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Visuospatial Reasoning
by Kay OwensThis book develops the theoretical perspective on visuospatial reasoning in ecocultural contexts, granting insights on how the language, gestures, and representations of different cultures reflect visuospatial reasoning in context. For a number of years, two themes in the field of mathematics education have run parallel with each other with only a passing acquaintance. These two areas are the psychological perspective on visuospatial reasoning and ecocultural perspectives on mathematics education. This volume examines both areas of research and explores the intersection of these powerful ideas. In addition, there has been a growing interest in sociocultural aspects of education and in particular that of Indigenous education in the field of mathematics education. There has not, however, been a sound analysis of how environmental and cultural contexts impact visuospatial reasoning, although it was noted as far back as the 1980s when Alan Bishop developed his duality of visual processing and interpreting visual information. This book provides this analysis and in so doing not only articulates new and worthwhile lines of research, but also uncovers and makes real a variety of useful professional approaches in teaching school mathematics. With a renewed interest in visuospatial reasoning in the mathematics education community, this volume is extremely timely and adds significantly to current literature on the topic.
Vital Directions for Mathematics Education Research
by Keith R LeathamThis book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical "research agenda projects," which seek to outline specific research questions that the field should address around a central topic.
Vital Statistics: Summary of a Workshop
by National Research Council of the National AcademiesVital statistics, the records of birth and death, are a critical national information resource for understanding public health. Over the past few decades, the specific program that gathers the data has evolved into a complex cooperative program between the federal and state governments for social measurement. The Vital Statistics Cooperative Program (VSCP) is currently maintained by the National Center for Health Statistics (NCHS). The U.S. vital statistics system relies on the original information reported by myriad individuals, channeled through varying state and local information systems, and coordinated and processed by a federal statistical agency that has experienced relatively flat funding for many years. The challenges facing the vital statistics system and the continuing importance of the resulting data make it an important topic for examination. A workshop, held by the National Academies and summarized in this volume, considered the importance of adequate vital statistics. In particular, the workshop assessed both current and emerging uses of the data, considered the methodological and organizational features of compiling vital data, and identified possible visions for the vital statistics program.
Vital Statistics on American Politics
by Jeffrey L. Bernstein Amanda C. ShannonThere is no other source that provides in one place the wide range and depth of insight found in Vital Statistics on American Politics (VSAP), published since 1988. VSAP provides historical and statistical information on all aspects of American politics: Political parties Voter turnout Public opinion Campaign finance Media perspective and influence, congressional membership and voting patterns The presidency and executive branch Military policy and spending Supreme Court and federal court make-up and caseloads Foreign, social, and economic policy In over 230 tables and figures, students and professional researchers will find chapters devoted to key subject areas such as elections and political parties, public opinion and voting, the media, the three branches of U.S. government, foreign, military, social and economic policy, and much more. This book provides a vivid and multifaceted portrait of the broad spectrum of United States politics and policies. Along with updated and new data content, this edition offers brand new data literacy lessons that take a "guide on the side" approach to teach data researchers how to wade through the sea of data and do the difficult work of grappling for the meaning of the data on their own. Lessons include understanding descriptive representation data, comparing data over time, noticing gaps in data, unpacking dichotomies of public opinion, and more.
Vital Statistics on American Politics
by Jeffrey L. Bernstein Amanda C. ShannonThere is no other source that provides in one place the wide range and depth of insight found in Vital Statistics on American Politics (VSAP), published since 1988. VSAP provides historical and statistical information on all aspects of American politics: Political parties Voter turnout Public opinion Campaign finance Media perspective and influence, congressional membership and voting patterns The presidency and executive branch Military policy and spending Supreme Court and federal court make-up and caseloads Foreign, social, and economic policy In over 230 tables and figures, students and professional researchers will find chapters devoted to key subject areas such as elections and political parties, public opinion and voting, the media, the three branches of U.S. government, foreign, military, social and economic policy, and much more. This book provides a vivid and multifaceted portrait of the broad spectrum of United States politics and policies. Along with updated and new data content, this edition offers brand new data literacy lessons that take a "guide on the side" approach to teach data researchers how to wade through the sea of data and do the difficult work of grappling for the meaning of the data on their own. Lessons include understanding descriptive representation data, comparing data over time, noticing gaps in data, unpacking dichotomies of public opinion, and more.
