- Table View
- List View
Ensemble Classification Methods with Applications in R
by Esteban Alfaro Matías Gámez Noelia GarcíaAn essential guide to two burgeoning topics in machine learning – classification trees and ensemble learning Ensemble Classification Methods with Applications in R introduces the concepts and principles of ensemble classifiers methods and includes a review of the most commonly used techniques. This important resource shows how ensemble classification has become an extension of the individual classifiers. The text puts the emphasis on two areas of machine learning: classification trees and ensemble learning. The authors explore ensemble classification methods’ basic characteristics and explain the types of problems that can emerge in its application. Written by a team of noted experts in the field, the text is divided into two main sections. The first section outlines the theoretical underpinnings of the topic and the second section is designed to include examples of practical applications. The book contains a wealth of illustrative cases of business failure prediction, zoology, ecology and others. This vital guide: Offers an important text that has been tested both in the classroom and at tutorials at conferences Contains authoritative information written by leading experts in the field Presents a comprehensive text that can be applied to courses in machine learning, data mining and artificial intelligence Combines in one volume two of the most intriguing topics in machine learning: ensemble learning and classification trees Written for researchers from many fields such as biostatistics, economics, environment, zoology, as well as students of data mining and machine learning, Ensemble Classification Methods with Applications in R puts the focus on two topics in machine learning: classification trees and ensemble learning.
Ensemble Methods: Foundations and Algorithms (Chapman & Hall/CRC Machine Learning & Pattern Recognition)
by Zhi-Hua ZhouAn up-to-date, self-contained introduction to a state-of-the-art machine learning approach, Ensemble Methods: Foundations and Algorithms shows how these accurate methods are used in real-world tasks. It gives you the necessary groundwork to carry out further research in this evolving field.After presenting background and terminology, the book cover
Ensemble Methods: Foundations and Algorithms (Chapman & Hall/CRC Machine Learning & Pattern Recognition)
by Zhi-Hua ZhouEnsemble methods that train multiple learners and then combine them to use, with Boosting and Bagging as representatives, are well-known machine learning approaches. It has become common sense that an ensemble is usually significantly more accurate than a single learner, and ensemble methods have already achieved great success in various real-world tasks.Twelve years have passed since the publication of the first edition of the book in 2012 (Japanese and Chinese versions published in 2017 and 2020, respectively). Many significant advances in this field have been developed. First, many theoretical issues have been tackled, for example, the fundamental question of why AdaBoost seems resistant to overfitting gets addressed, so that now we understand much more about the essence of ensemble methods. Second, ensemble methods have been well developed in more machine learning fields, e.g., isolation forest in anomaly detection, so that now we have powerful ensemble methods for tasks beyond conventional supervised learning.Third, ensemble mechanisms have also been found helpful in emerging areas such as deep learning and online learning. This edition expands on the previous one with additional content to reflect the significant advances in the field, and is written in a concise but comprehensive style to be approachable to readers new to the subject.
Entanglement in Spin Chains: From Theory to Quantum Technology Applications (Quantum Science and Technology)
by Abolfazl Bayat Sougato Bose Henrik JohannessonThis book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.
Entdecken und Begründen im Mathematikunterricht: Von der Abduktion zum Argument (Kölner Beiträge zur Didaktik der Mathematik)
by Michael MeyerDas Entdecken und das Begründen im Mathematikunterricht bilden das Thema der vorliegenden Arbeit. Sowohl auf theoretischer als auch auf empirischer Basis wird eine mathematikdidaktische Theorie vorgestellt, die sowohl Begründungen als auch Entdeckungen sowie ihre Zusammenhänge beim Mathematiklernen zu analysieren ermöglicht. So wird es möglich, die Kreativität von Hypothesen, die Plausibilität von Hypothesen, den Begründungsbedarf von Hypothesen, die Schlüssigkeit bzw. Überzeugungskraft von Begründungen sowie die Interaktionsprozesse zwischen Lehrer*innen und Schüler*innen beim Entdecken und Begründen zu erfassen. Rekonstruktionen mathematischer Lernprozesse verdeutlichen die Anwendbarkeit und innere Kohärenz des erstellten Begriffsnetzes.
