Relative entropy has played a significant role in various fields of mathematics and physics as the quantum version of the Kullback-Leibler divergence in classical theory. Many variations of relative entropy have been introduced so far with applications to quantum information and related subjects. Typical examples are three different classes, called the standard, the maximal, and the measured f-divergences, all of which are defined in terms of (operator) convex functions f on (0,8) and have respective mathematical and information theoretical backgrounds. The a-Rényi relative entropy and its new version called the sandwiched a-Rényi relative entropy have also been useful in recent developments of quantum information.
In the first half of this monograph, the different types of quantum f-divergences and the Rényi-type divergences mentioned above in the general von Neumann algebra setting are presented for study. While quantum information has been developing mostly in the finite-dimensional setting, it is widely believed that von Neumann algebras provide the most suitable framework in studying quantum information and related subjects. Thus, the advance of quantum divergences in von Neumann algebras will be beneficial for further development of quantum information.
Quantum divergences are functions of two states (or more generally, two positive linear functionals) on a quantum system and measure the difference between the two states. They are often utilized to address such problems as state discrimination, error correction, and reversibility of quantum operations. In the second half of the monograph, the reversibility/sufficiency theory for quantum operations (quantum channels) between von Neumann algebras via quantum f-divergences is explained, thus extending and strengthening Petz' previous work.
For the convenience of the reader, an appendix including concise accounts of von Neumann algebras is provided.
The package of Gromov's pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics. The Kuranishi structure was introduced by two of the authors of the present volume in the mid-1990s to apply this machinery on general symplectic manifolds without assuming any specific restrictions. It was further amplified by this book's authors in their monograph Lagrangian Intersection Floer Theory and in many other publications of theirs and others. Answering popular demand, the authors now present the current book, in which they provide a detailed, self-contained explanation of the theory of Kuranishi structures.
Part I discusses the theory on a single space equipped with Kuranishi structure, called a K-space, and its relevant basic package. First, the definition of a K-space and maps to the standard manifold are provided. Definitions are given for fiber products, differential forms, partitions of unity, and the notion of CF-perturbations on the K-space. Then, using CF-perturbations, the authors define the integration on K-space and the push-forward of differential forms, and generalize Stokes' formula and Fubini's theorem in this framework. Also, "virtual fundamental class" is defined, and its cobordism invariance is proved.
Part II discusses the (compatible) system of K-spaces and the process of going from "geometry" to "homological algebra". Thorough explanations of the extension of given perturbations on the boundary to the interior are presented. Also explained is the process of taking the "homotopy limit" needed to handle a system of infinitely many moduli spaces. Having in mind the future application of these chain level constructions beyond those already known, an axiomatic approach is taken by listing the properties of the system of the relevant moduli spaces and then a self-contained account of the construction of the associated algebraic structures is given. This axiomatic approach makes the exposition contained here independent of previously published construction of relevant structures.
This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields.
These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions.
It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.
This book offers a wide-ranging and up-to-date overview of the basic science underlying PET and
its preclinical and clinical applications in modern medicine. In addition, it provides the reader with a sound understanding of the scientific principles and use of PET in routine practice and biomedical imaging research. The opening sections address the fundamental physics, radiation safety, CT scanning dosimetry, and dosimetry of PET radiotracers, chemistry and regulation of PET radiopharmaceuticals, with information on labeling strategies, tracer quality control, and regulation of radiopharmaceutical production in Europe and the United States. PET physics and instrumentation are then discussed, covering the basic principles of PET and PET scanning systems, hybrid PET/CT and PET/MR imaging, system calibration, acceptance testing, and quality control. Subsequent sections focus on image reconstruction, processing, and quantitation in PET and hybrid PET and on imaging artifacts and correction techniques, with particular attention to partial volume correction and motion artifacts. The book closes by examining clinical applications of PET and hybrid PET and their physiological and/or molecular basis in conjunction with technical foundations in the disciplines of oncology, cardiology and neurology, PET in pediatric malignancy and its role in radiotherapy treatment planning. Basic Science of PET Imaging will meet the needs of nuclear medicine practitioners, other radiology specialists, and trainees in these fields.
