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Dynamics of Liquid Solidification
by Zygmunt LipnickiThis monograph comprehensively describes phenomena of heat flow during phase change as well as the dynamics of liquid solidification, i. e. the development of a solidified layer. The book provides the reader with basic knowledge for practical designs, as well as with equations which describe processes of energy transformation. The target audience primarily comprises researchers and experts in the field of heat flow, but the book may also be beneficial for both practicing engineers and graduate students.
Dynamics of Markets: The New Financial Economics (2nd edition)
by Joseph L. MccauleyThis second edition presents the advances made in finance market analysis since 2005. The book provides a careful introduction to stochastic methods along with approximate ensembles for a single, historic time series. The new edition explains the history leading up to the biggest economic disaster of the 21st century. Empirical evidence for finance market instability under deregulation is given, together with a history of the explosion of the US Dollar worldwide. A model shows how bounds set by a central bank stabilized FX in the gold standard era, illustrating the effect of regulations. The book presents economic and finance theory thoroughly and critically, including rational expectations, cointegration and arch/garch methods, and replaces several of those misconceptions by empirically based ideas. This book will be of interest to finance theorists, traders, economists, physicists and engineers, and leads the reader to the frontier of research in time series analysis.
Dynamics of Mechanical Systems with Non-Ideal Excitation
by Livija Cveticanin Miodrag Zukovic Jose Manoel BalthazarIn this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame – non-ideal source system, non-ideal rotor system, planar mechanism – non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called ‘Sommerfeld effect’, resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems.
Dynamics of Nonlinear Time-Delay Systems
by Dharmapuri Vijayan Senthilkumar Muthusamy LakshmananSynchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.
Dynamics of Number Systems
by Petr KůrkaThis book is a source of valuable and usefulinformation on the topics of dynamics of number systems and scientificcomputation with arbitrary precision. It is addressed to scholars, scientistsand engineers, and graduate students. The treatment is elementary andself-contained with relevance both for theory and applications. The basicprerequisite of the book is linear algebra and matrix calculus.
Dynamics of Partial Differential Equations
by C. Eugene Wayne Michael I. WeinsteinThis book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
Dynamics of Physiological Control: Contributions in Honor of Michael C. Mackey (Lecture Notes on Mathematical Modelling in the Life Sciences)
by Benoît Perthame Angela Stevens Yoichiro MoriThis book provides an overview of recent mathematical models for dynamics in cellular systems and offers a unique vision of the field by prominent experts. It covers, among others, the regulatory basis of oscillations in biological systems; ergodic and chaotic properties in biological models with the example of maturity distribution of precursors of blood cells; time-delayed feedbacks; mathematical models of cell division and heterogeneous stem cell regeneration; quantitative mathematical modeling of glucose regulation; data-driven models of chemotherapy-induced neutropenia; and effects of irradiation and antioxidants in Alzheimer’s disease. This book is directed towards mathematicians interested in learning about modeling in cellular systems and is accessible also to theoreticians in biology and medicine.
Dynamics of Poverty in Rural Bangladesh
by Noriatsu Matsui Yukio Ikemoto Pk. Md. RahmanThe study of poverty dynamics is important for effective poverty alleviation policies because the changes in income poverty are also accompanied by changes in socioeconomic factors such as literacy, gender parity in school, health care, infant mortality, and asset holdings. In order to examine the dynamics of poverty, information from 1,212 households in 32 rural villages in Bangladesh was collected in December 2004 and December 2009. This book reports the analytical results from quantitative and qualitative surveys from the same households at two points of time, which yielded the panel data for understanding the changes in situations of poverty. Efforts have been made to include the most recent research from diverse disciplines including economics, statistics, anthropology, education, health care, and vulnerability study. Specifically, findings from logistic regression analysis, polychoric principal component analysis, kernel density function, income mobility with the help of the Markov chain model, and child nutrition status from anthropometric measures have been presented. Asset holdings and liabilities of the chronically poor as well as those of three other economic groups (the descending non-poor, the ascending poor, and the non-poor) are analyzed statistically. The degrees of vulnerability to poverty are examined by years of schooling, landholding size, gender of household head, social capital, and occupation. The multiple logistic regression model was used to identify important risk factors for a household's vulnerability. In 2009, some of the basic characteristics of the chronically poor were: higher percentage and number of female-headed households, higher dependency ratio, lower levels of education, fewer years of schooling, and limited employment. There was a low degree of mobility of households from one poverty status to another in the period 2004-2009, implying that the process of economic development and high economic growth in the macroeconomy during this time failed to improve the poverty situation in rural Bangladesh.
