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The Becher Wetlands - A Ramsar Site : Evolution of Wetland Habitats and Vegetation Associations on a Holocene Coastal Plain, South-Western Australia
This book is a landmark study of the Holocene evolution and functioning of a suite of seasonal wetland basins in the temperate coastal zone of Western Australia. In 2001, a series of discrete small scale wetlands on the Becher cuspate foreland in Western Australia, were nominated as a Ramsar site because of their scientific values. These values pertained to their setting, their method of formation and deepening, their history of infilling, their complex hydrological mechanisms, and their dynamic hydrochemical and vegetation responses. The wetlands were the subjects of intense curiosity, observation, measurement, and experiment, for over 10 years. The results of this interest and passion are presented here in order to demonstrate the considerable importance of what lay beneath the ordinary surface.Amongst the new ideas presented in the book are the importance of stratigraphy in understanding wetland development, the significance of physiographic setting in determining wetland development, and the unravelling of several different evolutionary pathways in wetlands of the same basic origin.
The Baobabs : Pachycauls of Africa, Madagascar and Australia
This is the only comprehensive account of all eight species in the genus Adansonia. It describes the historical background from the late Roman period to the present. It covers the extraordinary variety of economic uses of baobabs, famous trees, folk traditions and mythology, art associations, life cycle, natural history, cultivation, conservation, distribution and ecology, and phytogeography. There are also appendices on vernacular names, gazetteer, economics, nutrition and forest mensuration. This book fills a gap in the botanical literature. It deals with a genus that has fascinated and intrigued scientists and lay persons for centuries.
Symmetry in modeling and analysis of dynamic systems
Real-world systems exhibit complex behavior, therefore novel mathematical approaches or modifications of classical ones have to be employed to precisely predict, monitor, and control complicated chaotic and stochastic processes. One of the most basic concepts that has to be taken into account while conducting research in all natural sciences is symmetry, and it is usually used to refer to an object that is invariant under some transformations including translation, reflection, rotation or scaling.The following Special Issue is dedicated to investigations of the concept of dynamical symmetry in the modelling and analysis of dynamic features occurring in various branches of science like physics, chemistry, biology, and engineering, with special emphasis on research based on the mathematical models of nonlinear partial and ordinary differential equations.
Symmetries and Overdetermined Systems of Partial Differential Equations
Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogenous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week summer program considered the symmetries preserving various natural geometric structures. Often these structures are themselves derived from partial differential equations whilst their symmetries turn out to be contrained by overdetermined systems. This leads to further topics including separation of variables, conserved quantities, superintegrability, parabolic geometry, represantation theory, the Bernstein-Gelfand-Gelfand complex, finite element schemes, exterior differential systems and moving frames.
Sturm-Liouville Theory and its Applications
Undergraduate textbooks on Fourier series which follow a pointwise approach to convergence miss the rich geometric content which comes with treating the subject within the inner product space L2. This book, developed from a course taught to senior undergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The basic results of this theory, namely the orthogonality and completeness of its eigenfunctions, are established in Chapter 2; the remaining chapters present examples and applications. The last two chapters, on Fourier and Laplace transformations, while not part of the Sturm-Liouville theory, extend the Fourier series method for representing functions to integral representations.
Structured Population Models in Biology and Epidemiology
Consists of six chapters written by leading researchers in mathematical biology. These chapters present recent and important developments in the study of structured population models in biology and epidemiology. Topics include population models structured by age, size, and spatial position; size-structured models for metapopulations, macroparasitc diseases, and prion proliferation; models for transmission of microparasites between host populations living on non-coincident spatial domains; spatiotemporal patterns of disease spread; method of aggregation of variables in population dynamics; and biofilm models. It is suitable as a textbook for a mathematical biology course or a summer school at the advanced undergraduate and graduate level. It can also serve as a reference book for researchers looking for either interesting and specific problems to work on or useful techniques and discussions of some particular problems.
