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Modelling our Changing World (Palgrave Texts in Econometrics)
by Jennifer L. Castle David F. HendryThis open access book focuses on the concepts, tools and techniques needed to successfully model ever-changing time-series data. It emphasizes the need for general models to account for the complexities of the modern world and how these can be applied to a range of issues facing Earth, from modelling volcanic eruptions, carbon dioxide emissions and global temperatures, to modelling unemployment rates, wage inflation and population growth.Except where otherwise noted, this book is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0.
Models for Tropical Climate Dynamics: Waves, Clouds, and Precipitation (Mathematics of Planet Earth #3)
by Boualem KhouiderThis book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.
Models, Mindsets, Meta: Essays Dedicated to Bernhard Steffen on the Occasion of His 60th Birthday (Lecture Notes in Computer Science #11200)
by Tiziana Margaria Susanne Graf Kim G. LarsenThis Festschrift volume is published in honor of Bernhard Steffen, Professor at the Technical University of Dortmund, on the occasion of his 60th birthday. His vision as well as his theoretical and practical work span the development and implementation of novel, specific algorithms, and the establishment of cross-community relationships with the effect to obtain simpler, yet more powerful solutions. He initiated many new lines of research through seminal papers that pioneered various fields, starting with the Concurrency Workbench, a model checking toolbox that significantly influenced the research and development of mode based high assurance systems worldwide. The contributions in this volume reflect the breadth and impact of his work. The introductory paper by the volume editors, the 23 full papers and two personal statements relate to Bernhard’s research and life. This volume, the talks and the entire B-Day at ISoLA 2018 are a tribute to the first 30 years of Bernhard’s passion, impact and vision for many facets of computer science in general and for formal methods in particular. Impact and vision include the many roles that formal methods-supported software development should play in education, in industry and in society.
Models of Neurons and Perceptrons: Selected Problems and Challenges (Studies In Computational Intelligence #770)
by Andrzej BieleckiThis book describes models of the neuron and multilayer neural structures, with a particular focus on mathematical models. It also discusses electronic circuits used as models of the neuron and the synapse, and analyses the relations between the circuits and mathematical models in detail. The first part describes the biological foundations and provides a comprehensive overview of the artificial neural networks. The second part then presents mathematical foundations, reviewing elementary topics, as well as lesser-known problems such as topological conjugacy of dynamical systems and the shadowing property. The final two parts describe the models of the neuron, and the mathematical analysis of the properties of artificial multilayer neural networks. Combining biological, mathematical and electronic approaches, this multidisciplinary book it useful for the mathematicians interested in artificial neural networks and models of the neuron, for computer scientists interested in formal foundations of artificial neural networks, and for the biologists interested in mathematical and electronic models of neural structures and processes.
A Model–Theoretic Approach to Proof Theory (Trends in Logic #51)
by Henryk KotlarskiThis book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory.In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial independence results. Next, the volume examines a variety of proofs of Gödel's incompleteness theorems. The presented proofs differ strongly in nature. They show various aspects of incompleteness phenomena. In additon, coverage introduces some classical methods like the arithmetized completeness theorem, satisfaction predicates or partial satisfaction classes. It also applies them in many contexts. The fourth chapter defines the method of indicators for obtaining independence results. It shows what amount of transfinite induction we have in fragments of Peano arithmetic. Then, it uses combinatorics of large sets of the first chapter to show independence results. The last chapter considers nonstandard satisfaction classes. It presents some of the classical theorems related to them. In particular, it covers the results by S. Smith on definability in the language with a satisfaction class and on models without a satisfaction class. Overall, the book's content lies on the border between combinatorics, proof theory, and model theory of arithmetic. It offers readers a distinctive approach towards independence results by model-theoretic methods.
Modern Computational Finance: AAD and Parallel Simulations
by Leif Andersen Antoine SavineArguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware.AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance.Danske Bank's wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank's systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives software.This volume is a complete, self-contained learning reference for AAD, and its application in finance. AAD is explained in deep detail throughout chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation and acceleration with expression templates.The book comes with professional source code in C++, including an efficient, up to date implementation of AAD and a generic parallel simulation library. Modern C++, high performance parallel programming and interfacing C++ with Excel are also covered. The book builds the code step-by-step, while the code illustrates the concepts and notions developed in the book.
