the inexperienced ones. The range of treated topics is quite wide and covers the main basic notions of the scientific research which is based upon mathematical models. We start from vector spaces and Lebesgue integral to reach the frontier of theoretical research such as the study of critical exponents for semilinear elliptic equations and recent problems in fluid dynamics. This long route passes through the theory of Banach and Hilbert spaces, Sobolev spaces, differential equations, Fourier and Laplace transforms, before which we recall some appropriate tools of Complex Analysis. We give all the proofs that have some didactic or applicative interest, while we omit the ones which are too technical or require too high level knowledge. This book has the ambitious purpose to be useful to a broad variety of readers. The first possible beneficiaries are of course the second or third year students of a scientific course of degree: in what follows they will find the topics that are necessary to approach more advanced studies in Mathematics and in other fields, especially Physics and Engineering. This text could be also useful to graduate students who want to start a Ph.D. course: indeed it contains the matter of a multidisciplinary Ph.D. course given by Filippo Gazzola for several years at Politecnico di Milano. Finally, this book could be addressed also to the ones who have already left education far-back but occasionally need to use mathematical tools: we refer both to university professors and their research, and to professionals and designers who want to model a certain phenomenon, but also to the nostalgics of the good old days when they were students.ALBERTO FERRERO got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Università del Piemonte Orientale.FILIPPO GAZZOLA got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano.¿MAURIZIO ZANOTTI got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano.