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Tensor Products of C*-Algebras and Operator Spaces: The Connes–Kirchberg Problem (London Mathematical Society Student Texts #96)
by Gilles PisierBased on the author's university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck's famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.
Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
by Eva B. Vedel Jensen Markus KiderlenThe purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
Tensor-Valued Random Fields for Continuum Physics (Cambridge Monographs on Mathematical Physics)
by Anatoliy Malyarenko Martin Ostoja-StarzewskiMany areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields in terms of one- and two-point correlation functions for tensors of ranks 1 through 4. Working from the standpoint of invariance of physical laws with respect to the choice of a coordinate system, spatial domain representations, as well as their wavenumber domain counterparts are rigorously given in full detail. The book also discusses, an introduction to a range of continuum theories requiring TRFs, an introduction to mathematical theories necessary for the description of homogeneous and isotropic TRFs, and a range of applications including a strategy for simulation of TRFs, ergodic TRFs, scaling laws of stochastic constitutive responses, and applications to stochastic partial differential equations. It is invaluable for mathematicians looking to solve problems of continuum physics, and for physicists aiming to enrich their knowledge of the relevant mathematical tools.
TensorFlow 2 Pocket Reference: Building and Deploying Machine Learning Models
by Kc TungThis easy-to-use reference for TensorFlow 2 design patterns in Python will help you make informed decisions for various use cases. Author KC Tung addresses common topics and tasks in enterprise data science and machine learning practices rather than focusing on TensorFlow itself.When and why would you feed training data as using NumPy or a streaming dataset? How would you set up cross-validations in the training process? How do you leverage a pretrained model using transfer learning? How do you perform hyperparameter tuning? Pick up this pocket reference and reduce the time you spend searching through options for your TensorFlow use cases.Understand best practices in TensorFlow model patterns and ML workflowsUse code snippets as templates in building TensorFlow models and workflowsSave development time by integrating prebuilt models in TensorFlow HubMake informed design choices about data ingestion, training paradigms, model saving, and inferencingAddress common scenarios such as model design style, data ingestion workflow, model training, and tuning
Tensorial Methods and Renormalization in Group Field Theories
by Sylvain CarrozzaThe main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.
Tensors and the Clifford Algebra: Application to the Physics of Bosons and Fermions
by Alphonse Charlier Alain Berard Marie-France Charlier Daniele FristotThis practical reference and text presents the applications of tensors, Lie groups and algebra to Maxwell, Klein-Gordon and Dirac equations, making elementary theoretical physics comprehensible and high-level theoretical physics accessible.;Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.;With over 2800 display equations and 14 appendixes, this book should be a useful reference for mathematical physicists and applied mathematicians, and an important text for upper-level undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity and field theory courses.
Tensors, Differential Forms, and Variational Principles
by David Lovelock Hanno RundIncisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Tensors for Physics
by Siegfried HessThis book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i. e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.
Teoria della Probabilità: Variabili aleatorie e distribuzioni (UNITEXT #123)
by Andrea PascucciIl libro fornisce un'introduzione concisa ma rigorosa alla Teoria della Probabilità. Fra i possibili approcci alla materia si è scelto quello più moderno, basato sulla teoria della misura: pur richiedendo un grado di astrazione e sofisticazione matematica maggiore, esso è indispensabile a fornire le basi per lo studio di argomenti più avanzati come i processi stocastici, il calcolo differenziale stocastico e l'inferenza statistica. Nato dall'esperienza di insegnamento del corso di Probabilità e Statistica Matematica presso la Laurea Triennale in Matematica dell'Università di Bologna, il testo raccoglie materiale per un insegnamento semestrale in corsi di studio scientifici (Matematica, Fisica, Ingegneria, Statistica...), assumendo come prerequisito il calcolo differenziale e integrale di funzioni di più variabili. I quattro capitoli del libro trattano i seguenti argomenti: misure e spazi di probabilità; variabili aleatorie; successioni di variabili aleatorie e teoremi limite; attesa e distribuzione condizionata. Il testo include una raccolta di esercizi risolti.
