"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

Your Essential Guide to Quantitative Hedge Fund Investing provides a conceptual framework for understanding effective hedge fund investment strategies. The book offers a mathematically rigorous exploration of different topics, framed in an easy to digest set of examples and analogies, including stories from some legendary hedge fund investors. Readers will be guided from the historical to the cutting edge, while building a framework of understanding that encompasses it all. Features Filled with novel examples and analogies from within and beyond the world of finance Suitable for practitioners and graduate-level students with a passion for understanding the complexities that lie behind the raw mechanics of quantitative hedge fund investment A unique insight from an author with experience of both the practical and academic spheres.

This textbook, designed for a single semester course, begins with basic set theory, and moves briskly through fundamental, exponential, and logarithmic functions. Limits and derivatives finish the preparation for economic applications, which are introduced in chapters on univariate functions, matrix algebra, and the constrained and unconstrained optimization of univariate and multivariate functions. The text finishes with chapters on integrals, the mathematics of finance, complex numbers, and differential and difference equations.

Rich in targeted examples and explanations, Mathematical Economics offers the utility of a handbook and the thorough treatment of a text. While the typical economics text is written for two semester applications, this text is focused on the essentials. Instructors and students are given the concepts in conjunction with specific examples and their solutions.

Unlike other books that focus only on selected specific subjects this book provides both a broad and rich cross-section of contemporary approaches to stochastic modeling in finance and economics; it is decision making oriented. The material ranges from common tools to solutions of sophisticated system problems and applications.
In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities.
Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects.
Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study. Selected examples of successful applications in finance, production planning and management of technological processes and electricity generation are presented. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories.
In Part IV, the sections devoted tostochastic calculus cover also more advanced topics such as DDS Theorem or extremal martingale measures, which make it possible to treat more delicate models in Mathematical Finance (complete markets, optimal control, etc.)
Audience: Students and researchers in probability and statistics, econometrics, operations research and various fields of finance, economics, engineering, and insurance.

This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI). Generally speaking, FSI is among the most popular and intriguing problems in applied sciences and includes industrial as well as biological applications. Various fundamental aspects of FSI are addressed from different perspectives, with a focus on biomedical applications. More specifically, the book presents a mathematical analysis of basic questions like the well-posedness of the relevant initial and boundary value problems, as well as the modeling and the numerical simulation of a number of fundamental phenomena related to human biology. These latter research topics include blood flow in arteries and veins, blood coagulation and speech modeling. We believe that the variety of the topics discussed, along with the different approaches used to address and solve the corresponding problems, will help readers to develop a more holistic view of the latest findings on the subject, and of the relevant open questions. For the same reason we expect the book to become a trusted companion for researchers from diverse disciplines, such as mathematics, physics, mathematical biology, bioengineering and medicine."

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.

This book presents details of a text-to-speech synthesis procedure using epoch synchronous overlap add (ESOLA), and provides a solution for development of a text-to-speech system using minimum data resources compared to existing solutions. It also examines most natural speech signals including random perturbation in synthesis. The book is intended for students, researchers and industrial practitioners in the field of text-to-speech synthesis.

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars' GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming."

This thesis examines the Z box contribution to the weak charge of the proton. Here, by combining recent parity-violating electron-deuteron scattering data with our current understanding of parton distribution functions, the author shows that one can limit this model dependence. The resulting construction is a robust model of the and Z structure functions that can also be used to study a variety of low-energy phenomena. Two such cases are discussed in this work, namely, the nucleon's electromagnetic polarizabilities and quark-hadron duality. By using phenomenological information to constrain the input structure functions, this important but previously poorly understood radiative correction is determined at the kinematics of the parity-violating experiment, QWEAK, to a degree of precision more than twice that of the previous best estimate. A detailed investigation into available parametrizations of the electromagnetic and interference cross-sections indicates that earlier analyses suffered from the inability to correctly quantify their model dependence.

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers. Members of the editorial board of this series consists of following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), A. Yamazaki (Hitotsubashi Univ.) - Editors: R. Anderson (U.C.Berkeley), C. Castaing (Univ. Montpellier II), F. H. Clarke (Univ. Lyon I), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Fukuoka Univ.), J. -M. Grandmont (CREST-CNRS), N. Hirano (Yokohama National Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Hitotsubashi Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), K. Kamiya (Univ. Tokyo), K. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), T. Maruyama (Keio Univ.), H. Matano (Univ. Tokyo), K. Nishimura (Kyoto Univ.), M. K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ).

Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.

