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Measure of Noncompactness, Fixed Point Theorems, and Applications
The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem.Key Highlights: Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem Discusses best proximity point results using measure of noncompactness and its applications Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.
Measuring and Modeling Health Care Costs (National Bureau of Economic Research Studies in Income and Wealth #76)
Health care costs represent a nearly 18% of U.S. gross domestic product and 20% of government spending. While there is detailed information on where these health care dollars are spent, there is much less evidence on how this spending affects health. The research in Measuring and Modeling Health Care Costs seeks to connect our knowledge of expenditures with what we are able to measure of results, probing questions of methodology, changes in the pharmaceutical industry, and the shifting landscape of physician practice. The research in this volume investigates, for example, obesity’s effect on health care spending, the effect of generic pharmaceutical releases on the market, and the disparity between disease-based and population-based spending measures. This vast and varied volume applies a range of economic tools to the analysis of health care and health outcomes. Practical and descriptive, this new volume in the Studies in Income and Wealth series is full of insights relevant to health policy students and specialists alike.
Measuring Economic Sustainability and Progress (National Bureau of Economic Research Studies in Income and Wealth #72)
Since the Great Depression, researchers and statisticians have recognized the need for more extensive methods for measuring economic growth and sustainability. The recent recession renewed commitments to closing long-standing gaps in economic measurement, including those related to sustainability and well-being. The latest in the NBER’s influential Studies in Income and Wealth series, which has played a key role in the development of national account statistics in the United States and other nations, this volume explores collaborative solutions between academics, policy researchers, and official statisticians to some of today’s most important economic measurement challenges. Contributors to this volume extend past research on the integration and extension of national accounts to establish an even more comprehensive understanding of the distribution of economic growth and its impact on well-being, including health, human capital, and the environment. The research contributions assess, among other topics, specific conceptual and empirical proposals for extending national accounts.
Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table
Since 1969, the international chemistry community has only held conferences on the topic of the Periodic Table three times, and the 2012 conference in Cusco, Peru was the first in almost a decade. The conference was highly interdisciplinary, featuring papers on geology, physics, mathematical and theoretical chemistry, the history and philosophy of chemistry, and chemical education, from the most reputable Periodic Table scholars across the world. Eric Scerri and Guillermo Restrepo have collected fifteen of the strongest papers presented at this conference, from the most notable Periodic Table scholars. The collected volume will contain pieces on chemistry, philosophy of science, applied mathematics, and science education.
Mesoscale Modeling of the Atmosphere (Meteorological Monographs)
This book provides an overview of several components of mesoscale modeling: boundary conditions, subgrid-scale parameterization, moisture processes, and radiation. Also included are mesoscale model comparisons using data from the U.S. Army's Project WIND (Winds in Non-uniform Domains).
Methods and Applications of Autonomous Experimentation (Chapman & Hall/CRC Computational Science)
Autonomous Experimentation is poised to revolutionize scientific experiments at advanced experimental facilities. Whereas previously, human experimenters were burdened with the laborious task of overseeing each measurement, recent advances in mathematics, machine learning and algorithms have alleviated this burden by enabling automated and intelligent decision-making, minimizing the need for human interference. Illustrating theoretical foundations and incorporating practitioners’ first-hand experiences, this book is a practical guide to successful Autonomous Experimentation. Despite the field’s growing potential, there exists numerous myths and misconceptions surrounding Autonomous Experimentation. Combining insights from theorists, machine-learning engineers and applied scientists, this book aims to lay the foundation for future research and widespread adoption within the scientific community. This book is particularly useful for members of the scientific community looking to improve their research methods but also contains additional insights for students and industry professionals interested in the future of the field.
Micro-Approaches to Demographic Research (Routledge Library Editions: Demography #3)
Originally published in 1988, this collection of essays was the first attempt by population scientists to incorporate some of the methods and materials of anthropologists into their work. The essays bridge the gap in the conceptualisation and organisation of field research by 2 sets of social scientists – demographers and social anthropologists – who share an interest in the explanation of particular patterns of population composition and change.
