Matematik

Unravel the intricate relationship between quantum mechanics and highly-curved spacetime in this groundbreaking book by Dr. Kuro Aksara. Through advanced mathematical analysis, Aksara explores the fusion of quantum mechanics and general relativity, and delves into the quantum dynamics of black holes, quantum cosmology, entanglement, quantum gravity, quantum technology, and more. Prepare to embark on a quantum voyage into the unknown, where the boundaries of our understanding are pushed to their limits.

Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3 rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.

In the rapidly evolving landscape of nonlinear control systems, this reprint stands as a beacon of knowledge, showcasing the remarkable progress made over the last few decades. With a focus on design methodologies and their applications, this text employs various mathematical tools to address the myriad challenges inherent in nonlinearly controlled systems.This reprint extends its reach beyond traditional boundaries, presenting applications of nonlinear control across diverse fields such as energy, health care, robotics, biology, and big data research. As technology continues to advance, nonlinear control emerges as a critical player in shaping the future of theory and technology adoption across these domains.Despite the wealth of the existing literature, synthesizing control strategies for a broader class of nonlinear systems, especially those integrated with emerging technologies in communication and computation, remains a formidable task. This reprint addresses this gap, providing a cutting-edge collection of articles that push the boundaries of both theoretical background and practical applications. With its emphasis on novel developments and the broader class of applications, this reprint opens doors to new possibilities, making it a must-read for anyone seeking to navigate the intricate challenges of nonlinear control systems in the 21st century.

"Differential Equations" by Dr. Upton is a captivating journey through the mathematical landscapes of calculus, offering a rich exploration of historical context, first and second-order equations, systems, Laplace transforms, numerical methods, and real-world applications. With insightful content and advanced topics, this book inspires a deep understanding of complex concepts while providing practical applications in science and engineering.

This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.

Voronoi diagrams, named after the Russian mathematician Georgy Feodosievych Voronoy, are geometric structures that have been extensively studied in Computational Geometry. A Voronoi diagram can be constructed for a set of geometric objects called sites. The geometric objects can be points, lines, circles, curves, surfaces, spheres, etc. A Voronoi diagram divides the space into regions called Voronoi cells such that there is a Voronoi cell corresponding to each object in the input set. A Voronoi cell is a set of points closer to the corresponding object than any other object in the input set. Applications of the Voronoi diagram can be seen in various ¿elds of science and engineering. Voronoi diagram is used in the motion planning and collision avoidance for robotic motion. Candeloro used the Voronoi diagram of a point set in a 3D space to develop a path-planning system for Unmanned Underwater Vehicles (UUVs). In town planning, the Voronoi diagram can be used for the e¿cient allocation of resources. Image segmentation and feature extraction are other areas where properties of the Voronoi diagram are utilized. similar applications can be seen in disease research and diagnosis. Voronoi diagram of a set of circles is used for sensor deployment where the radius of a circle represents the range of a sensor. It is also used in cable packing of electric wires to ¿nd the enclosing circle with a minimum radius.

El objetivo de la obra es contribuir a la calidad del proceso de enseñanza-aprendizaje de resolución de problemas matemáticos en la disciplina Matemática en la Escuela de Formación de Profesores para la Enseñanza Primaria en Angola. La estrategia tiene una naturaleza didáctica, puesto que está dirigida a la transformación del proceso de enseñanza-aprendizaje, considerando la actividad del profesor en unidad indisoluble con la actividad de los estudiantes y el grupo, así como la relación dialéctica de los componentes didácticos, tiene en cuenta una visión sistémica de la resolución de problemas matemáticos, a partir de la integración de la enseñanza basada en problemas y la enseñanza de la resolución de problemas que potencia la utilización de las TIC, de los procedimientos heurísticos y de los componentes metacognitivos y afectivo, en correspondencia con las necesidades formativas de los estudiantes y el grupo. Los resultados de la consulta a especialista y de la aplicación de la estrategia mediante un pre-experimento permitieron comprobar que la estrategia didáctica elaborada es viable, pues se corroboran cambios en el proceso de enseñanza-aprendizaje.