Environmental chemistry is a fast developing science aimed at deciphering fundamental mechanisms ruling the behaviour of pollutants in ecosystems. Applying this knowledge to current environmental issues leads to the remediation of environmental media, and to new, low energy, low emission, sustainable processes. Chapters review analysis and remediation of pollutants such as greenhouse gases, chiral pharmaceuticals, dyes, chlorinated organics, arsenic, toxic metals and pathogen in air, water, plant and soil. Several highlights include the overlooked impact of air pollutants from buildings for health risk, innovative remediation techniques such as bioreactors for gas treatment, electrochemical cleaning of pharmaceuticals, sequestration on Fe-Mn nodules, phytoremediation and photocatalytical inactivation of microbial pathogens. This book will be a valuable source of information for engineers and students developing novel applied techniques to monitor and clean pollutants in air, wastewater, soils and sediments.
"The understandings which children have of Indigenous identity provide means by which to explore the ways in which Indigenous identity is both projected and constructed in society. These understandings play a powerful part in the ways in which Indigenous peoples are positioned in the mainstream society with which they are connected. The research presented in this edited collection uses children's drawings to illuminate and explore the images children, both mainstream and Indigenous, have of Indigenous peoples. The data generated by this process allows exploration of the ways in which Indigenous identity is understood globally, through a series of locally focussed studies connected by theme and approach. The data serves to illuminate both the space made available by mainstream groups, and aspects of modernity accommodated within the Indigenous sense of self. Our aim within this project has been to analyse and discuss the ways in which children construct identity, both their own and that of others. Children were asked to share their thoughts through drawings which were then used as the basis for conversation with the researchers. In this way the interaction between mainstream modernity and traditional Indigenous identity is made available for discussion and the connection between children's lived experiences of identity and the wider global discussion is both immediately enacted and located within broader international understandings of Indigenous cultures and their place in the world."
Composite structures and products have developed tremendously since the publication of the first edition of this work in 1986. This new edition of the now classic 1986 text has been written to educate the engineering reader in the various aspects of mechanics for using composite materials in the design and analysis of composite structures and products. Areas dealt with include manufacture, micromechanical properties, structural design, joints and bonding and a much needed introduction to composite design philosophy. Each chapter is concluded by numerous problems suitable for home assignments or examination. A solution guide is available on request from the authors.
This book summarizes assessments of the Paris Agreement to provide an excellent introduction to this research field. The AIM/CGE (Asia-Pacific Integrated Modeling /Computable General Equilibrium) model, which is the core of AIM modeling framework, is used for the assessment. The first part focuses on global issues, presenting both short-term (a few decades) and long-term (century scale) assessments in the context of the Agreement's ultimate climate goal. It also discusses policy implementation and climate risk.Part 2 is a collection of assessments of individual Asian countries, providing insights into the national situations and detailed analyses. It includes contributions from Asian countries as well as NIES (National Institute for Environmental Studies, Japan) members. The main conclusion is that many countries require changes to their energy systems change and societal transformation in order to meet emissions targets. Part 3 describes in detail the AIM/CGE model, which is used to evaluate the climate and energy policies by simulating the future economic and energy and environmental situation in the Asia-Pacific region. This section can be used as a standard text on CGE modelling in climate change mitigation.