The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Gottingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. The Theory of the Top: Volume III. Perturbations: Astronomical and Geophysical Applications is the third installment in a series of four self-contained English translations that provide insights into kinetic theory and kinematics."

The aim of this book is to extend the understanding of the fundamental role of generalizations of Lie and related non-commutative and non-associative structures in Mathematics and Physics. This is a thematic volume devoted to the interplay between several rapidly exp- ding research ?elds in contemporary Mathematics and Physics, such as generali- tions of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, n- commutative geometry and applications in Physics and beyond. The speci?c ?elds covered by this volume include: * Applications of Lie, non-associative and non-commutative associative structures to generalizations of classical and quantum mechanics and non-linear integrable systems, operadic and group theoretical methods; * Generalizations and quasi-deformations of Lie algebras such as color and super Lie algebras, quasi-Lie algebras, Hom-Lie algebras, in?nite-dimensional Lie algebras of vector ?elds associated to Riemann surfaces, quasi-Lie algebras of Witt type and their central extensions and deformations important for in- grable systems, for conformal ? eld theory and for string theory; * Non-commutative deformation theory, moduli spaces and interplay with n- commutativegeometry,algebraicgeometryandcommutativealgebra,q-deformed differential calculi and extensions of homological methods and structures; * Crossed product algebras and actions of groups and semi-groups, graded rings and algebras, quantum algebras, twisted generalizations of coalgebras and Hopf algebra structures such as Hom-coalgebras, Hom-Hopf algebras, and super Hopf algebras and their applications to bosonisation, parastatistics, parabosonic and parafermionic algebras, orthoalgebas and root systems in quantum mechanics;

This textbook is a comprehensive introduction to computational mathematics and scientific computing suitable for undergraduate and postgraduate courses. It presents both practical and theoretical aspects of the subject, as well as advantages and pitfalls of classical numerical methods alongside with computer code and experiments in Python. Each chapter closes with modern applications in physics, engineering, and computer science. No previous experience in Python is required Simplified computer code for fast-paced learning and transferable skills development Includes practical problems ideal for project assignments and distance learning Presents both intuitive and rigorous faces of modern scientific computing Provides an introduction to neural networks and machine learning

This book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems. Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Besides, the electromagnetic parameters of complex medium such as the permittivity and conductivity are retrieved by a cascaded framework in Chapter 4. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 5. Finally, in Chapter 6, a series of the latest advanced frameworks and the corresponding physics applications are introduced. As deep learning techniques are experiencing vigorous development in computational physics, more people desire related reading materials. This book is intended for graduate students, professional practitioners, and researchers who are interested in DL for computational physics.

Eschewing a more theoretical approach, Portfolio Optimization shows how the mathematical tools of linear algebra and optimization can quickly and clearly formulate important ideas on the subject. This practical book extends the concepts of the Markowitz "budget constraint only" model to a linearly constrained model.

Only requiring elementary linear algebra, the text begins with the necessary and sufficient conditions for optimal quadratic minimization that is subject to linear equality constraints. It then develops the key properties of the efficient frontier, extends the results to problems with a risk-free asset, and presents Sharpe ratios and implied risk-free rates. After focusing on quadratic programming, the author discusses a constrained portfolio optimization problem and uses an algorithm to determine the entire (constrained) efficient frontier, its corner portfolios, the piecewise linear expected returns, and the piecewise quadratic variances. The final chapter illustrates infinitely many implied risk returns for certain market portfolios.

Drawing on the author 's experiences in the academic world and as a consultant to many financial institutions, this text provides a hands-on foundation in portfolio optimization. Although the author clearly describes how to implement each technique by hand, he includes several MATLAB programs designed to implement the methods and offers these programs on the accompanying CD-ROM.

Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics.

This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." We would like to thank the scientific organizers: John Goutsias (Johns Hopkins University), Ronald P.S. Mahler (Lockheed Martin), and Hung T. Nguyen (New Mexico State University) for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the Army Research Office (ARO), the Office ofNaval Research (0NR), and the Eagan, MinnesotaEngineering Center ofLockheed Martin Tactical Defense Systems, whose financial support made the summer program possible. Avner Friedman Robert Gulliver v PREFACE "Later generations will regard set theory as a disease from which one has recovered. " - Henri Poincare Random set theory was independently conceived by D.G. Kendall and G. Matheron in connection with stochastic geometry. It was however G.

