This volume is a collection of research contributions highlighting recent advances in partial differential equations, inverse and boundary value problems, spectral analysis, and fractional calculus. The book reflects current trends in mathematical analysis and mathematical physics, explores the unique solvability of inverse problems for a wide range of differential equations, and demonstrates the growing importance of fractional and nonlocal operators in the modelling of complex phenomena. By showcasing the rich interplay between inverse problems, spectral methods, and fractional differential equations, this collection offers valuable insights into emerging directions of research and serves as a useful resource for researchers, graduate students, and specialists working in these fields. The volume aims to stimulate further research, collaboration, and innovation in these dynamic areas of modern mathematics.

The current volume is a comprehensive collection showcasing the latest advancements in the fields of Analysis and Partial Differential Equations (PDE) in Latin America. This book, which continues the series dedicated to Latin American mathematical research, highlights innovative perspectives from this vibrant community. It features contributions from leading researchers, each providing new insights and exploring future directions in Analysis and PDE. The book aims to bring greater visibility to the substantial mathematical activity in Latin America, which is often published in Spanish and remains less known in the broader mathematical literature typically written in English. It provides a unique view into the dynamic research landscape of Latin America, highlighting both theoretical advancements and practical applications, such as models for epidemics, population dynamics, climatological risks, and medical diagnostics. Analysis and PDE are highly active areas in mathematics due to their wide-ranging applications, from physical phenomena like heat diffusion to biological models describing the cardiovascular system. These fields, with over 200 years of tradition, are deeply integrated with modern numerical methods and are linked to problems in artificial intelligence, big data, and control theory. Latin America, with its vast Spanish-speaking community and significant mathematical output, is a key player in these fields. This book aims to popularize the region's innovative research, presenting important results from young and established Latin American mathematicians. Their work addresses local challenges with global relevance, providing insights valuable to other regions with similar conditions. In particular, this book includes contributions from some speakers at the ICMAM Latin America 2025 conference.

This proceedings volume gathers peer-reviewed works presented at the "Arithmetic, K-Theory, and Algebraic Cycles" international conference held at Ohio State University, USA, from May 27-31, 2025. Papers in this volume cover cutting-edge aspects of these theories, offering a snapshot of leading research in arithmetic and algebraic geometry, K-theory, and algebraic cycles. Contributions were submitted by researchers from the Americas, Europe, and Asia, with participation mostly in person. As a result of fertile cooperation between renowned researchers in the field and junior researchers, this volume will be of special appeal to both experienced mathematicians and graduate students seeking new avenues of research. Inhaltsverzeichnis Chapter 1 Tame and Curve-tame cohomology of ${\mathbb A}^1$ invariant \'etale sheaves.- Chapter 2 Zero cycles on bi-elliptic surfaces.- Cahpter 3 The Motivic and \'Etale Becker-Gottlieb transfer: the construction of the transfer.- Cahpter 4 The Motivic and \'Etale Becker-Gottlieb transfer and splittings.- Cahpter 5 Some remarks on Chow correspondences.- Chapter 6 Elementary interactions between line bundles, algebraic cycles and gerbes.- Chapter 7 Brauer groups of smooth split toric schemes and their fans.- Cahpter 8 Brauer groups of Horospherical varieties.- Chapter 9 On presentations of K-groups by generators and relations.- Chapter 10 Three vignettes on hypergeometric normal functions. Autorenportrait Roy Joshua is a full professor at the Ohio State University, USA. His research fields are algebraic geometry, K-theory, and arithmetic geometry. He has published over 46 papers in leading journals in his field. Patrick Brosnan is a full professor at the University of Maryland, College Park, USA. He currently works in algebraic geometry and has a number of publications in leading journals in his field. Connor Cassady is a visiting assistant professor at Colgate University. He received his PhD in Mathematics (2023) from the University of Pennsylvania under the supervision of Dr. David Harbater and was an Assistant Professor at the Ohio State University from August, 2023 through May, 2026.

This monograph presents a comprehensive treatment of Banach spaces with the Daugavet property and the geometric and operator-theoretic ideas that have emerged from Daugavet's celebrated norm identity. Covering more than sixty years of research, it brings together classical foundations and modern developments, with particular emphasis on the substantial progress achieved over the past quarter-century. Through a coherent and carefully organised exposition, the book highlights the connections between the main themes of the subject and provides a unified perspective on a diverse body of results. The presentation combines mathematical depth with a strong pedagogical orientation, making advanced developments accessible without sacrificing rigour.

