The Completeness of Scientific Theories deals with the role of theories in measurement. Theories are employed in measurements in order to account for the operation of the instruments and to correct the raw data obtained. These observation theories thus guarantee the reliability of measurement procedures. In special cases a theory can be used as its own observation theory. In such cases it is possible, relying on the theory itself, to analyze the measuring procedures associated with theoretical states specified within its framework. This feature is called completeness. The book addresses the assets and liabilities of theories exhibiting this feature. Chief among the prima-facie liabilities is a testability problem. If a theory that is supposed to explain certain measurement results at the same time provides the theoretical means necessary for obtaining these results, the threat of circularity arises. Closer investigation reveals that various circularity problems do indeed emerge in complete theories, but that these problems can generally be solved. Some methods for testing and confirming theories are developed and discussed. The particulars of complete theories are addressed using a variety of theories from the physical sciences and psychology as examples. The example developed in greatest detail is general relativity theory, which exhibits an outstanding degree of completeness. In this context a new approach to the issue of the conventionality of physical geometry is pursued. The book contains the first systematic analysis of completeness; it thus opens up new paths of research. For philosophers of science working on problems of confirmation, theory-ladenness of evidence, empiricaltestability, and space--time philosophy (or students in these areas).

One of the ?rst Computer Science sites in Italy, in recent years, the Friuli region has become a very active hub in Computational Physics and other applications of Informatics to Human and Natural Sciences. In particular the University of Udine has developed a tradition in innovative cross-disciplinary research areas involving Computer Science and Physics, providing digital tools for laboratories such as NASA and CERN. The sixth International Symposium "Frontiers of Fundamental and Compu- tional Physics" (FFP6) aimed at providing a platform for a wide range of phy- cists to meet and share thoughts on the latest trends in various research areas including High Energy Physics, Theoretical Physics, Gravitation and Cosmology, Astrophysics, Condensed Matter Physics, Fluid Mechanics. Such frontier lines were uni?ed by the use of computers as an, often primary, research instrument, or dealing with issues related to information theory. The present Sixth International Symposium in the series wasorganizedatthe UniversityofUdine,Italyfrom26thto29th ofSeptember2004. TheUniversity of in the Udine and the B. M. Birla Science Centre in Hyderabad have collaborated organization of this Symposium and the edition of these Proceedings, under the auspices of their joint initiative the International Institute of ApplicableMat- maticsand InformationSciences. ThecontributionsintheProceedingsaregrouped as follows: * Field Theory, Relativity and Cosmology * Foundations of Physics and of Information Sciences * Nuclear and High-Energy Particle Physics and Astrophysics; Astroparticle Physics * Complex Systems; Fluid Mechanics * New Approaches to Physics Teaching ThisSymposiumhadanattendanceofover100participants. Therewere63- pers/presentations, including 4 introductory invited lectures delivered by the - belLaureatesL. CooperandG. 'tHooft,andbytheeminentphysicistsY.

This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the "A-model" half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the "BCOV" B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician's point-of-view, including such topics as polyvector fields and primitive forms, Givental's ancestor potential, and integrable systems.

We live in complicated, dangerous times. They are also hyper-technical times. As citizens who will elect future presidents of the most powerful and influential country in the world, we need to know truly understand, not just rely on television's talking heads if Iran's nascent nuclear capability is a genuine threat to the West, if biochemical weapons are likely to be developed by terrorists, if there are viable alternatives to fossil fuels that should be nurtured and supported by the government, if nuclear power should be encouraged, and if global warming is actually happening. This book is written in everyday, nontechnical language on the science behind the concerns that our nation faces in the immediate future. Even active readers of serious journalism will be surprised by the lessons that the book contains. It is "must-have" information for all presidents and citizens of the twenty-first century."

Das Buch behandelt Matrizengleichungen und -funktionen sowie die computergerechte Darstellung und Losung der Bewegungsgleichungen von Schwingungssystemen mit endlich vielen Freiheitsgraden und fuhrt in die Grundlagen der Naherungsmethoden von Rayleigh und Ritz ein. Das Eigenwertproblem wird, anders als sonst ublich, von einem allgemeinen Standpunkt aus betrachtet. Dadurch gewinnt die Darstellung an Verstandlichkeit und an Anwendungsbreite. Das Buch ist sowohl fur Studierende als auch fur Physiker und Ingenieure in der Praxis geschrieben.

In the present edition I have included "Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.

From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other monographs, while others are for the first time included in a book." -- Mathematica "Each chapter begins with an excellent summary of the content and ends with an exercise section... This is really an outstanding book, well written and beautifully produced. It is both a graduate text and a monograph, so it can be recommended to graduate students as well as to specialists." -- Publicationes Mathematicae Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simplyconnected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond.

The continuous evolution and development of experimental techniques is at the basis of any fundamental achievement in modern physics. Strongly correlated systems (SCS), more than any other, need to be investigated through the greatest variety of experimental techniques in order to unveil and crosscheck the numerous and puzzling anomalous behaviors characterizing them. The study of SCS fostered the improvement of many old experimental techniques, but also the advent of many new ones just invented in order to analyze the complex behaviors of these systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. The volume presents a representative collection of the modern experimental techniques specifically tailored for the analysis of strongly correlated systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for any other researcher in the field who appreciates consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.