Vitiation of Contracts
by Gareth SparkVitiation of Contracts proposes a new theory to explain the rationale of general vitiating factors in English contract law. It provides a clear link to voluntariness as the foundation of contractual liability and compares the English position, in light of this theory, with the Principles of International Commercial Contracts (PICC), the Principles of European Contract Law (PECL), the Draft Common Frame of Reference (DCFR) and the US Restatement (Second) of Contracts.
Vito Volterra
by Giovanni Paoloni Angelo Guerraggio Kim WilliamsVito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterra's most important contributions to mathematics and their applications, as well as his outstanding organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theory and population dynamics (Lotka-Volterra model). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He became involved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche, CNR). During the First World War he was active in military research. After the war he took a clear stand against fascism, which was the starting point for his exclusion. In 1926 he resigned as president of the world famous Accademia Nazionale dei Lincei and was later on excluded from the academy. In 1931 he was one of the few university lecturers who denied to swear an oath of allegiance to the fascistic regime. In 1938 he suffered from the impact of the racial laws. The authors draw a comprehensive picture of Vito Volterra, both as a great mathematician and an organizer of science.
Vitushkin’s Conjecture for Removable Sets
by James DudziakVitushkin's conjecture, a special case of Painlevé's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters 1-5 of the book provide important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin's conjecture. The fourth chapter contains a proof of Denjoy's conjecture that employs Melnikov curvature. A brief postscript reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture. This text can be used for a topics course or seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.
VLSI Analog Filters
by P.V. Ananda MohanGreat strides have been made in the development of analog filters over the past few decades. The first book to treat these recent advances in depth, "VLSI Analog Filters" provides a comprehensive guide for researchers and upper-level graduate students, which fully prepares readers for professional work. In particular, the work covers active R filters, OTA-C filters, and switched-capacitor filters, including topics such as differential output opamps, sensitivity analysis for passive components, multiple-feedback techniques, double-sampling, and N-path filters. Throughout the book, exercises are included to reinforce understanding of concepts, and simulations are used to enhance connections to practical applications. This advanced textbook is suitable for engineering graduate students studying analog filter design, offering a full course that can feed seamlessly to employment industry. At the same time, it serves as an extremely valuable reference for researchers and engineers looking to gain a deeper understanding of the field.
VLSI Design and Test: 23rd International Symposium, VDAT 2019, Indore, India, July 4–6, 2019, Revised Selected Papers (Communications in Computer and Information Science #1066)
by Rohit Sharma Virendra Singh Sudeb Dasgupta Anirban Sengupta Santosh Kumar VishvakarmaThis book constitutes the refereed proceedings of the 23st International Symposium on VLSI Design and Test, VDAT 2019, held in Indore, India, in July 2019. The 63 full papers were carefully reviewed and selected from 199 submissions. The papers are organized in topical sections named: analog and mixed signal design; computing architecture and security; hardware design and optimization; low power VLSI and memory design; device modelling; and hardware implementation.