Dynamics of Rational Negotiation: Game Theory, Language Games and Forms of Life
by Margit Gaffal Jesús Padilla GálvezThis book uses game theory to analyze the strategies developed in negotiation processes. Offering a detailed analysis of competition and cooperation, it explores various bargaining strategies that result from the application of Nash equilibrium and mixed strategies. Employing a blend of game theory and real-world examples, the authors describe typical negotiation scenarios and unveil the art of negotiation strategy – dissecting both competitive and cooperative tactics.This comprehensive analysis explores the multifaceted dimensions of negotiation, highlighting not only formal aspects but also the economic, social, political, and human factors at play. The authors discuss the basic structures of cooperative and non-cooperative games and conduct a comprehensive analysis of the language games that take place in negotiations. They examine how negotiators belonging to different forms of life can trade with each other when their respective language games are different and prone to misinterpretation. The book also probes arbitration and mediation as conflict-resolution tools within this intricate landscape. Designed for the curious minds seeking insight into negotiation strategies, as well as students and scholars of diverse fields, this book fosters an understanding of negotiation's labyrinthine pathways. "Dynamics of Rational Negotiation" unlocks the door to negotiation's complexities, inviting readers to unravel the layers of human interaction.
Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures
by G. Ladas Mustafa R.S. KulenovicThis self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stabili
Dynamics of Statistical Experiments
by Dmitri KorolioukThis book is devoted to the system analysis of statistical experiments, determined by the averaged sums of sampling random variables. The dynamics of statistical experiments are given by difference stochastic equations with a speci?ed regression function of increments – linear or nonlinear. The statistical experiments are studied by the sample volume increasing (N ??), as well as in discrete-continuous time by the number of stages increasing (k ??) for different conditions imposed on the regression function of increments. The proofs of limit theorems employ modern methods for the operator and martingale characterization of Markov processes, including singular perturbation methods. Furthermore, they justify the representation of a stationary Gaussian statistical experiment with the Markov property, as a stochastic difference equation solution, applying the theorem of normal correlation. The statistical hypotheses verification problem is formulated in the classification of evolutionary processes, which determine the dynamics of the predictable component. The method of stochastic approximation is used for classifying statistical experiments.
Dynamics of Transcendental Functions
by Xin-Hou Hua Chung-Chun YangIn this extensive work, the authors give a complete self-contained exposition on the subject of classic function theory and the most recent developments in transcendental iteration. They clearly present the theory of iteration of transcendental functions and their analytic and geometric aspects. Attention is concentrated for the first time on the d
Dynamics of Tree-Type Robotic Systems
by Jayanta Kumar Dutt Subir Kumar Saha Suril Vijaykumar ShahThis book addresses dynamic modelling methodology and analyses of tree-type robotic systems. Such analyses are required to visualize the motion of a system without really building it. The book contains novel treatment of the tree-type systems using concept of kinematic modules and the corresponding Decoupled Natural Orthogonal Complements (DeNOC), unified representation of the multiple-degrees-of freedom-joints, efficient recursive dynamics algorithms, and detailed dynamic analyses of several legged robots. The book will help graduate students, researchers and practicing engineers in applying their knowledge of dynamics for analysis of complex robotic systems. The knowledge contained in the book will help one in virtual testing of robot operation, trajectory planning and control.
Dynamics of the Axially Moving Orthotropic Web
by Krzysztof MarynowskiA material continuum moving axially at high speed can be met in numerous different technical applications. These comprise band saws, web papers during manufacturing, processing and printing processes, textile bands during manufacturing and processing, pipes transporting fluids, transmission belts as well as flat objects moving at high speeds in space. In all these so varied technical applications, the maximum transport speed or the transportation speed is aimed at in order to increase efficiency and optimize investment and performance costs of sometimes very expensive and complex machines and installations. The dynamic behavior of axially moving systems very often hinders from reaching these aims. The book is devoted to dynamics of axially moving material objects of low flexural stiffness that are referred to as webs. Webs are moving at high speed, for example, in paper production the paper webs are transported with longitudinal speeds of up to 3000 m/min. Above the critical speed one can expect various dynamical instabilities mainly of divergent and flutter type. The up-to-date state of investigations conducted in the field of the axially moving system dynamics is presented in the beginning of the book. Special attention is paid on nonlinear dynamic investigations of translating systems. In the next chapters various mathematical models that can be employed in dynamic investigations of such objects and the results of analysis of the dynamic behavior of the axially moving orthotropic material web are presented. To make tracing the dynamic considerations easier, a paper web is the main object of investigations in the book.