Enterprise Information Systems: 22nd International Conference, ICEIS 2020, Virtual Event, May 5–7, 2020, Revised Selected Papers (Lecture Notes in Business Information Processing #417)
by Joaquim Filipe Slimane Hammoudi Michał Śmiałek Alexander BrodskyThis book constitutes extended, revised and selected papers from the 22nd International Conference on Enterprise Information Systems, ICEIS 2020, held online during May 5-7, 2020.The 41 papers presented in this volume were carefully reviewed and selected for inclusion in this book from a total of 255 submissions. They were organized in topical sections as follows: database and information systems integration; artificial intelligence and decision support systems; information systems analysis and specification; software agents and internet computing; human-computer interaction; and enterprise architecture.
Enterprise Information Systems: 23rd International Conference, ICEIS 2021, Virtual Event, April 26–28, 2021, Revised Selected Papers (Lecture Notes in Business Information Processing #455)
by Joaquim Filipe Slimane Hammoudi Michał Śmiałek Alexander BrodskyThis book contains extended, revised and selected papers from the 23rd International Conference on Enterprise Information Systems, ICEIS 2021, held online during April 2021. The 26 papers presented in this volume were carefully reviewed and selected for inclusion from a total of 241 submissions. They are grouped in sections on databases and information systems integration, artificial intelligence and decision support systems, information systems analysis and specification, software agents and internet computing, human-computer interaction, and enterprise architecture.
Enterprise Information Systems: 24th International Conference, ICEIS 2022, Virtual Event, April 25–27, 2022, Revised Selected Papers (Lecture Notes in Business Information Processing #487)
by Joaquim Filipe Slimane Hammoudi Michał Śmiałek Alexander BrodskyThis book constitutes the refereed post-conference proceedings of the 24th International Conference on Enterprise Information Systems, ICEIS 2022, This conference was held virtually due to the COVID-19 crisis, during April 25-27, 2022.The 20 full papers included in this book were carefully reviewed and selected from 197 submissions. They were organized in topical sections as follows: Databases and Information Systems Integration; Artificial Intelligence and Decision Support Systems; Information Systems Analysis and Specification; Human-Computer Interaction; and Enterprise Architecture.
Enterprise Information Systems: 25th International Conference, ICEIS 2023, Prague, Czech Republic, April 24–26, 2023, Revised Selected Papers, Part I (Lecture Notes in Business Information Processing #518)
by Joaquim Filipe Slimane Hammoudi Michał Śmiałek Alexander BrodskyThis two-volume set constitutes the refereed post-conference proceedings of the 25th International Conference on Enterprise Information Systems, ICEIS 2023, which was held in Prague, Czech Republic, during April 2023. The 41 full papers and 66 short papers presented were carefully reviewed and selected from 213 submissions. They are organized in topical sections as follows: Part One : Databases and Information Systems Integration; Artificial Intelligence and Decision Support Systems; and Information Systems Analysis and Specification. Part Two : Software Agents and Internet Computing; Human-Computer Interaction; and Enterprise Architecture.
Enterprise Information Systems: 25th International Conference, ICEIS 2023, Prague, Czech Republic, April 24–26, 2023, Revised Selected Papers, Part II (Lecture Notes in Business Information Processing #519)
by Joaquim Filipe Slimane Hammoudi Michał Śmiałek Alexander BrodskyThe two-volume set LNBIP 518 and 519 constitutes the refereed post-conference proceedings of the 25th International Conference on Enterprise Information Systems, ICEIS 2023, which was held in Prague, Czech Republic, during April 2023. The 30 full papers included in these proceedings were carefully reviewed and selected from a total of 213 submissions. They are organized in topical sections as follows: Part One : Databases and Information Systems Integration; Artificial Intelligence and Decision Support Systems; and Information Systems Analysis and Specification. Part Two : Software Agents and Internet Computing; Human-Computer Interaction; and Enterprise Architecture.