Teoria della Probabilità: Processi e calcolo stocastico (UNITEXT #156)
by Andrea PascucciQuesto libro offre un approccio moderno alla teoria dei processi stocastici in tempo continuo e del calcolo differenziale stocastico. I contenuti vengono trattati in modo rigoroso, completo e autonomo. Nella prima parte, viene introdotta la teoria dei processi di Markov e delle martingale, con un approfondimento sul moto Browniano e il processo di Poisson. Di seguito, è sviluppata la teoria dell'integrazione stocastica per semi-martingale continue. Una parte sostanziosa è dedicata alle equazioni differenziali stocastiche, ai principali risultati di risolubilità e unicità in senso debole e forte, alle equazioni stocastiche lineari e alla relazione con le equazioni differenziali alle derivate parziali deterministiche. Ogni capitolo è corredato di numerosi esempi. Questo testo nasce dall'esperienza più che ventennale di insegnamento in corsi su processi e calcolo stocastico presso le lauree magistrali in Matematica, in Quantitative finance e i corsi post-laurea in Matematica per le applicazioni e in Finanza matematica dell'Università di Bologna. Il libro raccoglie materiale per almeno due insegnamenti semestrali in corsi di studio scientifici (Matematica, Fisica, Ingegneria, Statistica, Economia...) e intende fornire un solido background a coloro che sono interessati allo sviluppo della teoria e delle applicazioni del calcolo stocastico. Questo testo completa il percorso iniziato col primo volume di Teoria della Probabilità - Variabili aleatorie e distribuzioni, attraverso una selezione di temi classici avanzati di analisi stocastica.
Terahertz Antenna Technology for Space Applications (SpringerBriefs in Electrical and Computer Engineering)
by Balamati Choudhury Aniruddha R. Sonde Rakesh Mohan JhaThis book explores the terahertz antenna technology towards implementation of compact, consistent and cheap terahertz sources, as well as the high sensitivity terahertz detectors. The terahertz EM band provides a transition between the electronic and the photonic regions thus adopting important characteristics from these regimes. These characteristics, along with the progress in semiconductor technology, have enabled researchers to exploit hitherto unexplored domains including satellite communication, bio-medical imaging, and security systems. The advances in new materials and nanostructures such as graphene will be helpful in miniaturization of antenna technology while simultaneously maintaining the desired output levels. Terahertz antenna characterization of bandwidth, impedance, polarization, etc. has not yet been methodically structured and it continues to be a major research challenge. This book addresses these issues besides including the advances of terahertz technology in space applications worldwide, along with possibilities of using this technology in deep space networks.
Terminological Dictionary of Automatic Control, Systems and Robotics (Intelligent Systems, Control and Automation: Science and Engineering #104)
by Rihard Karba Juš Kocijan Tadej Bajd Mojca Žagar Karer Gorazd KarerThis dictionary contains terms from the fields of automatic control, which includes mathematical modelling, simulation of dynamic systems, automation technology with its corresponding elements, and robotics. It also includes signal processing, information technologies and production technologies.The terminological dictionary is primarily aimed at experts and students who deal with control technology and dynamic systems in both technical and non-technical domains. To be able to use the dictionary, at least basic knowledge in this field is required. In the dictionary users will find concise terminological definitions. A concept may be designated by different terms; therefore, cross-references are used. The aim of the dictionary is to collect and unify – at least to an achievable extent – the terminology in the field of automatic control, dynamic systems and robotics.