In the second half of the 19th and the first half of the 20th century, nearly one-third of the population of today¿s Slovenia permanently settled in countries around the world. Many more were traveling back and forth, searching for work to ensure the survival of the family members left behind at home and the prosperity for the families and communities they were creating abroad. From one of the smallest nations in Europe, barely reaching one and a half million inhabitants at the time, people departed in numbers reaching 440,000. This book tells their stories, about the "daring dreams of the future," as the Slovenian poet Oton ¿upanc¿ic¿¿whose words open the book¿so beautifully put it. The people who left took recipes for their foods, accordions for their music, and love for their culture and language, which was, and has remained, a linguistic island between Vienna and Venice. In their new communities, they built homes, churches, and cultural institutions that have survived until today.

"From the New York Times bestselling author of The Signal and the Noise, the definitive guide to our era of risk-and the players raising the stakes In the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates "The River," or those whose mastery of risk allows them to shape-and dominate-so much of modern life. These professional risk takers-poker players and hedge fund managers, crypto true-believers and blue-chip art collectors-can teach us much about navigating the uncertainty of the 21st century. By embedding within the worlds of Doyle Brunson, Peter Thiel, Sam Bankman-Fried, Sam Altman, and many others, Silver offers insight into a range of issues that affect us all, from the frontiers of finance to the future of AI. The River has increasing amounts of wealth and power in our society, and understanding their mindset-including the flaws in their thinking-is key to understanding what drives technology and the global economy today. There are certain commonalities in this otherwise diverse group: high tolerance for risk; appreciation of uncertainty; affinity for numbers; skill at de-coupling; self-reliance and a distrust of the conventional wisdom. For the River, complexity is baked in, and the work is how to navigate it, without going beyond the pale. Taking us behind-the-scenes from casinos to venture capital firms to the FTX inner sanctum to meetings of the effective altruism movement, On the Edge is a deeply-reported, all-access journey into a hidden world of powerbrokers and risk takers"--

The mathematical theory of tangles, the centrepiece of the celebrated Robertson-Seymour theory of graph minors, finds precise structure in imprecise data. Assuming only basic undergraduate mathematics, this book shows how tangles can identify, relate, and structure types in data: of behaviour, political views, texts, or proteins.

Diagnostische Kompetenz ist eine der zentralen Kompetenzen von Lehrkräften. Diese Kompetenz hängt von der jeweiligen diagnostischen Situation ab. Das Analysieren von reichhaltigen Schüler*innendokumenten, wie sie zum Beispiel bei der Bearbeitung offener Lernangebote entstehen, wurde als diagnostische Situation bisher kaum betrachtet. Das vorliegende Buch widmet sich daher der Operationalisierung und Förderung diagnostischer Kompetenz bezüglich der Analyse von Schüler*innendokumenten zu offenen Lernangeboten der Arithmetik. Dazu wird eine Operationalisierung der diagnostischen Kompetenz und insbesondere des diagnostichen Denkens als Synthese bisheriger Forschung vorgeschlagen. Die Operationalisierung stützt sich auf die Adaption epistemischer Aktivitäten und einen adaptierten Prozess des Anpassens und Vergleichens. Weiter werden zwei empirische Studien vorgestellt, die die Wirksamkeit verschiedener Interventionen zur Förderung diagnostischer Kompetenz nachweisen können.

Dieses essential stellt in kondensierter Form eine Neuinterpretation der Weierstraß'schen Konstruktion der reellen Zahlen vor: Ein vergleichsweise neuer Quellenfund lässt darauf schließen, dass der Weierstraß¿sche Zahlbegriff bereits auf Mengenbegriffen basierte und somit sehr viel elementarer ist, als bislang angenommen wurde.Die beiden bislang bekanntesten Alternativdefinitionen der reellen Zahlen ¿ mittels rationaler Folgen und Konvergenz (Cantor) bzw. als Segmente (Dedekind) ¿ werden hier ebenfalls kurz erläutert und mit der Weierstraß¿schen Konstruktion verglichen.Eine ausführliche Darstellung anhand der Originalquellen findet sich in Spalt, Die Grundlegung der Analysis durch Karl Weierstraß (Springer Spektrum, 2022).

This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.