Modern Mathematics and Mechanics: Fundamentals, Problems and Challenges (Understanding Complex Systems)
by Victor A. Sadovnichiy Michael Z. ZgurovskyIn this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.
Modern Methods in Operator Theory and Harmonic Analysis: OTHA 2018, Rostov-on-Don, Russia, April 22-27, Selected, Revised and Extended Contributions (Springer Proceedings in Mathematics & Statistics #291)
by Alexey Karapetyants Vladislav Kravchenko Elijah LiflyandThis proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018.The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant.Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.
Modern Multidimensional Calculus (Dover Books on Mathematics)
by Marshall Evans MunroeA second-year calculus text, this volume is devoted primarily to topics in multidimensional analysis. Concepts and methods are emphasized, and rigorous proofs are sometimes replaced by relevant discussion and explanation. Because of the author's conviction that the differential provides a most elegant and useful tool, especially in a multidimensional setting, the notion of the differential is used extensively and matrix methods are stressed in the study of linear transformations.The first three chapters offer introductory material on functions and variables, differentials, and vectors in the plane. Succeeding chapters examine topics in linear algebra, partial derivatives, and applications as well as topics in vector differential calculus. The final chapters explore multiple integrals in addition to line and surface integrals. Exercises appear throughout the text, and answers are provided, making the book ideal for self-study.
Modern Music-Inspired Optimization Algorithms for Electric Power Systems: Modeling, Analysis and Practice (Power Systems)
by Mohammad Kiani-Moghaddam Mojtaba Shivaie Philip D. WeinsierIn today’s world, with an increase in the breadth and scope of real-world engineering optimization problems as well as with the advent of big data, improving the performance and efficiency of algorithms for solving such problems has become an indispensable need for specialists and researchers. In contrast to conventional books in the field that employ traditional single-stage computational, single-dimensional, and single-homogeneous optimization algorithms, this book addresses multiple newfound architectures for meta-heuristic music-inspired optimization algorithms. These proposed algorithms, with multi-stage computational, multi-dimensional, and multi-inhomogeneous structures, bring about a new direction in the architecture of meta-heuristic algorithms for solving complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data. The architectures of these new algorithms may also be appropriate for finding an optimal solution or a Pareto-optimal solution set with higher accuracy and speed in comparison to other optimization algorithms, when feasible regions of the solution space and/or dimensions of the optimization problem increase. This book, unlike conventional books on power systems problems that only consider simple and impractical models, deals with complicated, techno-economic, real-world, large-scale models of power systems operation and planning. Innovative applicable ideas in these models make this book a precious resource for specialists and researchers with a background in power systems operation and planning.Provides an understanding of the optimization problems and algorithms, particularly meta-heuristic optimization algorithms, found in fields such as engineering, economics, management, and operations research;Enhances existing architectures and develops innovative architectures for meta-heuristic music-inspired optimization algorithms in order to deal with complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data;Addresses innovative multi-level, techno-economic, real-world, large-scale, computational-logical frameworks for power systems operation and planning, and illustrates practical training on implementation of the frameworks using the meta-heuristic music-inspired optimization algorithms.
Modern Statistical Methods for Spatial and Multivariate Data (STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health)
by Norou DiawaraThis contributed volume features invited papers on current models and statistical methods for spatial and multivariate data. With a focus on recent advances in statistics, topics include spatio-temporal aspects, classification techniques, the multivariate outcomes with zero and doubly-inflated data, discrete choice modelling, copula distributions, and feasible algorithmic solutions. Special emphasis is placed on applications such as the use of spatial and spatio-temporal models for rainfall in South Carolina and the multivariate sparse areal mixed model for the Census dataset for the state of Iowa. Articles use simulated and aggregated data examples to show the flexibility and wide applications of proposed techniques.Carefully peer-reviewed and pedagogically presented for a broad readership, this volume is suitable for graduate and postdoctoral students interested in interdisciplinary research. Researchers in applied statistics and sciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration.