Microstructure and Phase Transition (The IMA Volumes in Mathematics and its Applications #54)
This IMA Volume in Mathematics and its Applications MICROSTRUCTURE AND PHASE TRANSITION is based on the proceedings of a workshop which was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." We thank R. Fosdick, M.E. Gurtin, W.-M. Ni and L.A. Peletier for organizing the year-long program and, especially, D. Kinderlehrer, R. James, M. Luskin and J. Ericksen for organizing the meeting and editing these proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, and the National Science Foun dation. A vner Friedman Willard Miller. Jr. PREFACE Much of our traditional knowledge of materials and processes is achievf'd by observa tion and analysis of small departures from equilibrium. Many materials, especially modern alloys, ceramics, and their composites, experience not only larger but more dramatic changes, such as the occurrence of phase transitions and t.he creation of defect structures, when viewed at the microscopic scale. How is this observed, how can it be interpreted, and how does it influence macroscopic behavior? These are the principle concerns of this volume, which constitutes the proceedings of an IMA workshop dedicated to these issues.
Modal View of Atmospheric Variability: Applications of Normal-Mode Function Decomposition in Weather and Climate Research (Mathematics of Planet Earth #8)
This book reviews the theory and applications of the normal-mode functions in numerical weather prediction and weather and climate dynamics. The normal-mode functions, the eigensolutions of the linearized primitive equations describing the evolution of atmospheric winds and mass variables, have been used for a long time. They have played an important role in the development of data assimilation schemes and the initialization of numerical weather prediction models. Chapters also present how the normal modes can be applied to many theoretical and numerical problems in the atmospheric sciences, such as equatorial wave dynamics, baroclinic instability, energy transfers, and predictability across scales.
Modeling Excitable Tissue: The EMI Framework (Simula SpringerBriefs on Computing #7)
This open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.
Modeling, Simulation and Optimization of Fluid Dynamic Applications (Lecture Notes in Computational Science and Engineering #148)
This book describes recent collaborations combining the expertise of applied mathematicians, engineers and geophysicists within a research training group (RTG) on "Modeling, Simulation and Optimization of Fluid Dynamic Applications”, funded by the Deutsche Forschungsgemeinschaft (DFG). The focus is on mathematical modeling, adaptive discretization, approximation strategies and shape optimization with PDEs. The balanced research program is based on the guiding principle that mathematics drives applications and is inspired by applications. With this leitmotif the RTG advances research in Modeling, Simulation and Optimization by an interdisciplinary approach, i.e., to stimulate fundamental education and research by highly complex applications and at the simultaneously transfer tailored mathematical methods to applied sciences. The reported research involves nine projects and addresses challenging fluid dynamic problems inspired by applied sciences, such as climate research & meteorology, energy, aerospace & marine engineering, or medicine. More fundamental research concerning analysis, approximation and numerics is also covered.The material represents a successful attempt to exchange research paradigms between different disciplines and thus displays a modern approach to basic research into scientifically and societally relevant contemporary problems.
Modeling, Stochastic Control, Optimization, and Applications (The IMA Volumes in Mathematics and its Applications #164)
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
Modern Developments in Multivariate Approximation: 5th International Conference, Witten-Bommerholz (Germany), September 2002 (International Series of Numerical Mathematics #145)
This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods. The main topics are:- applications of multivariate approximation in finance- approximation and stable reconstruction of images, data reduction- multivariate splines for Lagrange interpolation and quasi-interpolation- radial basis functions- spherical point sets- refinable function vectors and non-stationary subdivision- applications of adaptive wavelet methods- blending functions and cubature formulae- singularities of harmonic functionsThe book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics.