Entire Slice Regular Functions
by Daniele C. Struppa Irene Sabadini Fabrizio ColomboThis Briefs volume develops the theory of entire slice regular functions. It is the first self-contained, monographic work on the subject, offering all the necessary background information and detailed studies on several central topics, including estimates on the minimum modulus of regular functions, relations between Taylor coefficients and the growth of entire functions, density of their zeros, and the universality properties. The proofs presented here shed new light on the nature of the quaternionic setting and provide inspiration for further research directions. Also featuring an exhaustive reference list, the book offers a valuable resource for graduate students, postgraduate students and researchers in various areas of mathematical analysis, in particular hypercomplex analysis and approximation theory.
Entrepreneurial Complexity: Methods and Applications
by Matthias Dehmer Frank Emmert-Streib Herbert JodlbauerEntrepreneurial Complexity: Methods and Applications deals with theoretical and practical results of Entrepreneurial Sciences and Management (ESM), emphasising qualitative and quantitative methods. ESM has been a modern and exciting research field in which methods from various disciplines have been applied. However, the existing body of literature lacks the proper use of mathematical and formal models; individuals who perform research in this broad interdisciplinary area have been trained differently. In particular, they are not used to solving business-oriented problems mathematically. This book utilises formal techniques in ESM as an advantage for developing theories and models which are falsifiable. Features Discusses methods for defining and measuring complexity in entrepreneurial sciences Summarises new technologies and innovation-based techniques in entrepreneurial sciences Outlines new formal methods and complexity-models for entrepreneurship To date no book has been dedicated exclusively to use formal models in Entrepreneurial Sciences and Management
Entrepreneurial Finance
by M. J. AlhabeebFeaturing key topics within finance, small business management, and entrepreneurship to develop and maintain prosperous business venturesWith a comprehensive and organized approach to fundamental financial theories, tools, and management techniques, Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business equips readers with the necessary fundamental knowledge and advanced skills to succeed in small firm and business settings. With a unique combination of topics from finance, small business management, and entrepreneurship, the book prepares readers for the challenges of today's economy.Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business begins with key concepts of small business management and entrepreneurship, including management tools and techniques needed to establish, run, and lead business ventures. The book then delves into how small businesses are operated, managed, and controlled. General finance skills and methods are integrated throughout, and the book also features:Numerous practical examples and scenarios that provide a real-world perspective on entrepreneurship and small business managementA brief summary, list of key concepts, and ten discussion questions at the end of each chapter to prepare readers for the challenges of today's economyA practical guide to the complete life of a small business, from establishing a new venture to training and developing young entrepreneurs tasked with maintaining and developing a prosperous economyAn in-depth discussion of the entire process of writing a successful business plan, including the rationale, significance, and requirementsTechniques needed to solidify the free enterprise tradition, develop entrepreneurial strategies, and grow small businessesEntrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business is an ideal textbook for upper-undergraduate and first-year graduate courses in entrepreneurial finance within business, economics, management science, and public administration departments. The book is also useful for MBA-level courses as well as for business and management PhD majors as a resource in methodology. The book is also an idea reference for entrepreneurs, business managers, market analysts, and decision makers who require information about the theoretical and quantitative aspects of entrepreneurial finance.
