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Die Rolle der Position der Fragestellung beim Textverstehen von mathematischen Modellierungsaufgaben: Zwei empirische Studien mit Befragungen und Eye-Tracking-Technologie (Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik)
by Valentin BöswaldDas Verstehen der Realsituation in Modellierungsaufgaben ist eine notwendige Bedingung für einen korrekten Lösungsprozess. Eine Determinante des Textverstehens ist das Leseziel. Durch dieses kann die Aufmerksamkeit beim Lesen und Verstehen eines Textes auf lesezielrelevante Informationen gerichtet werden. Das Leseziel sollte sich konkretisieren lassen, indem die zu einer Modellierungsaufgabe zugehörige Fragestellung dem Aufgabentext vorangestellt wird. Frühere Studien zeigen, dass die Spezifizierung des Leseziels über die Voranstellung von Fragestellungen vor den Text positive Effekte auf das Leseverhalten, das Textverstehen und die Effizienz dabei induzieren kann. In zwei Studien mit Lernenden der gymnasialen Oberstufe und aus Erweiterungskursen der Realschule wurde überprüft, inwiefern diese Ergebnisse sich auf Modellierungsaufgaben übertragen lassen. In Studie 1 (N = 192) wurde der Einfluss der Position der Fragestellung auf die Lese- und Bearbeitungsdauer, das Textverstehen und das Mathematisieren bei Modellierungsaufgaben untersucht. In Studie 2 (N = 75) wurde zudem überprüft, inwiefern die Position der Fragestellung das Leseverhalten und die Aufmerksamkeitsallokation auf (ir-)relevante Informationen in den verschiedenen Phasen des Leseprozesses beeinflusst.
Conjugate Duality in Convex Optimization (Lecture Notes in Economics and Mathematical Systems #637)
by Radu Ioan BotThe results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.
Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers (Lecture Notes in Computer Science #9201)
by Francisco Botana Pedro QuaresmaThis book constitutes the thoroughly refereed post-workshop proceedings of the 10th International Workshop on Automated Deduction in Geometry, ADG 2014, held in Coimbra, Portugal, in July 2014. The 11 revised full papers presented in this volume were carefully selected from 20 submissions. The papers show the trend set of current research in automated reasoning in geometry.
Automated Deduction in Geometry: 6th International Workshop, ADG 2006, Pontevedra, Spain, August 31-September 2, 2006, Revised Papers (Lecture Notes in Computer Science #4869)
by Francisco Botana Tomas RecioThe papers in this volume show the lively variety of topics and methods in automated deduction in geometry, and their applicability to different branches of mathematics as well as to other sciences and technologies. The book is made up of the thoroughly refereed post-proceedings of the 6th International Workshop on Automated Deduction in Geometry, ADG 2006, held at Pontevedra, Spain, in 2006. There are a total of 13 revised full papers selected from a number of submissions.
Functional Analysis and Applied Optimization in Banach Spaces: Applications to Non-Convex Variational Models
by Fabio BotelhoThis book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
by Fabio Silva BotelhoThe first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.
Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
by Fabio Silva BotelhoThe first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.
The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering
by Fabio Silva BotelhoThe book includes theoretical and applied results of a generalization of the numerical method of lines. A Ginzburg-Landau type equation comprises the initial application, with detailed explanations about the establishment of the general line expressions. Approximate numerical procedures have been developed for a variety of equation types, including the related algorithms and software. The applications include the Ginzburg-Landau system in superconductivity, applications to the Navier-Stokes system in fluid mechanics and, among others, models in flight mechanics. In its second and final parts, the book develops duality principles and numerical results for other similar and related models. The book is meant for applied mathematicians, physicists and engineers interested in numerical methods and concerning duality theory. It is expected the text will serve as a valuable auxiliary project tool for some important engineering and physics fields of research.
The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering
by Fabio Silva BotelhoThe book includes theoretical and applied results of a generalization of the numerical method of lines. A Ginzburg-Landau type equation comprises the initial application, with detailed explanations about the establishment of the general line expressions. Approximate numerical procedures have been developed for a variety of equation types, including the related algorithms and software. The applications include the Ginzburg-Landau system in superconductivity, applications to the Navier-Stokes system in fluid mechanics and, among others, models in flight mechanics. In its second and final parts, the book develops duality principles and numerical results for other similar and related models. The book is meant for applied mathematicians, physicists and engineers interested in numerical methods and concerning duality theory. It is expected the text will serve as a valuable auxiliary project tool for some important engineering and physics fields of research.