1 Grundlagen.- 1.1 Allgemeine Grundlagen.- 1.1.1 Ziele und Aufgaben.- 1.1.2 Methoden.- 1.1.3 Geschichte und Einordnung.- 1.1.3.1 Geschichte der Bauwerksvermessung.- 1.1.3.2 Geschichte des Vermessungswesens.- 1.1.3.3 Geschichte der Architekturphotogrammetrie.- 1.1.4 Rechtliche Grundlagen und Rahmenbedingungen.- 1.1.4.1 Internationale Vereinbarungen und Organisationen.- 1.1.4.2 Baugesetzbuch, Denkmalpflegegesetze, Vermessungsgesetze.- 1.2 Messgroessen und Masseinheiten.- 1.2.1 Strecken.- 1.2.2 Winkel.- 1.3 Bezugssysteme und Koordinaten.- 1.3.1 Bezugsflachen.- 1.3.2 Koordinaten.- 1.3.3 Koordinatensysteme.- 1.3.3.1 Polarkoordinaten.- 1.3.3.2 Lokale Koordinatensysteme.- 1.3.3.3 Regionale Koordinatensysteme.- 1.3.3.4 Globale Koordinatensysteme.- 1.3.3.5 Geographische Koordinaten.- 1.3.3.6 Geozentrische Koordinaten.- 1.3.4 Koordinatentransformationen.- 1.3.4.1 Translation (2D).- 1.3.4.2 Massstabslose Transformation (2D).- 1.3.4.3 AEhnlichkeitstransformation (2D).- 1.3.4.4 Vereinfachte AEhnlichkeitstransformation mit 2 Passpunkten (2D).- 1.3.4.5 Affintransformation (2D).- 1.3.4.6 Weitere ebene Koordinatentransformationen.- 1.3.4.7 Raumliche Koordinatentransformation (3D).- 1.3.5 Festpunktfelder.- 1.3.5.1 Netz trigonometrischer Punkte zur Lagedefinition.- 1.3.5.2 Hoehennetz.- 1.3.6 Vermessungsnetze fur die Bauwerksvermessung.- 1.3.6.1 Netzdesign.- 1.3.6.2 Vermarkung.- 1.3.6.3 Design und Fertigung von Punktsignalisierungen.- 1.3.6.4 Auswahl naturlicher Passpunkte.- 1.3.6.5 Schnurnetz zur temporaren Vermarkung.- 1.3.6.6 Punktubersichten und Einmessskizzen.- 1.4 Fehlerlehre und Statistik.- 1.4.1 Fehlerarten und ihre Wirkung.- 1.4.1.1 Zufallige Fehler.- 1.4.1.2 Systematische Fehler.- 1.4.1.3 Grobe Fehler.- 1.4.2 Fehlerfortpflanzung und Ausgleichsrechnung.- 1.4.3 Rechenscharfe und Rundung.- 1.4.4 Toleranzen im Bauwesen.- 2 Dokumentation von Gebauden und Ensembles.- 2.1 Amtliche Dokumentation.- 2.1.1 Katasterunterlagen.- 2.1.2 Amtliche Karten.- 2.1.3 Lageplan.- 2.1.4 Geoinformationssysteme (GIS).- 2.2 Plane.- 2.2.1 Grundriss.- 2.2.2 Schnitt.- 2.2.3 Ansicht.- 2.2.4 Detaildarstellungen.- 2.2.5 Massstabe und Detaillierungsgrad.- 2.2.6 Materialien und Aufbewahrung.- 2.3 3D-Beschreibungen.- 2.3.1 CAD-Modell.- 2.3.2 Animation.- 2.3.3 Virtual Reality.- 2.3.4 Augmented Reality.- 2.4 Fotografie.- 2.4.1 Analoge Fotografie.- 2.4.1.1 Fotografisches Material.- 2.4.1.2 Kameras.- 2.4.1.3 Objektive.- 2.4.1.4 Licht.- 2.4.1.5 Belichtung.- 2.4.1.6 Archivierungen von Fotomaterialien.- 2.4.2 Digitale Bilder.- 2.4.2.1 Flachensensoren.- 2.4.2.2 Zeilenkameras.- 2.4.2.3 Spezialkameras.- 2.4.3 Scannen analoger Fotovorlagen.- 2.4.4 Digitale Bildverarbeitung.- 2.5 Textliche und hybride Beschreibungen.- 2.5.1 Raumbuch.- 2.5.2 Hypertext Dokumente.- 2.5.3 Informationssystem.- 2.6 Archivierung digitaler Daten.- 2.6.1 Datentrager.- 2.6.2 Datenformate.- 2.6.2.1 Texte.- 2.6.2.2 Datenbanken.- 2.6.2.3 Vektordaten.- 2.6.2.4 Rasterdaten.- 2.6.2.5 Hypermedia.- 3 Erfassung von Messelementen.- 3.1 Messprinzipien.- 3.1.1 Vom-Grossen-ins-Kleine.- 3.1.2 UEberbestimmungen.- 3.1.3 Vermeidung von systematischen Fehlern.- 3.2 Gerate und Instrumente.- 3.2.1 Bauteile, Kleingerate und Zubehoer.- 3.2.1.1 Lote und Libellen.- 3.2.1.2 Fernrohr.- 3.2.1.3 Stative.- 3.2.1.4 Fluchtstab.- 3.2.1.5 Nivellierlatten und Kleingerat.- 3.2.1.6 Aufstellen eines Instruments.- 3.2.2 Winkelmessung.- 3.2.2.1 Bestimmung rechter Winkel.- 3.2.2.2 Theodolit.- 3.2.2.3 Satzmessung.- 3.2.2.4 Berechnung von Richtungswinkeln aus Koordinaten.- 3.2.3 Streckenmessung.- 3.2.3.1 Streckenmessung mit dem Messband.- 3.2.3.2 Optische Streckenmessung.- 3.2.3.3 Elektro-optische Entfernungsmessung (EDM).- 3.2.4 Hoehenmessung.- 3.2.4.1 Einfache Werkzeuge.- 3.2.4.2 Nivellement.- 3.2.4.3 Rotationslaser.- 3.3 Beschaffung einer Vermessungsausrustung.- 4 Messverfahren.- 4.1 Schrittskizze.- 4.2 Handaufmass.- 4.3 Punktbestimmung ohne Theodolit.- 4.3.1 Bogenschlag.- 4.3.2 Einbindeverfahren.- 4.3.3 Orthogonalverfahren.- 4.3.4