Multicultural America [4 volumes]: An Encyclopedia of the Newest Americans [4 volumes]
This encyclopedia contains 50 thorough profiles of the most numerically significant immigrant groups now making their homes in the United States, telling the story of our newest immigrants and introducing them to their fellow Americans.One of the main reasons the United States has evolved so quickly and radically in the last 100 years is the large number of ethnically diverse immigrants that have become part of its population. People from every area of the world have come to America in an effort to realize their dreams of more opportunity and better lives, either for themselves or for their children.This book provides a fascinating picture of the lives of immigrants from 50 countries who have contributed substantially to the diversity of the United States, exploring all aspects of the immigrants' lives in the old world as well as the new. Each essay explains why these people have come to the United States, how they have adjusted to and integrated into American society, and what portends for their future. Accounts of the experiences of the second generation and the effects of relations between the United States and the sending country round out these unusually rich and demographically detailed portraits.
Multilingualism in Mathematics Education in Africa (Multilingualisms and Diversities in Education)
This book brings together the first book collection of African research in mathematics education in multilingual societies andchronicles current research in different linguistic contexts across the African continent, (including Algeria, Namibia, Malawi, Morocco, Rwanda, South Africa) on issues of multilingualism in mathematics education, but more importantly, it foregrounds pertinent issues for future research. With many of the authors building on earlier path-breaking African research, the book is a unique contribution of careful thinking through how linguistic diversity and multilingualism manifest in ways that differ from one geopolitical context to another. This volume is an important contribution to the growing recognition of multilingualism as the global 'linguistic dispensation' in mathematics education. It is an invitation to how we might (as an international community where more and more multilingualism is the norm rather than an exception) pay more attention to the multilingual agency and capabilities of both students and teachers in order to better harness the epistemic potential of multiple languages in contexts of language diversity in mathematics education.
Multiplex and Multilevel Networks
The science of networks represented a substantial change in the way we see natural and technological phenomena. Now we have a better understanding that networks are, in most cases, networks of networks or multi-layered networks. This book provides a summary of the research done during one of the largest and most multidisciplinary projects in network science and complex systems (Multiplex). The science of complex networks originated from the empirical evidence that most of the structures of systems such as the internet, sets of protein interactions, and collaboration between people, share (at least qualitatively) common structural properties. This book examines how properties of networks that interact with other networks can change dramatically. The authors show that, dependent on the properties of links that interconnect two or more networks, we may derive different conclusions about the function and the possible vulnerabilities of the overall system of networks. This book presents a series of novel theoretical results together with their applications, providing a comprehensive overview of the field.
Multivariable Operator Theory: The Jörg Eschmeier Memorial Volume
Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Nanoelectronic Coupled Problems Solutions (Mathematics in Industry #29)
Designs in nanoelectronics often lead to challenging simulation problems and include strong feedback couplings. Industry demands provisions for variability in order to guarantee quality and yield. It also requires the incorporation of higher abstraction levels to allow for system simulation in order to shorten the design cycles, while at the same time preserving accuracy. The methods developed here promote a methodology for circuit-and-system-level modelling and simulation based on best practice rules, which are used to deal with coupled electromagnetic field-circuit-heat problems, as well as coupled electro-thermal-stress problems that emerge in nanoelectronic designs. This book covers: (1) advanced monolithic/multirate/co-simulation techniques, which are combined with envelope/wavelet approaches to create efficient and robust simulation techniques for strongly coupled systems that exploit the different dynamics of sub-systems within multiphysics problems, and which allow designers to predict reliability and ageing; (2) new generalized techniques in Uncertainty Quantification (UQ) for coupled problems to include a variability capability such that robust design and optimization, worst case analysis, and yield estimation with tiny failure probabilities are possible (including large deviations like 6-sigma); (3) enhanced sparse, parametric Model Order Reduction techniques with a posteriori error estimation for coupled problems and for UQ to reduce the complexity of the sub-systems while ensuring that the operational and coupling parameters can still be varied and that the reduced models offer higher abstraction levels that can be efficiently simulated. All the new algorithms produced were implemented, transferred and tested by the EDA vendor MAGWEL. Validation was conducted on industrial designs provided by end-users from the semiconductor industry, who shared their feedback, contributed to the measurements, and supplied both material data and process data. In closing, a thorough comparison to measurements on real devices was made in order to demonstrate the algorithms’ industrial applicability.