Stochastic Ordinary and Stochastic Partial Differential Equations : Transition from Microscopic to Macroscopic Equations
This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation. A detailed analysis of the SODEs and (quasi-linear) SPDEs is presented. Semi-linear (parabolic) SPDEs are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids.
Statistical quantitative methods in finance : From theory to quantitative portfolio management
Explores the theoretical foundations of statistical models, from ordinary least squares (OLS) to the generalized method of moments (GMM) used in econometrics. additionally, the book delves into non-linear methods and bayesian approaches, which are becoming increasingly popular among practitioners thanks to advancements in computational resources. the book also offers valuable insights into quantitative portfolio management, showcasing how traditional data science tools can be enhanced with machine learning models. these enhancements are illustrated through real-world examples from finance and econometrics, accompanied by python code.
Standard Monomial Theory : Invariant Theoretic Approach
This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory on the one hand and standard monomial theory for Schubert varieties in certain special flag varieties - the ordinary, orthogonal, and symplectic Grassmannians - on the other. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection. The book also treats, in the last chapter, some other applications of standard monomial theory, e.g., to the study of certain naturally occurring affine algebraic varieties that, like determinantal varieties, can be realized as open parts of Schubert varieties.
Stability of Nonautonomous Differential Equations
Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Stability of Dynamical Systems : Continuous, Discontinuous, and Discrete Systems
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics.
Spectral Methods : Fundamentals in Single Domains
Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions.
Spectral Methods : Evolution to Complex Geometries and Applications to Fluid Dynamics
Spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of their 1988 book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since then.The recent companion book Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions.
Social Networks and the Semantic Web
Social Networks and the Semantic Web combines the concepts and the methods of two fields of investigation, which together have the power to aid in the analysis of the social Web and the design of a new class of applications that combine human intelligence with machine processing. Social Network Analysis and the emerging Semantic Web are also the fields that stand to gain most from the new Web in achieving their full potential. On the one hand, the social Web delivers social network data at an extraordinary scale, with a dynamics and precision that has been outside of reach for more traditional methods of observing social structure and behavior. In realizing this potential, the technology of the Semantic Web provides the key in aggregating information across heterogeneous sources. The Semantic Web itself benefits by incorporating user-generated metadata and other clues left behind by users.
Scientific Computing with MATLAB and Octave
This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of ordinary and partial differential equations.
Scaling of Differential Equations
Serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales.
Revision Sinus Surgery
In this extraordinary guide, the world’s most prominent rhinologists illustrate their experiences in the diagnosis and management of recurrent sinus disease and skull base lesions. Chapters are lavishly illustrated and cover: preoperative planning / medical management / relevant surgical techniques/ how to avoid complications / management of complications. This invaluable resource is designed to prevent complications and improve the outcomes of revision sinus surgeries. Both practicing and in-training otolaryngologists can use this comprehensive volume as an all-in-one source for the evaluation and management of recurrent sinus disease and skull base pathology.
Representation and Control of Infinite-Dimensional Systems
The book is structured into five parts. Part I reviews basic optimal control and game theory of finite dimensional systems, which serves as an introduction to the book. Part II deals with time evolution of some generic controlled infinite dimensional systems and contains a fairly complete account of semigroup theory. It incorporates interpolation theory and exhibits the role of semigroup theory in delay differential and partial differential equations. Part III studies the generic qualitative properties of controlled systems. Parts IV and V examine the optimal control of systems when performance is measured via a quadratic cost. Boundary control of parabolic and hyperbolic systems and exact controllability are also covered.
Relativity and the Dimensionality of the World
The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension.
Real World Justice : Grounds, Principles, Human Rights, and Social Institutions
The importance of this global justice approach reaches well beyond philosophy. It enables ordinary citizens to understand their options and responsibility for global institutional factors, and it challenges social scientists to address the causes of poverty and hunger that act across borders.The present volume addresses four main topics regarding global justice: The normative grounds for claims regarding the global institutional order, the substantive normative principles for a legitimate global order, the roles of legal human rights standards, and some institutional arrangements that may make the present world order less unjust.