Dynamics of the Chemostat: A Bifurcation Theory Approach
by Abdelhamid Ajbar Khalid AlhumaiziA ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors' extensive work in this
Dynamics of the Unicycle: Modelling And Experimental Verification (SpringerBriefs in Applied Sciences and Technology)
by Tomasz Kapitaniak Michał Niełaczny Barnat WiesławThis book presents a three-dimensional model of the complete unicycle–unicyclist system. A unicycle with a unicyclist on it represents a very complex system. It combines Mechanics, Biomechanics and Control Theory into the system, and is impressive in both its simplicity and improbability. Even more amazing is the fact that most unicyclists don’t know that what they’re doing is, according to science, impossible – just like bumblebees theoretically shouldn’t be able to fly. This book is devoted to the problem of modeling and controlling a 3D dynamical system consisting of a single-wheeled vehicle, namely a unicycle and the cyclist (unicyclist) riding it. The equations of motion are derived with the aid of the rarely used Boltzmann–Hamel Equations in Matrix Form, which are based on quasi-velocities. The Matrix Form allows Hamel coefficients to be automatically generated, and eliminates all the difficulties associated with determining these quantities. The equations of motion are solved by means of Wolfram Mathematica. To more faithfully represent the unicyclist as part of the model, the model is extended according to the main principles of biomechanics. The impact of the pneumatic tire is investigated using the Pacejka Magic Formula model including experimental determination of the stiffness coefficient. The aim of control is to maintain the unicycle–unicyclist system in an unstable equilibrium around a given angular position. The control system, based on LQ Regulator, is applied in Wolfram Mathematica. Lastly, experimental validation, 3D motion capture using software OptiTrack – Motive:Body and high-speed cameras are employed to test the model’s legitimacy. The description of the unicycle–unicyclist system dynamical model, simulation results, and experimental validation are all presented in detail.
Dynamics with Chaos and Fractals (Nonlinear Systems and Complexity #29)
by Marat Akhmet Mehmet Onur Fen Ejaily Milad AlejailyThe book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.
Dynamics with Chaos and Fractals (Nonlinear Systems and Complexity #29)
by Marat Akhmet Mehmet Onur Fen Ejaily Milad AlejailyThe book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.
Dynamics, Economic Growth, and International Trade
by Bjarne S. Jensen Kar-Yiu WongWhile endogenous growth theory has claimed success in modeling various factors of growth and providing an analysis of sustainable economic growth, most of the growth models in published work are for closed economies. The omission of international trade, which is often regarded as the engine of growth, greatly reduces their usefulness. The theory of international trade, on the other hand, is characterized by models that are mainly static. While interest in the dynamics of trade has been growing, there is still little work in this area. The success of the newly industrialized economies that have adopted trade-oriented policies suggests how limited present trade theory is in explaining and analyzing the growth of these economies. The work collected here serves to bridge the "old" growth theory and "new" growth theory; merge growth and trade theory; suggest new analysis and techniques of economic growth; and provide analysis of new issues related to growth and trade. The first chapter surveys endogenous growth and international trade and critically reviews the endogenous growth theory with a unified framework, covering the work on both closed and open economies. Three chapters examine the dynamics of some basic trade models; two chapters focus on growth and trade with endogenous accumulation of human and public capital; two chapters on economic growth, technological progress, and international trade; and two chapters on growth and international factor movements.
Dynamics, Games and Science
by Marcelo Viana Jean-Pierre Bourguignon Alberto Adrego Pinto Rolf JeltschThe focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing problems of an economic and social nature and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global economic and social challenges. Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has developed highly complex systems, including economic and financial systems; the World Wide Web; frameworks for resource management, transportation, energy production and utilization; health care delivery, and social organizations. This development has increased to the point where it impacts the stability and equilibrium in human societies. Issues such as financial and economic crisis, sustainability, management of resources, risk analysis, and global integration have come to the fore. Written by some of the world's leading specialists, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Dynamics, Games and Science II, held in Lisbon, Portugal, 28 August -6 September 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book describes the state of the art in advanced research and ultimate techniques in modeling natural, economic and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences, focusing mainly on dynamical systems, game theory and applied sciences.
Dynamics, Geometry, Number Theory: The Impact of Margulis on Modern Mathematics
by David Fisher, Dmitry Kleinbock, and Gregory SoiferThis definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.
Dynamics, Information and Complexity in Quantum Systems (Theoretical and Mathematical Physics)
by Fabio BenattiThis second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts: Part One: Classical Dynamical SystemsAddresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity.Includes a survey of the theory of simple perceptrons and their storage capacity. Part Two: Quantum Dynamical SystemsFocuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems.Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom.Introduces a model of quantum perceptron whose storage capacity is computed and compared with the classical one. Part Three: Quantum Dynamical Entropies and ComplexitiesDevoted to quantum dynamical entropies and algorithmic complexities. This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.