Real Analysis and Applications
by Fabio Silva BotelhoThis textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.
Cloud-native Observability With Opentelemetry: Learn To Gain Visibility Into Systems By Combining Tracing, Metrics, And Logging With Opentelemetry (PDF)
by Alex Boten Charity MajorsLeverage OpenTelemetry's API, libraries, tools and the collector to produce and collect telemetry along with using open-source tools to analyze distributed traces, check metrics and logs, and gain insights into application health Key Features Get to grips with OpenTelemetry, an open-source cloud-native software observability standard Use vendor-neutral tools to instrument applications to produce better telemetry and improve observability Understand how telemetry data can be correlated and interpreted to understand distributed systems Book Description Cloud-Native Observability with OpenTelemetry is a guide to helping you look for answers to questions about your applications. This book teaches you how to produce telemetry from your applications using an open standard to retain control of data. OpenTelemetry provides the tools necessary for you to gain visibility into the performance of your services. It allows you to instrument your application code through vendor-neutral APIs, libraries and tools.
The Sexuality-Reproduction Nexus and the Three Demographic Transitions: An Integrative Framework (SpringerBriefs in Population Studies)
by Nikolai BotevThis monograph outlines an integrative framework that conceptualizes the role of relations of control in human reproduction and long-term population dynamics. It thereby draws on the demographic transition theory, sexuality studies, Foucault’s concept of bio-power and sexuality as key to social control, cognate concepts and theories, and on findings from demography, anthropology, archaeology and other disciplines. The framework is based on the premise that four demographic regimes can be identified over the course of human history. They are defined by the primary locus and modus of control over reproduction. The framework questions some of the basic postulates in population studies, including how demographic transitions are interpreted. As such this book contributes to the debate on the longer-term trends in population dynamics and the relations of power and control in human reproduction.
Advances in Modeling and Simulation: Festschrift for Pierre L'Ecuyer
by Zdravko Botev Alexander Keller Christiane Lemieux Bruno TuffinThis book celebrates the career of Pierre L’Ecuyer on the occasion of his 70th birthday. Pierre has made significant contributions to the fields of simulation, modeling, and operations research over the last 40 years. This book contains 20 chapters written by collaborators and experts in the field who, by sharing their latest results, want to recognize the lasting impact of Pierre’s work in their research area. The breadth of the topics covered reflects the remarkable versatility of Pierre's contributions, from deep theoretical results to practical and industry-ready applications. The Festschrift features article from the domains of Monte Carlo and quasi-Monte Carlo methods, Markov chains, sampling and low discrepancy sequences, simulation, rare events, graphics, finance, machine learning, stochastic processes, and tractability.
Transport Processes at Fluidic Interfaces (Advances in Mathematical Fluid Mechanics)
by Dieter Bothe Arnold ReuskenThere are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface.This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”
Fuzzy Logic: Einführung in Theorie und Anwendungen (Springer-Lehrbuch)
by Hans-Heinrich BotheDer Begriff Fuzzy Logic wird überall dort gebraucht, wo ein Systemverhalten nicht genau beschrieben werden kann. In der Theorie unscharfer Mengen können im Gegensatz zur klassischen Theorie auch fließende Übergänge beschrieben werden. Dieses Buch liefert eine Einführung in die Theorie und aktuelle Anwendungsmöglichkeiten der Fuzzy Logic. Beispiele aus der Elektronik erläutern wesentliche Elemente der Fuzzy Logic.
Algorithms for Computational Biology: Third International Conference, AlCoB 2016, Trujillo, Spain, June 21-22, 2016, Proceedings (Lecture Notes in Computer Science #9702)
by María Botón-Fernández Carlos Martín-Vide Sergio Santander-Jiménez Miguel A. Vega-RodríguezThis book constitutes the proceedings of the Third InternationalConference on Algorithms for Computational Biology, AlCoB 2016, held inTrujillo, Spain, in June 2016.The 13 full papers presented in this volume were carefully reviewed andselected from 23 submissions. They are organized in the following topical sections: biological networks and modelling; biological structure processing; phylogenetics; and sequence analysis and rearrangement. In addition one invited talk is included.