Dieses Buch ist eine Open-Access-Publikation unter einer CC BY-NC-ND 4.0 Lizenz.In Zusammenarbeit mit den Lehrkräften und SchülerInnen der SchlaU-Schule entstanden,bietet der erste Band aus der SchlaU-Materialreihe "Deutsch als Zweitsprache" hochwertigeund umfangreiche Lehr- und Lernmaterialien. Erfolgreiche Lern- und Schulerfahrungender SchülerInnen stehen dabei im Mittelpunkt. Der vorliegende Band ist konzipiert fürdie Alphabetisierung von neuzugewanderten Jugendlichen und jungen Erwachsenen,insbesondere mit Fluchterfahrung. Mit alltäglichen, lebensweltorientierten Bildern, Wörtern,Themen und Situationen lernen die SchülerInnen die deutsche Schrift und Sprache underhalten so die Chance auf Teilhabe an Bildung und Gesellschaft.Der Band bietet umfangreiche Materialien zur Alphabetisierung in Deutsch als Zweitsprache, abwechslungsreiche Übungen zu allen Fertigkeiten, angemessene Progression zur Förderung schulischer Schreib- und Lesekompetenz, binnendifferenzierende Aufgaben und Förderung der LernerInnenautonomie, relevante und interessante Themen (z.B. Schulalltag und Freizeit), authentische Personen und alltägliche Situationen aus dem schulanalogen Unterricht.Zusätzlich werden auf der Homepage der SchlaU-Werkstatt (schlau-werkstatt.de) weitere Materialien, wie ein Praxisleitfaden für Lehrkräfte, Audiodateien, zusätzliche Materialien, Tests etc. zur Verfügung gestellt. Hier kann die SchlaU-Lernbox Alphabetisierung außerdem als Printprodukt bestellt werden.
This book discusses the important issue of the socioeconomic and environmental impacts of agricultural residue burning, common in agricultural practices in many parts of the world. In particular, it focuses on the pollution caused by rice residue burning using primary survey data from Punjab, India. It discusses emerging solutions to agricultural waste burning that are cost-effective in terms of both money and time. The burning of agricultural residue causes severe pollution in land, water and air and contributes to increased ozone levels and climate change in the long term. However, appropriate assessments have not been undertaken so far to demonstrate the relevant impact of agriculture-based pollution, especially residue burning. This book addresses this gap in the literature. Punjab has been used as a case study as it is the chief granary of India, contributing to 27.2 percent of the Indian national produce of rice and 43.8 percent of wheat. It is presumed that the findings from this state will be useful not only for other agricultural areas in India, but across the world. This book, therefore, sensitizes policy makers, researchers and students about the impacts of air pollution caused by agricultural residue burning---a subject not much dealt in the literature---and provides a way forward.
About this book In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This volume reflects the multi-dimensional nature of the interplay between logic and science. It presents contributions from the world's leading scholars under the following headings: - Proof, Knowledge and Computation - Truth Values beyond Bivalence - Category-Theoretic Structures - Independence, Evaluation Games, and Imperfect Information - Dialogue and Pragmatics. The contents exemplify the liveliness of modern perspectives on the philosophy of logic and mathematics and demonstrate the growth of the discipline. It describes new trends, possible developments for research and new issues not normally raised in the standard agenda of the philosophy of logic and mathematics. It transforms rigid classical partitions into a more open field for improvisation. Written for: Logicians, philosophers, specialists of Cognitive Science and Computer Science, mathematicians, linguists Keywords: Foundations of Mathematics Games Logic Philosophy Semantics
About this textbook Operations Research is the application of scientific models, mathematical and statistical ones, to decision making problems, and PRINCIPLES OF MATHEMATICS IN OPERATIONS RESEARCH is a comprehensive survey of the mathematical concepts and principles of industrial mathematics. Its purpose is to provide students and professionals with an understanding of the fundamental mathematical principles used in Industrial Mathematics/OR in modeling problems and application solutions. Over the past seven years, all the concepts presented in each chapter have undergone the learning scrutiny of the author and his students. The conceptual relationships within the chapter material have been developed in the classroom experience working with the students' level of understanding. The illustrative material throughout the book (i.e., worked-out problems and examples of the mathematical principles) was refined for student comprehension as the manuscript developed through its iterations. The chapter exercises were formulated each year and refined from the previous year's exercises. The book uses a very broad spectrum of industrial mathematical applications, which include applications from deterministic (continuous, discrete, static, dynamic) modeling, combinatorics, regression, optimization, and graph theory. Also it's important to note that solutions of equation systems, geometric and conceptual visualization of abstract mathematical concepts have been included. In addition to the end-of-the-chapter exercises, active web resources have been provided at the end of each chapter as well. In sum, the author has carefully developed a pedagogically strong survey textbook of OR and Industrial Mathematics. Written for: Students, industry practitioners, and academic researchers Keywords: Kandiller Operations Research mathematics principles
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