Dynamics: A Lecturebook
by Charles M. Krousgrill Jeffrey F. RhoadsThis hybrid of textbook and lecture notes set is designed to provide an undergraduate-level, engineering-focused introduction to the topic of dynamics. To this end, the text covers the following key topical areas: Particle and Rigid Body Kinematics, including Cartesian, path, polar, and cylindrical descriptions of motion; relative and constrained motion; vector kinematics; instantaneous centers of rotation; and 2D and 3D moving reference frames. Particle and Rigid Body Kinetics, including Newtons Laws of Motion; the work-energy equation; and the linear and angular impulse-momentum equations. Introduction to Mechanical Vibrations, including equation of motion development; free vibration response; harmonic forced vibrations; base excitation; and rotating imbalance, all as applied to single-degree-of-freedom systems. The text provides pertinent background information, while emphasizing fundamental engineering principles, conceptual understanding, and optimal problem solving techniques. The Lecturebook also incorporates an extensive array of practical examples with which students can hone their skills. Key distinctions between the Lecturebook and most conventional texts include: Complete integration of factual information and student-produced notes. Removal of extraneous factual information. The inclusion of conceptual problems designed to exercise higher levels of learning. Lecture example, homework solution, and demonstration videos designed to aid asynchronous learning. The hybrid textbook/lecture note format provides most factual information in full, while brief and extended examples are provided with ample white space, allowing students to actively work the problems with the instructor s assistance in a classroom environment, or outside of the classroom on their own or with the assistance of online videos.
Dynamis: Ontology of the Incommensurable (Contributions to Hermeneutics #9)
by Gaetano ChiurazziThis book offers a new and original hypothesis on the origin of modal ontology, whose roots can be traced back to the mathematical debate about incommensurable magnitudes, which forms the implicit background for Plato’s later dialogues and culminates in the definition of being as dynamis in the Sophist. Incommensurable magnitudes – also called dynameis by Theaetetus – are presented as the solution to the problem of non-being and serve as the cornerstone for a philosophy of difference and becoming. This shift also marks the passage to another form of rationality – one not of the measure, but of the mediation. The book argues that the ontology and the rationality which arise out of the discovery of incommensurable constitutes a thread that runs through the entire history of philosophy, one that leads to Kantian transcendentalism and to the philosophies derived from it, such as Hegelianism and philosophical hermeneutics.Readers discover an insightful exchange with some of the most important issues in philosophy, newly reconsidered from the point of view of an ontology of the incommensurable. These issues include the infinite, the continuum, existence, and difference. This text appeals to students and researchers in the fields of ancient philosophy, German idealism, philosophical hermeneutics and the history of mathematics.
Dyskalkulie als Phänomen in der Grundschule aus mathematikdidaktischer Perspektive: Eine Fallstudie zu Diagnose und Intervention (BestMasters)
by Jenny KnöppelDas vorliegende Buch beschäftigt sich mit der Thematik der Dyskalkulie aus einer mathematikdidaktischen Perspektive. Den Kern bildet dabei eine Fallstudie mit einer Grundschülerin, bei der zuvor eine Dyskalkulie diagnostiziert wurde. Im Sinne des Case-Study-Ansatzes liegt der Fokus auf der genauen Beschreibung und Analyse des Falls unter Berücksichtigung verschiedener Datenquellen. Dazu werden im Verlauf der Studie Diagnosetests, Experteninterviews mit den Eltern, der Lehrperson und der Schülerin, sowie Analysen von Lösungsskizzen durchgeführt. Im Rahmen der Interviews und diagnostischer Gespräche mit der Schülerin werden insbesondere ihre Denkweisen und Lösungsprozesse beobachtet, beschrieben und somit die Kompetenzen und mögliche Hürden im Bereich der Arithmetik identifiziert. Auf Grundlage der Erkenntnisse aus den Diagnoseeinheiten werden entsprechende Interventionseinheiten konzipiert. Der Schwerpunkt der Beobachtungen und Analysen orientiert sich dabei an der Frage nach den Lernfortschritten, die sich im Verlauf der Förderung beschreiben lassen. Ziel dieser Studie ist es, einen Ansatz zu einem „ganzheitlichen“ Bild eines Falls zu skizzieren, um Perspektiven für Diagnose- und Fördermöglichkeiten aufzuzeigen und weitere Forschungsfragen und -anliegen zu generieren.