Moderne Datenanalyse mit R: Daten einlesen, aufbereiten, visualisieren, modellieren und kommunizieren (FOM-Edition)
by Sebastian SauerDie Kaufempfehlung, die Ihnen ein Webstore ausspricht, die Einschätzung, welcher Kunde kreditwürdig ist, oder die Analyse der Werttreiber von Immobilien – alle diese Beispiele aus dem heutigen Leben sind Ergebnis moderner Verfahren der Datenanalyse. Dieses Buch führt in solche statistische Verfahren anhand der Programmiersprache R ein. Ziel ist es, Leser mit der Art und Weise vertraut zu machen, wie führende Organisationen und Praktiker angewandte Statistik heute einsetzen. Weil sich mit der Digitalisierung auch die statistischen Verfahren verändert haben, vermittelt der Autor neben klassischen Analysemethoden wie Regression auch moderne Methoden wie Textmining und Random-Forest-Modelle. Dabei sind die Inhalte des Buchs durchgehend so aufbereitet, dass sie auch für Leser ohne umfangreiche mathematische Vorkenntnisse verständlich sind. Anhand von Fallbeispielen und Übungen werden die Leser durch alle Phasen der Datenanalyse geführt: Sie lernen, wie Daten eingelesen, aufbereitet, visualisiert, modelliert und kommuniziert werden können. Dabei wird vor allem die Aufbereitung, Umformung und Prüfung der Daten ausführlicher als in anderen Publikationen behandelt, da dieser Teil in der Praxis oft einen wesentlichen Teil des Aufwands ausmacht. Aber auch die Visualisierung bekommt viel Raum, denn gute Diagramme ermöglichen Einblicke, die Zahlen und Worte verbergen.Mit seinem praxisorientierten Ansatz will das Buch dazu befähigen,alle grundlegenden Schritte eines Datenanalyseprojekts durchzuführen,Daten kompetent in R zu bearbeiten,simulationsbasierte Inferenzstatistik anzuwenden und kritisch zu hinterfragen,klassische und moderne Vorhersagemethoden anzuwenden undbetriebswirtschaftliche Fragestellungen mittels datengetriebener Vorhersagemodelle zu beantworten.Sowohl Anwender ohne statistisches Grundlagenwissen als auch Nutzer mit Vorerfahrung lesen dieses Buch mit Gewinn. In verständlicher Sprache und anhand von anschaulichen Beispielen zeigt der Autor, wie moderne Datenanalyse heute funktioniert.
Moduli of K-stable Varieties (Springer INdAM Series #31)
by Giulio Codogni Ruadhaí Dervan Filippo VivianiThis volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, Italy in 2017. The content focuses on the existence problem for canonical Kähler metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys on this problem, notably in the case of Fano varieties, and original contributions addressing this and related problems. The papers in the latter group develop the theory of K-stability; explore canonical metrics in the Kähler and almost-Kähler settings; offer new insights into the geometric significance of K-stability; and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models. Reflecting the advances made in the area in recent years, the survey articles provide an essential overview of many of the most important findings. The book is intended for all advanced graduate students and researchers who want to learn about recent developments in the theory of moduli space, K-stability and Kähler-Einstein metrics.
Molecular Logic and Computational Synthetic Biology: First International Symposium, MLCSB 2018, Santiago, Chile, December 17–18, 2018, Revised Selected Papers (Lecture Notes in Computer Science #11415)
by Madalena Chaves Manuel A. MartinsThis book collects the revised selected proceedings of the First International Symposium in Molecular Logic and Computational Synthetic Biology ( MLCSB), held in Chile, Santiago, in December 2018. The volume contains 7 full revised papers along with 2 surveys from 19 submissions presented at the symposium. One of the goals of the MLCSB 2018 was to explore the potential of molecular logic frameworks to study the emerging behavioural patterns in biological networks, combining discrete, continuous and stochastic features, and resorting both to specific or general-purpose analysis and verification techniques.
