Mathematical Foundations of Infinite-Dimensional Statistical Models (1版)
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Quality Infrastructure Of Graphene And Related Two-dimensional Materials: Metrology
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【簡介】
Materials metrology, a burgeoning branch of the field, is a subject of intense scrutiny by both researchers and stakeholders. The focal points of their attention are twofold: understanding the objectives of material metrology research and determining effective methods for utilizing its findings. Researchers and stakeholders delve into the intricacies of ensuring traceability of complex units from equipment and maintaining consistency in measurement results across various methods. The application of materials metrology extends to calibrating equipment and/or measurement methods, as well as utilizing critical data for production assessments. Graphene's emergence sparked widespread interest across various fields. The rapid progress of graphene and related two-dimensional materials in both research and industrial applications necessitates robust support from metrology, standards, and conformity assessment, collectively known as national quality infrastructures (NQI). This book, using graphene and related two-dimensional materials as exemplars, explores fundamental concepts and terminologies of metrology and materials metrology, elucidates the technological framework of metrology and standards, and elaborates on various metrological techniques for the structural characterization of graphene and related materials, including Raman spectroscopy, X-ray diffraction, atomic force microscopy, and electron microscopy. Additionally, the book presents techniques for quality evaluation, such as X-ray photoelectron spectroscopy, inductively coupled plasma mass spectrometry, and Fourier transform infrared spectrometry. By leveraging established standard measurement instruments, reference materials, measurement methods, and interlaboratory comparisons, this book endeavors to attain accurate and consistent measurement results. Globally equivalent results can guarantee the quality of graphene products, fostering standardization, mass production, and sustainable advancement within the graphene industry
【目錄】
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Stochastic Models for Prices Dynamics in Energy and Commodity Markets: An Infinite-Dimensional Perspective
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This monograph presents a theory for random field models in time and space, viewed as stochastic processes with values in a Hilbert space, to model the stochastic dynamics of forward and futures prices in energy, power, and commodity markets.
In this book, the well-known Heath–Jarrow–Morton approach from interest rate theory is adopted and extended into an infinite-dimensional framework, allowing for flexible modeling of price stochasticity across time and along the term structure curve. Various models are introduced based on stochastic partial differential equations with infinite-dimensional Lévy processes as noise drivers, emphasizing random fields described by low-dimensional parametric covariance functions instead of classical high-dimensional factor models. The Filipović space, a separable Hilbert space of Sobolev type, is found to be a convenient state space for the dynamics of forward and futures term structures. The monograph provides a classification of important operators in this space, covering covariance operators and the stochastic modeling of volatility term structures, including the Samuelson effect. Fourier methods are employed to price many derivatives of interest in energy, power, and commodity markets, and sensitivity 'delta' expressions can be derived. Additionally, the monograph covers forward curve smoothing, the connection between forwards with fixed delivery and delivery period, as well as the classical theory of forward and futures pricing.
This monograph will appeal to researchers and graduate students interested in mathematical finance and stochastic analysis applied in the challenging markets of energy, power, and commodities. Practitioners seeking sophisticated yet flexible and analytically tractable risk models will also find it valuable.
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Seeing Four-Dimensional Space and Beyond Using Knots!
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According to string theory, our universe exists in a 10- or 11-dimensional space. However, the idea the space beyond 3 dimensions seems hard to grasp for beginners. This book presents a way to understand four-dimensional space and beyond: with knots! Beginners can see high dimensional space although they have not seen it.
With visual illustrations, we present the manipulation of figures in high dimensional space, examples of which are high dimensional knots and n-spheres embedded in the (n+2)-sphere, and generalize results on relations between local moves and knot invariants into high dimensional space.
Local moves on knots, circles embedded in the 3-space, are very important to research in knot theory. It is well known that crossing changes are connected with the Alexander polynomial, the Jones polynomial, HOMFLYPT polynomial, Khovanov homology, Floer homology, Khovanov homotopy type, etc. We show several results on relations between local moves on high dimensional knots and their invariants.
The following related topics are also introduced: projections of knots, knot products, slice knots and slice links, an open question: can the Jones polynomial be defined for links in all 3-manifolds? and Khovanov-Lipshitz-Sarkar stable homotopy type. Slice knots exist in the 3-space but are much related to the 4-dimensional space. The slice problem is connected with many exciting topics: Khovanov homology, Khovanv–Lipshits–Sarkar stable homotopy type, gauge theory, Floer homology, etc. Among them, the Khovanov–Lipshitz–Sarkar stable homotopy type is one of the exciting new areas; it is defined for links in the 3-sphere, but it is a high dimensional CW complex in general.
Much of the book will be accessible to freshmen and sophomores with some basic knowledge of topology.
Sample Chapter(s)
Introduction
Chapter 1: Local Moves on Knots: For Beginners
Chapter 2: Four-Dimensional Space ℝ4
Contents:
About the Author
Acknowledgment
Introduction
Local Moves On Knots: For Beginners
Four-Dimensional Space ℝ4
Local Moves in Higher-Dimensional Space: For Beginners
Knotted-Objects in 4-Space and Beyond
Local Moves on High-Dimensional Knots and Related Invariants
The Alexander and Jones Polynomials of One-Dimensional Links in ℝ3
Local Moves and Knot Polynomials in Higher Dimensions
Important Topics in Knot Theory
References
Index
Readership: Freshmen and sophomores of science and people with similar mathematical background; general public interested in science, sci-fiction, and high-dimensional space; novice researchers in knot theory.
原價:
2538
售價:
2411
現省:
127元
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Psychopathology and Life: A Dimensional Approach (4版)
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Overview
Present a contemporary, science-based view of psychopathology that emphasizes the individual first with Kearney’s ABNORMAL PSYCHOLOGY AND LIFE: A DIMENSIONAL APPROACH, 4E. This updated, concise edition features clinical cases and real first-person narratives that help students view abnormal behavior along a continuum. In keeping with this widely accepted dimensional view, students learn to place the behavior of an individual at the forefront of clinical definition, assessment and treatment. This edition also presents the features and epidemiologies, risk factors and prevention, assessment and treatment, and long-term prognosis and associated stigma of mental disorders. Special sections emphasize personal relevance for students and encourage them to become intelligent consumers of mental health information. MindTap digital resources are also available to reinforce understanding and guide students in applying key principles.
原價:
2200
售價:
2090
現省:
110元
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