Termofluidodinamica dei deflussi turbolenti: Fondamenti e modellazione
by Michele CiofaloIl testo fornisce i fondamenti teorici della turbolenza e una panoramica completa dei modelli di turbolenza, dai più semplici ai più avanzati, tra cui la simulazione diretta e la simulazione Large Eddy. Si concentra principalmente sui problemi di modellazione e calcolo e fornisce informazioni sulla teoria dei sistemi dinamici e sulle loro biforcazioni. Esamina anche aspetti della turbolenza che non sono trattati nella maggior parte dei libri esistenti su questo argomento, come la turbolenza in convezione libera e mista, la turbolenza transitoria e la transizione alla turbolenza. Il libro adotta la notazione tensoriale, che è la più appropriata per trattare quantità intrinsecamente tensoriali come le sollecitazioni e i tassi di deformazione, e per coloro che non hanno familiarità con essa viene fornita un'appendice sull'algebra tensoriale e sulla notazione tensoriale.
Ternary Networks
by Ilya Gertsbakh Yoseph Shpungin Radislav VaismanTernary means "based on three". This book deals with reliability investigations of networks whose components subject to failures can be in three states -up, down and middle (mid), contrary to traditionally considered networks having only binary (up/down) components. Extending binary case to ternary allows to consider more realistic and flexible models for communication, flow and supply networks
Ternary Quadratic Forms and Norms
by O. TausskyThis book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.
Territorial Division for Public Action (ISTE Invoiced)
by Antoine Laporte Antonine RibardièreThe reader may be amazed when they are faced with the sheer number of territorial divisions associated with public action, and full of questions. What justifies this diversity? What are the problems that arise from these divisions? Why don't the limits of public action simply follow administrative and political subdivisions? Territorial Division for Public Action focuses on the situation in France, proposing three different approaches. First, we consider the functions that are associated with these territorial divisions: equitable distribution of resources across the territory, administration and the management of public services. However, they are also a tool for maintaining power. Lastly, we consider the effects these divisions have on the implementation of public action and on socio-spatial structures. These divisions reflect political projects, which embody the issues as much as the partition design itself does. The recent reform of territorial regions, alongside a gradual imposition of intercommunal links in France, has given rise to political debates at both local and national levels.
Territorial Inequalities
by Magali Talandier Josselin TallecSpatial planning has embraced the idea of dealing with territorial inequalities by focusing on equipment logic on a national scale, and then economic development on a local scale. Today, this issue is creating new angles of debate with strong political resonances (e.g. Brexit, French gilets jaunes movement). Interpretations of these movements are often quick and binary, such as: the contrast between metropolises and peripheries, between cities and the countryside, between the north and the south or between the east and the west of the European Union. Territorial Inequalities sheds light on the social, political and operational implications of these divergences. The chapters cover the subject at different scales of action and observation (from the neighborhood to the world), but also according to their interdependences. To deal with such a vast and ambitious theme, the preferred approach is that of territorial development in terms of public policy, namely spatial planning.
Tessellations: Mathematics, Art, and Recreation
by Robert FathauerTessellations: Mathematics, Art and Recreation aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. Additionally, it covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Inclusion of special topics like spiral tilings and tessellation metamorphoses allows the reader to explore beautiful and entertaining math and art. The book has a particular focus on ‘Escheresque’ designs, in which the individual tiles are recognizable real-world motifs. These are extremely popular with students and math hobbyists but are typically very challenging to execute. Techniques demonstrated in the book are aimed at making these designs more achievable. Going beyond planar designs, the book contains numerous nets of polyhedra and templates for applying Escheresque designs to them. Activities and worksheets are spread throughout the book, and examples of real-world tessellations are also provided. Key features Introduces the mathematics of tessellations, including symmetry Covers polygonal, aperiodic, and non-Euclidean tilings Contains tutorial content on designing and drawing Escheresque tessellations Highlights numerous examples of tessellations in the real world Activities for individuals or classes Filled with templates to aid in creating Escheresque tessellations Treats special topics like tiling rosettes, fractal tessellations, and decoration of tiles
Tessellations
by Amy TaoPatterns are an important and often beautiful part of our world. One such pattern is a tessellation, or a series of shapes that is arranged in a manner that repeats itself with no gaps. Learn how to make your own tessellation with a fun craft!