Molekulare Populationsgenetik: Theoretische Konzepte und empirische Evidenz
by Wolfgang Stephan Anja C. HörgerDas Buch behandelt die genetische Vielfalt von Populationen von Organismen. Es erläutert, wie genetische Vielfalt gemessen wird und wie aus diesen Daten die Mechanismen untersucht werden können, die die Variabilität auf der Genomebene und damit die Mikroevolution einer Population beeinflussen. Ziel dieses Buches ist es, das Wirken der natürlichen Selektion im Genom zu verstehen und vom Einfluss neutraler Evolutionskräfte (wie genetischer Drift, Mutation und Rekombination) unterscheiden zu lernen. Dazu werden die grundlegenden theoretischen Konzepte der Populationsgenetik eingeführt und anhand von zahlreichen Beispielen aus allen Organismengruppen (Menschen, Tieren, Pflanzen und Mikroorganismen) veranschaulicht. Um das Verständnis der theoretischen Ableitungen von Hypothesen und der darauf basierenden Datenanalysen zu überprüfen und weiter zu vertiefen, schließt jedes Kapitel mit Übungsaufgaben und Lösungen ab.
Moments of Linear Positive Operators and Approximation (SpringerBriefs in Mathematics)
by Vijay Gupta Michael Th. RassiasThis book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.
Monographs in Tang Official Historiography: Perspectives from the Technical Treatises of the History of Sui (Sui shu) (Why the Sciences of the Ancient World Matter #3)
by Daniel Patrick Morgan Damien ChaussendeThis book examines the role of medieval authors in writing the history of ancient science. It features essays that explore the content, structure, and ideas behind technical writings on medieval Chinese state history. In particular, it looks at the Ten Treatises of the current History of Sui, which provide insights into the writing on the history of such fields as astronomy, astrology, omenology, economics, law, geography, metrology, and library science. Three treatises are known to have been written by Li Chunfeng, one of the most important mathematicians, astronomers, and astrologers in Chinese history.The book not only opens a new window on the figure of Li Chunfeng by exploring what his writings as a historian of science tell us about him as a scientist and vice versa, it also discusses how and on what basis the individual treatises were written.The essays address such themes as (1) the recycling of sources and the question of reliability and objectivity in premodern history-writing; (2) the tug of war between conservatism and innovation; (3) the imposition of the author’s voice, worldview, and personal and professional history in writing a history of a field of technical expertise in a state history; (4) the degree to which modern historians are compelled to speak to their own milieu and ideological beliefs.
Monte Carlo Simulation in Statistical Physics: An Introduction (Graduate Texts in Physics #Vol. 80)
by Dieter W. Heermann Kurt BinderThe sixth edition of this highly successful textbook provides a detailed introduction to Monte Carlo simulation in statistical physics, which deals with the computer simulation of many-body systems in condensed matter physics and related fields of physics and beyond (traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, these powerful simulation methods calculate probability distributions, making it possible to estimate the thermodynamic properties of various systems. The book describes the theoretical background of these methods, enabling newcomers to perform such simulations and to analyse their results. It features a modular structure, with two chapters providing a basic pedagogic introduction plus exercises suitable for university courses; the remaining chapters cover major recent developments in the field.This edition has been updated with two new chapters dealing with recently developed powerful special algorithms and with finite size scaling tools for the study of interfacial phenomena, which are important for nanoscience. Previous editions have been highly praised and widely used by both students and advanced researchers.
The Montessori Method: My First Book of Numbers
by The Montessori MethodLearn about numbers the Montessori way with this line of board books following the world-leading educational approach, THE MONTESSORI METHOD!Montessori education values the development of the whole child-physically, socially, emotionally, cognitively. These books tap into the Montessori Method at home, allowing children to discover and engage with concepts in a holistic way that promotes a drive for knowledge and self-motivation. In NUMBERS, children are invited to imagine, touch, mimic, and learn about numbers and how they function in the world around us. Infused with humor and math concepts that both engage and challenge children, this book is sure to inspire a generation of mathematicians!Learn more with THE MONTESSORI METHOD: FEELINGS!
Mordell–Weil Lattices (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics #70)
by Matthias Schütt Tetsuji ShiodaThis book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface.Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.