Entropy Measures for Environmental Data: Description, Sampling and Inference for Data with Dependence Structures (Advances in Geographical and Environmental Sciences)
by Daniela Cocchi Linda AltieriThis book shows how to successfully adapt entropy measures to the complexity of environmental data. It also provides a unified framework that covers all main entropy and spatial entropy measures in the literature, with suggestions for their potential use in the analysis of environmental data such as biodiversity, land use and other phenomena occurring over space or time, or both. First, recent literature reviews about including spatial information in traditional entropy measures are presented, highlighting the advantages and disadvantages of past approaches and the difference in interpretation of their proposals. A consistent notation applicable to all approaches is introduced, and the authors’ own proposal is presented. Second, the use of entropy in spatial sampling is focused on, and a method with an outstanding performance when data show a negative or complex spatial correlation is proposed. The last part of the book covers estimating entropy and proposes a model-based approach that differs from all existing estimators, working with data presenting any departure from independence: presence of covariates, temporal or spatial correlation, or both. The theoretical parts are supported by environmental examples covering point data about biodiversity and lattice data about land use. Moreover, a practical section is provided for all parts of the book; in particular, the R package SpatEntropy covers not only the authors’ novel proposals, but also all the main entropy and spatial entropy indices available in the literature. R codes are supplemented to reproduce all the examples. This book is a valuable resource for students and researchers in applied sciences where the use of entropy measures is of interest and where data present dependence on space, time or covariates, such as geography, ecology, biology and landscape analysis.
Entropy Methods for Diffusive Partial Differential Equations
by Ansgar JüngelThis book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Entropy and the Second Law of Thermodynamics: ... or Why Things Tend to Go Wrong and Seem to Get Worse
by Robert FleckThis book is a brief and accessible popular science text intended for a broad audience and of particular interest also to science students and specialists. Using a minimum of mathematics, a number of qualitative and quantitative examples, and clear illustrations, the author explains the science of thermodynamics in its full historical context, focusing on the concepts of energy and its availability and transformation in thermodynamic processes. His ultimate aim is to gain a deep understanding of the second law—the increase of entropy—and its rather disheartening message of a universe descending inexorably into chaos and disorder. It also examines the connection between the second law and why things go wrong in our daily lives. Readers will enhance their science literacy and feel more at home on the science side of author C. P. Snow's celebrated two-culture, science-humanities divide, and hopefully will feel more at home in the universe knowing that the disorder we deal with in our daily lives is not anyone's fault but Nature's.
Entropy and the Tao of Counting: A Brief Introduction to Statistical Mechanics and the Second Law of Thermodynamics (SpringerBriefs in Physics)
by Kim SharpThis book provides a complete and accurate atomic level statistical mechanical explanation of entropy and the second law of thermodynamics. It assumes only a basic knowledge of mechanics and requires no knowledge of calculus. The treatment uses primarily geometric arguments and college level algebra. Quantitative examples are given at each stage to buttress physical understanding. This text is of benefit to undergraduate and graduate students, as well as educators and researchers in the physical sciences (whether or not they have taken a thermodynamics course) who want to understand or teach the atomic/molecular origins of entropy and the second law. It is particularly aimed at those who, due to insufficient mathematical background or because of their area of study, are not going to take a traditional statistical mechanics course.
Entropy in Urban and Regional Modelling (Routledge Revivals #Vol. 1)
by Alan WilsonFirst published in 1970, this groundbreaking investigation into Entropy in Urban and Regional Modelling provides an extensive and detailed insight into the entropy maximising method in the development of a whole class of urban and regional models. The book has its origins in work being carried out by the author in 1966, when he realised that the well-known gravity model could be derived on the basis of an analogy with statistical, rather than Newtonian, mechanics. Subsequent investigation demonstrated that the entropy maximising method stems from an even higher level of generality, and the beginning of the book is devoted to an account of its importance and use as a general modelling tool. This reissue will be welcomed by a range of students and professionals from fields as diverse as urban and regional studies, economics, geography, planning, civil engineering, mathematics and statistics.
Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics (SpringerBriefs in Mathematical Physics #16)
by Takahiro SagawaRich information-theoretic structure in out-of-equilibrium thermodynamics exists in both the classical and quantum regimes, leading to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories such as matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it.The book focuses on both purely information-theoretic concepts and their physical implications. From the mathematical point of view, rigorous proofs of fundamental properties of entropies, divergences, and majorization are presented in a self-contained manner. From the physics perspective, modern formulations of thermodynamics are discussed, with a focus on stochastic thermodynamics and resource theory of thermodynamics. In particular, resource theory is a recently developed field as a branch of quantum information theory to quantify “useful resources” and has an intrinsic connection to various fundamental ideas of mathematics and information theory. This book serves as a concise introduction to important ingredients of the information-theoretic formulation of thermodynamics.