VMware vSphere 6.7 Cookbook: Practical recipes to deploy, configure, and manage VMware vSphere 6.7 components, 4th Edition
by Abhilash G BProven, actionable ways to install, manage, secure and monitor your vSphere 6.7 environments Key Features Get up to speed with the installation and life cycle management of a vSphere 6.7 environment, using a task-based approach Secure your vSphere environment using SSL Certificates Get introduced to the tools that are used to monitor the performance of the vSphere Environment Book Description VMware vSphere is the most comprehensive core suite of SDDC solutions on the market. It helps transform data centers into simplified on-premises private cloud infrastructures. This edition of the book focuses on the latest version, vSphere 6.7. The books starts with chapters covering the greenfield deployment of vSphere 6.7 components and the upgrade of existing vSphere components to 6.7. You will then learn how to configure storage and network access for a vSphere environment. Get to grips with optimizing your vSphere environment for resource distribution and utilization using features such as DRS and DPM, along with enabling high availability for vSphere components using vSphere HA, VMware FT, and VCHA. Then, you will learn how to facilitate large-scale deployment of stateless/stateful ESXi hosts using Auto Deploy. Finally, you will explore how to upgrade/patch a vSphere environment using vSphere Update Manager, secure it using SSL certificates, and then monitor its performance with tools such as vSphere Performance Charts and esxtop. By the end of this book, you'll be well versed in the core functionalities of vSphere 6.7 and be able to effectively deploy, manage, secure, and monitor your environment. What you will learn Deploy a new vSphere 6.7 environment or upgrade an existing vSphere environment to version 6.7 Learn how to configure and manage storage and network access for a vSphere environment Enable high availability for Hosts, VMs and vCenter Server Optimize your vSphere environment for resource distribution/utilization Patch or upgrade a vSphere environment using vSphere Update Manager Secure vSphere infrastructure components using SSL certificates Effectively monitor the performance of your vSphere environment Who this book is for If you are a systems administrator, support engineer, or anyone who wants to learn how to install, configure, and manage a vSphere environment in a quick, hands-on manner, then this book is for you. Consultants and infrastructure architects who wish to design and deploy vSphere 6.7 environments will also find this book helpful.
Volkswirtschaftslehre – mathematisch gedacht
by Mark SellenthinDieses Lehrbuch stellt die theoretischen Modelle der Volkswirtschaftslehre durch grundlegende mathematische Konzepte dar. Während eine wirtschaftswissenschaftliche akademische Karriere ohne fundierte Methodenkenntnisse undenkbar erscheint, sind in der akademischen Lehre die theoretischen Inhalte und die quantitativen Methoden zumeist relativ streng voneinander getrennt. Dieses Lehrbuch geht einen anderen Weg. Die Mathematik wird als lebendiger, integraler Bestandteil des wirtschaftswissenschaftlichen Studiums verstanden, ohne den weder ein tieferes theoretisches Verständnis noch eine empirische Anwendung möglich ist. Der Autor analysiert wesentliche Modelle aus der Mikro- und der Makroökonomik mit Hilfe mathematischer Ansätze. Der Anwendungsnutzen mathematischer Methoden steht dabei im Vordergrund und soll daher anhand von Musteraufgaben illustriert werden. Das vorliegende Lehrbuch richtet sich an Bachelorstudierende, die eine Einführung in die mathematische Modellierung grundlegender Modelle der Mikro- und Makroökonomik wünschen.Für die 2. Auflage wurde ein neues Kapitel zu den mathematischen Grundlagen ergänzt, das gebündelt alle benötigten Methoden für ein wirtschaftswissenschaftliches Studium vorstellt. Im Kapitel zur Makroökonomik wurde zudem die Makroökonomik offener Volkswirtschaften neu aufgenommen.
Vollständige Induktion: Beispiele und Aufgaben bis zum Umfallen
by Florian André DalwigkDein Professor spricht vom Beweisen mit vollständiger Induktion, aber du verstehst nur Bahnhof? Du willst endlich wissen, was es damit auf sich hat – und vor allem, wie du das in der Klausur hinkriegen sollst? In diesem Buch erfährst du es! Dabei ist es ganz egal, ob die Prüfung schon kurz bevor steht und du eine Rettung in letzter Sekunde suchst, oder ob du etwas mehr Zeit für die theoretischen Details und Hintergründe aufbringen kannst. Du wirst hier keine unverständlichen Floskeln finden, sondern Unterstützung auf Augenhöhe – von einem erfahrenen Tutor, der genau weiß, wo die größten Schwierigkeiten beim Verständnis und beim Lösen von Induktionsaufgaben liegen. Und nicht nur das: Neben einer anschaulichen Erklärung des Beweisschemas findest du in diesem Buch zahlreiche Beispiele und über 100 Aufgaben verschiedener Schwierigkeitsgrade – jeweils mit ausführlicher Schritt-für-Schritt-Lösung. So bekommst du Routine und wirst optimal auf die Klausur vorbereitet. Und falls doch noch Fragen offen sein sollten: In den FAQs werden die typischen Fragen von Studierenden zu Induktionsbeweisen verständlich beantwortet.