This book provides a captivating journey through the realms of classical and quantum systems as it unravels the profound influence that noise may have on their static and dynamic properties. The first part of the book offers succinct yet enlightening discussions on foundational topics related to noise. The second part focuses on a variety of applications, where a diverse spectrum of noise effects in physical systems comes to life, meticulously presented and thoughtfully analyzed. Whether you are a curious student or a dedicated researcher, this book is your key to gaining invaluable insights into noise effects in physical systems. ¿The book has the merit of presenting several topics scattered in the literature and could become a very useful reference.¿ Giovanni Jona-Lasinio, Sapienza ¿ Università di Roma, Italy

The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers¿ equations, and elliptic (Schrödinger) equation. Despite of a long history especially in development of the theoretical background of these methods there are open questions in their constructive implementation in numerical solving the multidimensional BVPs having additional requirement on physical parameters or desirable properties of its approximate solutions. Over the last two decades many papers on this topics have been published, in which new constructive approaches to numerically solving the multidimensional BVPs were proposed, and its highly desirable to systematically collect these results. This motivate us to write thus monograph based on our research results obtainedin collaboration with the co-authors. Since the topic is importance we believe that this book will be useful to readers, graduate students and researchers interested in the field of computational physics, applied mathematics, numerical analysis and applied sciences

In der Arbeit des Künstlers Titus Schade geht es um Malerei und um ihre visuelle Räumlichkeit. In seinen an Kulissen erinnernden Umgebungen entwickelt er Orte, die mal wie ein Modell, mal wie eine Theaterbühne wirken. So erfindet Schade in seinen Bildern eine Reihe verschiedener Architekturen und Ausstattungsstücke, die den Betrachter in private Räume führen. Dabei versucht er nicht, die Wirklichkeit abzubilden. Vielmehr arbeitet er mit Ersatzelementen, die er in einer in sich geschlossenen Umgebung anordnet. Seine Formen und die meist architektonischen Raumstrukturen werden auf geradezu barocke Art beleuchtet. Klassische Landschaften begegnen geometrischen Formen, deren Zeitlosigkeit eine universelle Lesart erlaubt. TITUS SCHADE (*1984, Leipzig), einer der bedeutendsten Künstler der jungen deutschen Malerei, war Schüler der Leipziger Akademie der Bildenden Künste, unter anderem bei Neo Rauch. Er lebt und arbeitet in Leipzig. Seine Arbeit wurde in zahlreichen Einzel- und Gruppenausstellungen in Deutschland gezeigt. Titus Schade wird vertreten durch die Galerie EIGEN + ART, Leipzig / Berlin.

This book presents the econometric foundations and applications of multi-dimensional panels, including modern methods of big data analysis. In light of the big data revolution and the emergence of higher dimensional panel data sets, it provides new results to synthesize existing knowledge on the field. The first, theoretical part of the volume is providing the econometric foundations to deal with these new high-dimensional panel data sets. It not only synthesizes our current knowledge, but mostly, presents new research results. The second empirical part of the book provides insight into the most relevant applications in this area. These chapters are a mixture of surveys and new results, always focusing on the econometric problems and feasible solutions.This second extended and revised edition provides an update of all existent chapters to reflect on new developments in the area as well as several new chapters on topics such as machine learning, nonparametric models,networks, and multi-dimensional panels in health economics. The book serves as a standard reference work, a textbook for graduate students in economics, and a source of background material for professionals conducting empirical studies.

This book aims to establish a systematic theory on the synchronization for wave equations with locally distributed controls. It is structured in two parts. Part I is devoted to internal controls, while Part II treats the case of mixed internal and boundary controls. The authors present necessary mathematical formulations and techniques for analyzing and solving problems in this area. They also give numerous examples and applications to illustrate the concepts and demonstrate their practical relevance. The book provides an overview of the field and offers an in-depth analysis of new results with elegant proofs. By reading this book, it can be found that due to the use of internal controls, more deep-going results on synchronization can be obtained, which makes the corresponding synchronization theory more precise and complete.Graduate students and researchers in control and synchronization for partial differential equations, functional analysis find this book useful. It is also an excellent reference in the field. Thanks to the explicit criteria given in this book for various notions of controllability and synchronization, researchers and practitioners can effectively use the control strategies described in this book and make corresponding decisions regarding system design and operation.