Entscheidungstheorie: Individuelle, strategische und kollektive Entscheidungen (Studienbücher Wirtschaftsmathematik)
by Erwin AmannIn diesem Buch werden aufbauend auf die Grundlagen individueller Entscheidungen unter Sicherheit und unter Unsicherheit die wesentlichen Modelle kollektiver Entscheidungen und kompetitiver Märkte sowie strategischer Entscheidungen in der Spieltheorie und Verhandlungstheorie vorgestellt. Entscheidungstheorie ist die Basis aller modernen mikroökonomischen Ansätze. Das Buch soll neben einem guten und möglichst umfassenden Einstieg auch die Option bieten, sich mit klaren mathematischen Begründungen formal vertraut zu machen. Es schafft damit die Basis, sich mit wissenschaftlichen entscheidungstheoretischen Arbeiten kompetent auseinanderzusetzen, aber auch diese Ansätze kritisch zu hinterfragen und eigene Modelle zu entwickeln. Das Lehrbuch für Studierende der Wirtschaftswissenschaften und der Wirtschaftsmathematik schlägt einen Bogen von Anwendungsbeispielen, grundlegenden theoretischen Konzepten bis hin zu den zentralen Beweisen. Zahlreiche unterstützende Grafiken und viele Aufgaben mit Lösungsansätzen erleichtern das Verständnis. In einem Anhang werden wesentliche Definitionen und Verfahren der Optimierung, fundamental für die Entscheidungstheorie, aufgeführt.
Entscheidungstheorie: Individuelle, strategische und kollektive Entscheidungen (Studienbücher Wirtschaftsmathematik)
by Erwin AmannIn diesem Lehrbuch werden aufbauend auf den Grundlagen individueller Entscheidungen unter Sicherheit und unter Unsicherheit die wesentlichen Modelle kollektiver Entscheidungen und kompetitiver Märkte sowie strategischer Entscheidungen in der Spieltheorie und Verhandlungstheorie vorgestellt. Entscheidungstheorie ist die Basis aller modernen mikroökonomischen Ansätze. Das Buch soll neben einem guten und möglichst umfassenden Einstieg auch die Option bieten, sich mit klaren mathematischen Begründungen formal vertraut zu machen. Es schafft damit die Basis, sich mit wissenschaftlichen entscheidungstheoretischen Arbeiten kompetent auseinanderzusetzen, aber auch diese Ansätze kritisch zu hinterfragen und eigene Modelle zu entwickeln. Das Lehrbuch für Studierende der Wirtschaftswissenschaften und der Wirtschaftsmathematik schlägt einen Bogen von Anwendungsbeispielen, grundlegenden theoretischen Konzepten bis hin zu den zentralen Beweisen. Zahlreiche unterstützende Grafiken und viele Aufgaben mit Lösungsansätzen erleichtern das Verständnis. In einem Anhang werden wesentliche Definitionen und Verfahren der Optimierung, fundamental für die Entscheidungstheorie, aufgeführt. Die vorliegende 2. Auflage wurde um eine ausführlichere Einleitung, zusätzliche Inhalte sowie per SN-Flashcards-App digital abrufbare Fragen und Antworten erweitert.
Entwicklung der Professionellen Unterrichtswahrnehmung: Eine Studie zur Entwicklung Studierender in universitären Praxisphasen (Perspektiven der Mathematikdidaktik)
by Anna Barbara OrschulikAnna Barbara Orschulik untersucht in diesem Buch die Entwicklung der professionellen Unterrichtswahrnehmung bei angehenden Lehrkräften im Rahmen von Praxisphasen an der Universität Hamburg, da diese Kompetenz eine hohe Bedeutung für die Qualität von Unterricht und die Leistungen der Lernenden hat. Auf Grundlage einer videobasierten Erhebung wird dabei der Frage nachgegangen, inwiefern sich die professionelle Unterrichtswahrnehmung entwickelt und worauf die festgestellte Entwicklung zurückgeführt werden kann. Die AutorinAnna Barbara Orschulik ist Lehrerin für Geografie und Mathematik und ist seit 5 Jahren ebenfalls in der Lehrerbildung an der Universität Hamburg tätig. Im Rahmen dieser Tätigkeit promovierte sie im Bereich der Mathematikdidaktik bei Prof. Dr. Gabriele Kaiser.
