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"A textbook covering the field of cosmology, describing processes in the universe starting from the big bang until the present day. The book is graduate-level and technical, but emphasizes pedagogical exposition, analogies, and worked examples. Data-analysis techniques and statistics are integrated with more theoretical topics to provide the tools necessary for research in the field"-- Provided by publisher.

"Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon-Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry"-- Back cover.

• Outline of the convex integration scheme
• Inductive assumptions
• Building blocks
• Mollification
• Cutoffs
• From q to q + 1: breaking down the main inductive estimates
• Proving the main inductive estimates
• Parameters.

"To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L̂2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates"-- Provided by publisher.
"A new threshold for the existence of weak solutions to incompressible Euler equations. To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L̂2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates"-- Provided by publisher.

• Constituents of the univariate antenna problem
• Functional and Fourier analytic auxiliaries
• Matricial methodologies of resolution
• Compact operator methodologies of resolution
• Example realizations light : univariate differentiation
• Reconstruction and regularization methods
• Regularization methodologies in geotechnology
• Lattice point and special function theoretic auxiliaries
• Sampling over continuously connected pointsets
• Sampling over discretely given pointsets
• Polyharmonic finite bandwidth sampling
• Polyharmonic infinite bandwidth sampling
• Polymetaharmonic finite bandwidth sampling
• Polymetaharmonic infinite bandwidth sampling
• Sampling methodologies in technology
• Recovery as interconnecting whole.

"The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science." -- Provided by publisher.

• Preliminaries on random variables
• Concentration of sums of independent random variables
• Random vectors in high dimensions
• Random matrices
• Concentration without independence
• Quadratic forms, symmetrization and contraction
• Random processes
• Chaining
• Deviations of random matrices and geometric consequences
• Sparse recovery
• Dvoretzky-Milman's theorem.

"High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression."--Publisher's description.

"In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents.In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data.The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions."-- Provided by publisher.

• Matter, Measurement, and Problem Solving
• Atoms and Elements
• Molecules, Compounds, and Chemical Equations
• Chemical Quantities and Aqueous Reactions
• Gases
• Thermochemistry
• The Quantum-Mechanical Model of the Atom
• Periodic Properties of the Elements
• Chemical Bonding I: The Lewis Theory
• Chemical Bonding II: Molecular Shapes, Valence Bond Theory, and Molecular Orbital Theory
• Liquids, Solids, and Intermolecular Forces
• Solids and Modern Material
• Solutions
• Chemical Kinetics
• Chemical Equilibrium
• Acids and Bases
• Aqueous Ionic Equilibrium
• Free Energy and Thermodynamics
• Electrochemistry
• Radioactivity and Nuclear Chemistry
• Organic Chemistry
• Biochemistry
• Chemistry of the Nonmetals
• Metals and Metallurgy
• Transition Metals and Coordination Compounds.

"The Fourth Edition of Niva Tro Chemistry: A Molecular Approach reinforces students development of 21st century skills including data interpretation and analysis, problem solving and quantitative reasoning, applying conceptual understanding to new situations and peer-to-peer collaboration. Nivaldo Tro presents chemistry visually through multi-level images- acroscopic, molecular, and symbolic representations- elping students see the connections between the world they see around them (macroscopic), the atoms and molecules that compose the world (molecular), and the formulas they write down on paper (symbolic). The benefits of Dr. Tro problem-solving approach are reinforced through digital, Interactive Worked Examples that provide students with an office-hour type of environment and expanded coverage on the latest developments in chemistry. New Key Concept Videos explain difficult concepts while new end-of-chapter problems including Group Work questions and Data Interpretation and Analysis questions engage students in applying their understanding of chemistry. The revision has been constructed to easily incorporate material for instructors and students to engage in Before, During, and After class activities."--Publisher's description.