Volterra and Functional Differential Equations (Lecture Notes In Pure And Applied Mathematics Ser.)
by Kenneth B. HannsgenThis book contains twenty four papers, presented at the conference on Volterra and Functional Differential Equations held in Virginia in 1981, on various topics, including Liapunov stability, Volterra equations, integral equations, and functional differential equations.
Volterra Integral Equations
by Hermann BrunnerCollocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.
Volume Conjecture for Knots (SpringerBriefs in Mathematical Physics #30)
by Hitoshi Murakami Yoshiyuki YokotaThe volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called R-matrix that is associated with the N-dimensional representation of the Lie algebra sl(2;C). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume.In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the case of hyperbolic knots by showing how the summation formula for the colored Jones polynomial “looks like” the hyperbolicity equations of the knot complement.We also describe a generalization of the volume conjecture that corresponds to a deformation of the complete hyperbolic structure of a knot complement. This generalization would relate the colored Jones polynomial of a knot to the volume and the Chern–Simons invariant of a certain representation of the fundamental group of the knot complement to the Lie group SL(2;C).We finish by mentioning further generalizations of the volume conjecture.
Volumetric Discrete Geometry (Discrete Mathematics and Its Applications)
by Karoly Bezdek Zsolt LangiVolume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the recent aspects of volume, introduces problems related to it, and presents methods to apply it to other geometric problems. Part I of the text consists of survey chapters of selected topics on volume and is suitable for advanced undergraduate students. Part II has chapters of selected proofs of theorems stated in Part I and is oriented for graduate level students wishing to learn about the latest research on the topic. Chapters can be studied independently from each other. Provides a list of 30 open problems to promote research Features more than 60 research exercises Ideally suited for researchers and students of combinatorics, geometry and discrete mathematics
Vom Referat bis zur Abschlussarbeit: Wissenschaftliche Texte perfekt produzieren, präsentieren und publizieren
by Bruno P. KremerDiese praxisnahe Anleitung bietet punktgenau dosiert „Erste Hilfe" beim Erstellen schriftlicher Arbeiten im Studium der naturwissenschaftlichen Fächer, aber auch in der gymnasialen Oberstufe oder im Beruf. Der Autor leistet Hilfestellung bei der Suche nach aktuellen Informationen, der Gliederung des Stoffs, beim korrekten Zitieren sowie der Gestaltung von Seitenlayout, Grafiken und Tabellen. Die 3. Auflage wurde überarbeitet und u. a. um einen Abschnitt speziell zur Bachelor-Arbeit ergänzt.
Vom Spiegel des Universums: Eine Geistesgeschichte der Mathematik
by Wolfgang Tschirk«Alle Formeln und Resultate sind fertig, nur den Weg muss ich noch finden, auf dem ich zu ihnen gelangen werde», soll Gauß einmal gesagt haben. Um den Weg, um die vielen Wege zu den Formeln und Resultaten der Mathematik, geht es in diesem Buch. Geboren aus der Lust am Wissen, genährt von der Naturphilosophie, begrenzt nur von den Grenzen des Denkens, stellt die Mathematik dessen Werkzeug und Gegenstand dar. Wir folgen ihren Spuren von der Antike bis in unsere Tage. In acht Kapiteln führt das Buch durch zweitausend Jahre Wissenschaft von den Zahlen, den Figuren, den Gleichungen, von Differential und Integral, vom Zufall, von den Räumen, den Mengen und den logischen Schlüssen.