Entwicklung der professionellen Kompetenz von Mathematiklehramtsstudierenden zur Bedeutung von Sprache: Eine qualitative Studie zur professionellen Unterrichtswahrnehmung und der Kompetenz zur Analyse von Textaufgaben (Perspektiven der Mathematikdidaktik)
by Nadine KrosankeDie qualitative Studie von Nadine Krosanke versteht sich als Forschungsbeitrag zur Untersuchung von Professionalisierungsprozessen von Lehrkräften im Hinblick auf Kompetenzen im Bereich Sprache im Mathematikunterricht. Dabei wird die Frage untersucht, inwiefern sich nach der Teilnahme an einem neu konzipierten Seminar an der Universität Hamburg bei den teilnehmenden Mathematiklehramtsstudierenden Zuwächse in der Kompetenz zur Analyse von potenziellen sprachlichen Hürden in Textaufgaben und hinsichtlich der professionellen Unterrichtswahrnehmung identifizieren lassen, insbesondere hinsichtlich der Bedeutung von Sprache beim fachlichen Lernen und Lehren.
Entwicklung mathematikspezifischer diagnostischer Kompetenz im Praxissemester von Studierenden im Lehramt Grundschule (Bielefelder Schriften zur Didaktik der Mathematik #17)
by Steffen DingemansDie Qualität eines Unterrichts, der sich an den individuellen Voraussetzungen der Schulkinder orientiert, hängt maßgeblich mit der diagnostischen Kompetenz der Lehrkraft zusammen. Folglich ist die Entwicklung dieser eine grundlegende Aufgabe aller drei Phasen der Lehrkräftebildung. In der vorliegenden Studie wird das Praxissemester als struktureller Bestandteil der ersten Phase der Lehramtsausbildung fokussiert und die Wirkung auf die Entwicklung mathematikspezifischer diagnostischer Kompetenz untersucht. Den Kern der als mixed-method angelegten längsschnittlichen Evaluation stellen vier Videovignetten dar, zu denen die Studierenden aus dem Grundschullehramt in einer Online-Umfrage mit offenen Antwortformaten aufgefordert wurden, die Lösungswege von Kindern zur Addition und Subtraktion fachlich angemessen zu analysieren. Die Ergebnisse bestätigen einerseits die geringe Effektivität vor allem der schulischen Praxisphase. Anderseits werden auf Basis der vorliegenden Daten relevante Bedingungsfaktoren herausgearbeitet und Verbesserungsmöglichkeiten für die universitäre und schulische Phase des Praxissemesters diskutiert.
Entwicklungen von Divisionsverständnissen bei Kindern in der Grundschule: Eine qualitative Längsschnittstudie (Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts #50)
by Myriam BurtscherEin tragfähiges Verständnis der Division ist für die Schülerinnen und Schüler weit über die Grundschule hinaus von großer Bedeutung. Wie eine Bestandaufnahme der einschlägigen empirischen Forschung auf internationaler Ebene deutlich macht, erweist sich unter den vier Grundrechenarten die Division für Lernende als die größte Herausforderung. Die vorliegende Forschungsarbeit untersucht Entwicklungsverläufe zum Verständnis der Division bei elf Grundschulkindern aus zwei verschiedenen Schulklassen über drei Schuljahre hinweg. Die Ergebnisse der Interviews zeigen, dass bei einigen der vier untersuchten Darstellungswechsel für die Kinder eine Reihe von Problemen und Schwierigkeiten auftraten, die insbesondere mit der Zwiegestalt der Division in Verbindung stehen.