Youth Development in South Africa: Harnessing the Demographic Dividend (Diverse Perspectives on Creating a Fairer Society)
by Botshabelo Maja and Busani NgcaweniThe African continent is colloquially referred to as the youngest in the world. Seizing on a topic underexplored in African research, Youth Development in South Africa: Harnessing the Demographic Dividend confronts the issues, challenges, and opportunities facing South Africa’s youth, resulting in a rich exploration of the South African corpus on youth development. Bringing together a diverse range of topics and research methodologies, contributors focus on the demographic dividend, South Africa’s relatively large population of young people, and the implications of harnessing this for economic growth and development within this country. Analysing model institutional and policy initiatives for youth development, contributors present a unique translation of ideas into practice, as well as attention to solutions. Highlighting challenges such as health pandemics, social media, and climate change, chapters cover questions surrounding youth aspirations, employment, and inclusivity. Showcasing the voices of researchers from across South Africa and the larger African continent, Youth Development in South Africa: Harnessing the Demographic Dividend is a compelling snapshot of thirty years of South Africa’s democratic dispensation and what it has meant for the youth of the country, as well as how its demographic dividend can be harnessed for a fairer society in the future.
Lectures on Algebraic and Differential Topology: Delivered at the 2. ELAM (Lecture Notes in Mathematics #279)
by R. Bott S. Gitler
Differential Forms in Algebraic Topology (Graduate Texts in Mathematics #82)
by Raoul Bott Loring W. TuDeveloped from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Complex Networks XV: Proceedings of the 15th Conference on Complex Networks, CompleNet 2024 (Springer Proceedings in Complexity)
by Federico Botta Mariana Macedo Hugo Barbosa Ronaldo MenezesThe International Conference on Complex Networks (CompleNet) brings together researchers and practitioners from diverse disciplines working on areas related to complex networks. CompleNet has been an active conference since 2009. Over the past two decades, we have witnessed an exponential increase in the number of publications and research centres dedicated to this field of Complex Networks (aka Network Science). From biological systems to computer science, from technical to informational networks, and from economic to social systems, complex networks are becoming pervasive for dozens of applications. It is the interdisciplinary nature of complex networks that CompleNet aims to capture and celebrate. The CompleNet conference is one of the most cherished events by scientists in our field. Maybe it is because of its motivating format, consisting of plenary sessions (no parallel sessions); or perhaps the reason is that it finds the perfect balance between young and senior participation, a balance in the demographics of the presenters, or perhaps it is just the quality of the work presented.
Multibody Dynamics: Computational Methods and Applications (Computational Methods in Applied Sciences #12)
by Carlo L. BottassoMultibody Dynamics is an area of Computational Mechanics which blends together various disciplines such as structural dynamics, multi-physics - chanics, computational mathematics, control theory and computer science, in order to deliver methods and tools for the virtual prototyping of complex mechanical systems. Multibody dynamics plays today a central role in the modeling, analysis, simulation and optimization of mechanical systems in a variety of ?elds and for a wide range of industrial applications. The ECCOMAS Thematic Conference on Multibody Dynamics was ini- ated in Lisbon in 2003, and then continued in Madrid in 2005 with the goal of providing researchers in Multibody Dynamics with appropriate venues for exchanging ideas and results. The third edition of the Conference was held at the Politecnico di Milano, Milano, Italy, from June 25 to June 28, 2007. The Conference saw the participation of over 250 researchers from 32 di?- ent countries, presenting 209 technical papers, and proved to be an excellent forum for discussion and technical exchange on the most recent advances in this rapidly growing ?eld.
Advanced Calculus for Economics and Finance: Theory and Methods (Classroom Companion: Economics)
by Giulio BottazziThis textbook provides a comprehensive introduction to mathematical calculus. Written for advanced undergraduate and graduate students, it teaches the fundamental mathematical concepts, methods and tools required for various areas of economics and the social sciences, such as optimization and measure theory. The reader will be introduced to topological, metric and normed spaces, learning about numerical sequences, series, and differential and integral calculus. These concepts are introduced using the axiomatic approach as a tool for logical reasoning, consistency, and formalization of ideas. The book follows a theorem-proving approach, stressing the limitations of applying the different theorems, while providing thought-provoking counter-examples. Each chapter features exercises that facilitate learning and allow students to apply and test important concepts and tools.
Hidden Harmony—Geometric Fantasies: The Rise of Complex Function Theory (Sources and Studies in the History of Mathematics and Physical Sciences)
by Umberto Bottazzini Jeremy GrayThis book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
Singular Integral Operators and Related Topics: Joint German-Israeli Workshop, Tel Aviv, March 1–10, 1995 (Operator Theory: Advances and Applications #90)
by A. Böttcher I. GohbergThis volume contains a selection of papers on modern operator theory and its applications, arising from a joint workshop on linear one-dimensional singular integral equations. The book is of interest to a wide audience in the mathematical and engineering sciences.