Vom Universum des Denkens: Eine Geistesgeschichte der Logik
by Wolfgang TschirkLogik ist überall: im vernunftgemäßen Urteil, in der Einsicht, die den Glauben ergänzt, in Sprache und Mathematik, in einer aufgeklärten Ethik und in der Frage nach der Wahrheit und den Grenzen des Wissens. Sie scheint unverzichtbar, selbstverständlich und immer schon da gewesen zu sein, solange Menschen denken. Doch auch die Logik musste erst geschaffen werden – auch sie blickt, wie alle klassischen Wissenschaften, auf ein fünfundzwanzig Jahrhunderte währendes Entstehen zurück, und viele der größten Geister haben an ihr gebaut. Davon berichtet dieses Buch.
Von der Mathematisierung in der Ökonomie zur modernen Finanzmathematik: Zeitzeugen berichten
by Agnes HandwerkUnterstützt von vielen historischen Dokumenten und Interviews mit Zeitzeugen geht dieses Werk auf ein bedeutsames Thema der Wissenschaftsgeschichte ein: die Entstehung der modernen Finanzmathematik in der zweiten Hälfte des letzten Jahrhunderts.Einführend geht der bekannte Finanzmathematiker Hans Föllmer auf die Entstehungsgeschichte dieser neuen akademischen Disziplin ein und berichtet, wie die neoklassische Wirtschaftstheorie in den 1960er Jahren immer weitere Verbreitung findet und mit ihrer Formalisierung junge Mathematiker anzieht. Dieser zunehmende wissenschaftliche Austausch zwischen Ökonomen und Mathematikern, wegweisend hier eine Gruppe um Werner Hildenbrand an der Universität Bonn, der auch Hans Föllmer angehört, führt zu einer Mathematisierung und damit grundlegenden Änderung der Finanzwissenschaft. Vor allem die Theoriebildung erhält einen enormen Aufschwung, stark unterstützt durch neugegründete Fachzeitschriften, was zu einer Festigung der Finanzmathematik als eigenständige akademische Disziplin führt. Das Buch stellt die Entwicklung dieser modernen Wissenschaft anschaulich, verständlich und anhand vieler Zeitzeugenberichte dar, geht am Ende aber auch auf Grundlagenfragen ein: Schon seit den 1990er Jahren, und dann vor allem nach der Finanzkrise 2008, stellen Wissenschaftler die Frage, ob sich gesellschaftliche Prozesse oder das Verhalten von Akteuren an Finanzmärkten überhaupt korrekt mit Methoden der Naturwissenschaften modellieren lassen.
Von der Relativitätstheorie zu den Maxwell-Gleichungen
by Jan-Markus SchwindtDie Elektrodynamik wird meistens in der historisch orientierten Reihenfolge behandelt, in der das elektrische und magnetische Feld zunächst als separate Objekte eingeführt und schließlich über die Maxwell-Gleichungen miteinander verknüpft werden. Die Lorentz-Symmetrie der Theorie und die Vereinigung der beiden Felder im Feldstärketensor werden üblicherweise erst am Ende gezeigt, obwohl sich die Gleichungen dadurch vereinfachen und sie erst so in allen Bezugssystemen gelten.Damit durchläuft der Studierende zwar die historische Entwicklung, muss aber dann zum Ende der Vorlesung alles rückblickend verstehen und neu einordnen. Dieses Buch geht den umgekehrten, deduktiven Weg, der die Elektrodynamik von vornherein auf das Fundament der Speziellen Relativitätstheorie stellt und von da aus – gegenüber dem üblichen Vorgehen sozusagen "rückwärts" – die bekannten Phänomene und Zusammenhänge ableitet. Dieses Vorgehen erlaubt eine wesentlich straffere und – was die Rolle des Elektromagnetismus im Gesamtzusammenhang der Theoretischen Physik angeht – klarere Behandlung.