Network Routing: Algorithms, Protocols, and Architectures (ISSN)
Network routing can be broadly categorized into Internet routing, PSTN routing, and telecommunication transport network routing. This book systematically considers these routing paradigms, as well as their interoperability. The authors discuss how algorithms, protocols, analysis, and operational deployment impact these approaches. A unique feature of the book is consideration of both macro-state and micro-state in routing; that is, how routing is accomplished at the level of networks and how routers or switches are designed to enable efficient routing.In reading this book, one will learn about 1) the evolution of network routing, 2) the role of IP and E.164 addressing in routing, 3) the impact on router and switching architectures and their design, 4) deployment of network routing protocols, 5) the role of traffic engineering in routing, and 6) lessons learned from implementation and operational experience. This book explores the strengths and weaknesses that should be considered during deployment of future routing schemes as well as actual implementation of these schemes. It allows the reader to understand how different routing strategies work and are employed and the connection between them. This is accomplished in part by the authors' use of numerous real-world examples to bring the material alive.Bridges the gap between theory and practice in network routing, including the fine points of implementation and operational experienceRouting in a multitude of technologies discussed in practical detail, including, IP/MPLS, PSTN, and optical networkingRouting protocols such as OSPF, IS-IS, BGP presented in detailA detailed coverage of various router and switch architecturesA comprehensive discussion about algorithms on IP-lookup and packet classificationAccessible to a wide audience due to its vendor-neutral approach
New Approaches to the Economics of Plant Health (Wageningen UR Frontis Series #20)
This book presents the outcomes of a workshop around the emerging area of the economics of plant health. The workshop was organized in Wageningen in July 2005 under the auspices of Frontis – Wageningen International Nucleus for Strategic Expertise. Plant health nowadays plays an increasing role in national and international policy making. This explains the interest of the Netherlands Ministry of Agriculture, Nature and Food Quality in this workshop. The increasing importance of plant health in international policy making also follows from the recent establishment of a scientific panel on plant health by the European Food Safety Authority. This panel has to advise the EU on policy issues in the area of plant health. Plant health issues have numerous economic dimensions. Measures to control quarantine diseases and invasive species are usually costly, whereas the potential benefits, e. g. , avoided losses, are often difficult to quantify. Quantifying the costs and benefits requires close collaboration between economists and epidemiologists. New GIS tools can play an important role in visualizing and modelling the combined economic and epidemiological consequences of control measures. Quarantine organisms and invasive species also frequently have impacts that go beyond agriculture. Impacts on landscapes and the environment call for the application of new approaches to measuring the economic impacts on society. This book presents a number of new approaches to economic modelling of plant health; it is primarily intended for policy makers and scientists working in the area of plant health.
New Essays on Belnap-Dunn Logic (Synthese Library #418)
This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic (FDE). It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn.Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions to computer science, such as knowledge representation and information processing.This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general.
New Trends in the Physics and Mechanics of Biological Systems: Lecture Notes of the Les Houches Summer School: Volume 92, July 2009 (Lecture Notes of the Les Houches Summer School)
In July 2009, many experts in the mathematical modelling of biological sciences gathered in Les Houches for a 4-week summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic is very wide, we focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modelling of particular systems in the biology of the cell, plants, microbes, and in physiology. These lecture notes are organised (as was the school) around five different main topics all connected by the common theme of continuum modelling for biological systems: Bio-fluidics, Bio-gels, Bio-mechanics, Bio-membranes, and Morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction to the readers who want to understand the basic problematic in modelling biological systems from a mechanics perspective.
Nonlinear and Convex Analysis: Proceedings in Honor of Ky Fan
This book contains expanded versions of the talks given at the conference held in honour of professor Ky Fan in California in 1985, as well as papers on nonlinear and convex analysis as contributions to Ky Fan. It also includes a list of publications by Ky Fan.
Nonlinear Diffusion Equations and Their Equilibrium States II: Proceedings of a Microprogram held August 25–September 12, 1986 (Mathematical Sciences Research Institute Publications #13)
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Novel Mathematics Inspired by Industrial Challenges (Mathematics in Industry #38)
This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.