Handbook of Alternative Data in Finance, Volume I motivates and challenges the reader to explore and apply Alternative Data in finance. The book provides a robust and in-depth overview of Alternative Data, including its definition, characteristics, difference from conventional data, categories of Alternative Data, Alternative Data providers, and more. The book also offers a rigorous and detailed exploration of process, application and delivery that should be practically useful to researchers and practitioners alike. Features Includes cutting edge applications in machine learning, fintech, and more Suitable for professional quantitative analysts, and as a resource for postgraduates and researchers in financial mathematics Features chapters from many leading researchers and practitioners.

Control theory methods in economics have historically developed over three phases. The first involved basically the feedback control rules in a deterministic framework which were applied in macrodynamic models for analyzing stabilization policies. The second phase raised the issues of various types of inconsistencies in deterministic optimal control models due to changing information and other aspects of stochasticity. Rational expectations models have been extensively used in this plan to resolve some of the inconsistency problems. The third phase has recently focused on the various aspects of adaptive control. where stochasticity and information adaptivity are introduced in diverse ways e.g . risk adjustment and risk sensitivity of optimal control, recursive updating rules via Kalman filtering and weighted recursive least squares and variable structure control methods in nonlinear framework. Problems of efficient econometric estimation of optimal control models have now acquired significant importance. This monograph provides an integrated view of control theory methods, synthesizing the three phases from feedback control to stochastic control and from stochastic control to adaptive control. Aspects of econometric estimation are strongly emphasized here, since these are very important in empirical applications in economics."

The two-volume work is intended to function as a textbook for graduate students in economics as well as a reference work for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate student in economics, these two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. Volume One covers basic set theory, sequences and series, continuous and semi-continuous functions, an introduction to general linear spaces, basic convexity theory, and applications to economics. Volume Two introduces general topology, the theory of correspondences on and into topological spaces, Banach spaces, topological vector spaces, and maximum, fixed-point, and selection theorems for such spaces.

This volume contains the proceedings of the IUTAM Symposium on Model Order Reduction of Coupled System, held in Stuttgart, Germany, May 22-25, 2018. For the understanding and development of complex technical systems, such as the human body or mechatronic systems, an integrated, multiphysics and multidisciplinary view is essential. Many problems can be solved within one physical domain. For the simulation and optimization of the combined system, the different domains are connected with each other. Very often, the combination is only possible by using reduced order models such that the large-scale dynamical system is approximated with a system of much smaller dimension where the most dominant features of the large-scale system are retained as much as possible. The field of model order reduction (MOR) is interdisciplinary. Researchers from Engineering, Mathematics and Computer Science identify, explore and compare the potentials, challenges and limitations of recent and new advances.