Magnetic Resonance Image Reconstruction: Theory, Methods and Applications presents the fundamental concepts of MR image reconstruction, including its formulation as an inverse problem, as well as the most common models and optimization methods for reconstructing MR images. The book discusses approaches for specific applications such as non-Cartesian imaging, under sampled reconstruction, motion correction, dynamic imaging and quantitative MRI. This unique resource is suitable for physicists, engineers, technologists and clinicians with an interest in medical image reconstruction and MRI.

In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

This volume presents selected papers from the 7th International Congress on Computational Mechanics and Simulation held at IIT Mandi, India. The papers discuss the development of mathematical models representing physical phenomena and applying modern computing methods and simulations to analyse them. The studies cover recent advances in the fields of nano mechanics and biomechanics, simulations of multiscale and multiphysics problems, developments in solid mechanics and finite element method, advancements in computational fluid dynamics and transport phenomena, and applications of computational mechanics and techniques in emerging areas. The volume will be of interest to researchers and academics from civil engineering, mechanical engineering, aerospace engineering, materials engineering/science, physics, mathematics and other disciplines.

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I* We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo* These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

This is a unique approach to noise theory and its application to physical measurements that will find its place among the graduate course books. In a very systematic way, the foundations are laid and applied in a way that the book will also be useful to those not focusing on optics. Exercises and solutions help students to deepen their knowledge.

This book is aimed at researchers, industry professionals and students interested in the broad ranges of disciplines related to condition monitoring of machinery working in non-stationary conditions. Each chapter, accepted after a rigorous peer-review process, reports on a selected, original piece of work presented and discussed at the International Conference on Condition Monitoring of Machinery in Non-stationary Operations, CMMNO'2018, held on June 20 - 22, 2018, in Santander, Spain. The book describes both theoretical developments and a number of industrial case studies, which cover different topics, such as: noise and vibrations in machinery, conditioning monitoring in non-stationary operations, vibro-acoustic diagnosis of machinery, signal processing, application of pattern recognition and data mining, monitoring and diagnostic systems, faults detection, dynamics of structures and machinery, and mechatronic machinery diagnostics.

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods.This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works.The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media m

The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

This book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems. Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Besides, the electromagnetic parameters of complex medium such as the permittivity and conductivity are retrieved by a cascaded framework in Chapter 4. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 5. Finally, in Chapter 6, a series of the latest advanced frameworks and the corresponding physics applications are introduced. As deep learning techniques are experiencing vigorous development in computational physics, more people desire related reading materials. This book is intended for graduate students, professional practitioners, and researchers who are interested in DL for computational physics.

The contributions gathered in this volume provide introductions to current problems in geospace electromagnetic radiation, guides to the associated literature and tutorial reviews of the relevant space physics. Students and scientists working on various aspects of the terrestrial aurora or magnetospheric and near-Earth heliospheric high-frequency waves will find this volume an indispensable companion for their studies.

This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods. Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes or classification of system states. The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.

The rare earths play a unique role in science. These seventeen related elements afford a panoply of subtle variations deriving from the systematic development of their electronic configurations, allowing a test of theory with excellent resolution. In contrast they find widespread use in even the most mundane processes such as steel making, for polishing materials and gasoline cracking catalysts. In between are exotic uses such as TV screen phosphors, lasers, high strength permanent magnets and chemical probes.
This multi-volume handbook covers the entire rare earth field in an integrated manner. Each chapter is a comprehensive up-to-date, critical review of a particular segment of the field. The work offers the researcher and graduate student alike, a complete and thorough coverage of this fascinating field.
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Devices and Related Properties.- The Properties of the Pseudospark Discharge.- Review of Superdense Glow Discharge.- Basic Mechanisms Contributing to the Hollow Cathode Effect.- Cathode-Related Processes in High-Current Density, Low Pressure Glow Discharges.- Comparison of Electrode Effects in High-Pressure and Low-Pressure Gas Discharges Like Spark-Gap and Pseudospark.- Experimental Review.- Mapping and Modeling of the Cathode Fall and Negative Glow Regions.- Emission Spectroscopy in Optically Thick Gas Discharges.- An Analysis of the High Current Glow Discharge Operation of the BLT Switch.- Laser-Induced Fluorescence Measurements of Number Densities of Neutral and Ionized Metal Atoms.- Streamers in Atmospheric Pressure N2: Empirical Results.- Theoretical Modeling.- The Solution of the Continuity Equations in Ionization and Plasma Growth.- Scaling Parameters for Optically Triggered Hollow Cathode Switches Obtained by Computer Simulation.- A Physical Model of Prebreakdown in the Hollow Cathode Pseudospark Discharge Based on Numerical Simulations.- Self-Consistent Models of DC and Transient Glow Discharges.- Weak Collisions in Strong Double Layers.- The Effect of Pendel Electrons on Breakdown and Sustainment of a Hollow Cathode Discharge.- A Two-Electron-Group Model for a High Current Pseudospark or Back- Lighted Thyratron Plasma.- Electron Ionization Rate Coefficients at Very High E/N.- New Applications.- Plasma-Based Device Concepts Based on the Pseudospark and BLT.- Emittance Measurement of a Pseudospark-Produced Electron Beam.- New Ways of Electron Emission for Power Switching and Electron Beam Generation.

This book, part of the seriesContributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.

The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson.

The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH)."