Morphodynamics in Aesthetics: Essays on the Singularity of the Work of Art (Lecture Notes in Morphogenesis)
by Stefania CaliandroThis book deals with the complexity of art by focusing on the singularity of the work of art. Gathering a selection of writings in art theory and semiotics, it explores the question of apprehending art from its perceptual aspects to aesthetic comprehension and understanding. Theoretical enquiries focus in particular on the dynamics of the perception of forms, the semiotic value of colour, the aesthetic phenomenon of empathy, the function of vision in relation to other senses and its faculty to lead, in a substantial way, to the embodiment of sense. These theoretical points are constantly observed with reference to the analysis of works of art, especially from the beginning of the modern era, when a renovated psychophysical approach oriented the evolution of contemporary aesthetics. Research into art theories sheds light on how differentials in topologic positions, dimensions, relationships and tones contribute to the arising of forms and colours in perception, and affect the perceiver. The essays presented address in different ways the emergence of sense, by conceiving it as deeply anchored to the dynamics of perception, in addition to the cognitive disposition and knowledge, regardless of whether or not the subject (artist or beholder) is aware of these processes. Through in-depth analyses identifying to what extent the aesthetic moment builds on perceptual and semiotic processes, works of art are revealed to be singularities, reflecting the correlation with morphodynamics in the sciences.
Motivational Profiles in TIMSS Mathematics: Exploring Student Clusters Across Countries and Time (IEA Research for Education #7)
by Gavin T. Brown Michalis P. Michaelides Hanna Eklöf Elena C. PapanastasiouThis open access book presents a person-centered exploration of student profiles, using variables related to motivation to do school mathematics derived from the IEA’s Trends in International Mathematics and Science Study (TIMSS) data. Statistical cluster analysis is used to identify groups of students with similar motivational profiles, across grades and over time, for multiple participating countries.While motivational variables systematically relate to school outcomes, linear relationships can obscure the diverse makeup of student subgroups, each with varying combinations of motivation, emotions, and attitudes. In this book, a person-centered analysis of distinct and meaningful motivational profiles and their differences on sociodemographic variables and mathematics performance broadens understanding about the role that motivation characteristics play in learning and achievement in mathematics. Exploiting the richness of IEA’s TIMSS data from many countries, extracted clusters reveal consistent, as well as certain nuanced patterns that are systematically linked to sociodemographic and achievement measures. Student clusters with inconsistent motivational profiles were found in all countries; mathematics self-confidence then emerged as the variable more closely associated with average achievement. The findings demonstrate that teachers, researchers, and policymakers need to take into account differential student profiles, prioritizing techniques that target skill and competence in mathematics, in educational efforts to develop student motivation.
Moving Boundary PDE Analysis: Biomedical Applications in R
by William SchiesserMathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.
m−Polar Fuzzy Graphs: Theory, Methods & Applications (Studies in Fuzziness and Soft Computing #371)
by Muhammad AkramThis book provides readers with an introduction to m-polar fuzzy graphs and m-polar fuzzy hypergraphs, covering both theories and applications. A special emphasis is given to m-polar fuzzy graphs at the aim of filling a gap in the literature, namely the absence of a mathematical approach to analyze multi-index, multipolar, and multi-attribute data. The book describes metrics and labeling in m-polar graphs, m-polar fuzzy matroids. It also discusses in detail important applications in decision-making problems and imaging processing. The book is expected to stimulate the curiosity of mathematics, computer scientists, and social scientists alike, and to provide both students and researchers with the necessary knowledge to understand and apply m−polar fuzzy graph theory.
Mulholland's The Nurse, The Math, The Meds: Drug Calculations Using Dimensional Analysis
by Susan TurnerMulholland’s The Nurse, The Math, The Meds, 4th Edition helps you overcome any math anxiety you may have by clearly explaining how to use dimensional analysis to minimize drug calculation errors. It shows how to analyze and set up problems, estimate a reasonable answer, and then evaluate the answer for accuracy. But first, a review of basic math ensures that you remember essential math skills. Updated by nursing educator Susan Turner, this edition includes plenty of practice exercises to help you understand and master each aspect of dimensional analysis.