Tessellations with Stars and Rosettes: Practical Constructions with Interactive Geometry Software (Compact Textbooks in Mathematics)
by Toni SellarèsThe main objective of the book is to teach how to practically construct periodic tessellations with stars and rosettes using an Interactive Geometry Software (IGS). Stars and rosettes are among the most characteristic geometric ornamental motifs of Islamic art. They are found on walls, ceilings, doors, and windows in both religious and secular buildings. Tessellations are repetitive patterns of shapes that fit together without gaps or overlaps, and they are periodic when they can be constructed by translations of a shape in two different directions. Periodic tessellations with stars and rosettes are complex and symmetrical compositions with rhythmic repetitions of profound beauty. An IGS allows to create and manipulate geometric constructions, producing accurate drawings. The book only assumes knowledge of basic geometric concepts and is self-contained while also providing all the necessary background information. Tessellations with Stars and Rosettes is aimed at students and graduates of mathematics, design, architecture, artists, and art historians, as well as anyone who wants to draw tessellations of stars and rosettes using IGS. It is suitable for a trimester or a semester course, and can also be used for self-study.
TEST Basic EPUB3 with MathML
by Diagram CenterThis EPUB has MathML which only has an alttext fallback within the MathML, There is no altimage fallback.
Test Calculus: Volume 2
by Tom M. ApostolAn introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation -- this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.
Test Configurations, Stabilities and Canonical Kähler Metrics: Complex Geometry by the Energy Method (SpringerBriefs in Mathematics)
by Toshiki MabuchiThe Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed.It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds. Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding’s functional, and plays a crucial role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.
Test-Driven Development with Java: Create higher-quality software by writing tests first with SOLID and hexagonal architecture
by Alan MellorDrive development with automated tests and gain the confidence you need to write high-quality softwareKey FeaturesGet up and running with common design patterns and TDD best practicesLearn to apply the rhythms of TDD – arrange, act, assert and red, green, refactorUnderstand the challenges of implementing TDD in the Java ecosystem and build a planBook DescriptionTest-driven development enables developers to craft well-designed code and prevent defects. It's a simple yet powerful tool that helps you focus on your code design, while automatically checking that your code works correctly. Mastering TDD will enable you to effectively utilize design patterns and become a proficient software architect.The book begins by explaining the basics of good code and bad code, bursting common myths, and why Test-driven development is crucial. You'll then gradually move toward building a sample application using TDD, where you'll apply the two key rhythms -- red, green, refactor and arrange, act, assert. Next, you'll learn how to bring external systems such as databases under control by using dependency inversion and test doubles. As you advance, you'll delve into advanced design techniques such as SOLID patterns, refactoring, and hexagonal architecture. You'll also balance your use of fast, repeatable unit tests against integration tests using the test pyramid as a guide. The concluding chapters will show you how to implement TDD in real-world use cases and scenarios and develop a modern REST microservice backed by a Postgres database in Java 17.By the end of this book, you'll be thinking differently about how you design code for simplicity and how correctness can be baked in as you go.What you will learnDiscover how to write effective test cases in JavaExplore how TDD can be incorporated into crafting softwareFind out how to write reusable and robust code in JavaUncover common myths about TDD and understand its effectivenessUnderstand the accurate rhythm of implementing TDDGet to grips with the process of refactoring and see how it affects the TDD processWho this book is forThis book is for expert Java developers and software architects crafting high-quality software in Java. Test-Driven Development with Java can be picked up by anyone with a strong working experience in Java who is planning to use Test-driven development for their upcoming projects.
TEST EPUB 3 with MathML Cloud
by Diagram CenterThis EPUB 3.0 has a clickable PNG Image of the math which links to the MathML Cloud’s copy of this same equation which could be explored on the web using MathJax and AT. It also has Alt describing the image and commented out MathML