TikZ is one of the most powerful systems for creating mathematical and technical illustrations in LaTeX, yet its extensive syntax and programming structure can make it challenging to learn. This book offers a practical approach that combines clear, systematic instruction with the capabilities of ChatGPT. Acting as tutor, coding assistant, debugger, and design partner, ChatGPT helps readers learn more quickly, experiment with confidence, and turn their ideas into polished figures. Each chapter is accompanied by a companion file, an optional supplement which explores the topic covered in greater depth. Companion files are hosted on GitHub; the link is included in the Introduction. Organized in three carefully structured levels-Beginner, Intermediate, and Advanced-the book progresses from fundamental drawing commands and node-based diagrams to coordinate calculations, graph drawing, reusable styles, custom keys, graphical components, layers, and professional workflows. Concise explanations, worked examples, exercises, capstone projects, and carefully designed prompts show not only how TikZ works, but also how to use ChatGPT effectively throughout the creative process. Written for students, researchers, educators, and authors in mathematics, computer science, engineering, and the sciences, the book emphasizes clear thinking, reusable design, and maintainable code. Readers will discover how sophisticated illustrations can grow from a small collection of fundamental ideas-and how TikZ and ChatGPT together can make the creation of accurate, elegant, publication-quality diagrams both accessible and enjoyable. Inhaltsverzeichnis I. The foundation (B): 50 commands.- 1 Getting started.- 2 Styling.- 3 Basic shapes and paths.- 4 Line, shape, and color style.- Node size and text formatting.- Beginner positioning.- 7 Beginner arrows, curves, and labels.- II. Intermediate TikZ.- 8 Paths, curves, and path labels.- 9 Coordinate calculations with calc.- 10 Loops and computed repetition.- 11 Matrices and structured layouts.- 12 Trees and hierarchical diagrams.- 13 Intersections and named paths.- Decorations and path effects.- 15 Scopes and transformations.- State diagrams and automata.- 17 Patters and backgrounds.- Commands and definitions for part III.- Part III Advanced TikZ.- 18 Pics and Keys.- 19 Custom shapes and anchors.- 20 Layers, backgrounds, and overlays.- 21 Advanced arrows and geometry.- 22 Graph drawing algorithms.- 23 Math computation.- 24 Clipping and transparency.- 25 Fitting and callouts.- 26 Externalization.- 27 Low-level PGF programming.- Commands and Definitions for Part IV.- Final Count. Autorenportrait George Grätzer is a Distinguished Professor Emeritus at the University of Manitoba. He has authored three other books on LaTeX: First Steps in LaTeX, Math into LateX, and Practical LaTeX. The book Math into LaTeX was chosen by the Mathematics Editor of Amazon.com as one of the ten best books of 2000. Grätzer has also written over 300 articles and more than 30 books on the subject of lattices and universal algebra. In addition, Grätzer is the founder of the international mathematical journal, Algebra Universalis; he was the editor-in-chief for about 50 years.

This volume presents selected papers from the "From Theory to Practice (T2P)" Workshop in Data Science held at the African Institute for Mathematical Sciences (AIMS) in Kigali, Rwanda. Written by experts from academia and industry, it aims to showcase cutting-edge developments and interdisciplinary approaches in data science. Topics covered include artificial intelligence, machine learning, statistics, quantum machine learning, and computational engineering. The volume will serve as a valuable reference for researchers, practitioners, and students looking to explore the latest trends and contributions in this evolving domain. Inhaltsverzeichnis Performance Analysis of Convolutional Neural Network Models for Breast Cancer Diagnosis.- Bellman operator convergence enhancements in reinforcement learning algorithms.- Investigating Higher-Order Connectivity for Epidemic Spread.

Dieses Buch führt in die Grundlagen der Gestaltung wirkungsvoller Präsentationsgrafiken mit der Open-Source-Software R ein: Anhand von 123 vollständigen Skript-Beispielen lernen Sie, aussagekräftige Abbildungen mit dem Base Graphics System von R zu erstellen bzw. individuell anzupassen - von Balken- und Säulendiagrammen, Bevölkerungspyramiden, Lorenzkurven, Boxplots und Streudiagrammen über Zeitreihen, Radardiagramme, Gantt-Diagramme, Heatmaps, Bump Charts, Mosaik- und Ballondiagramme bis hin zu unterschiedlichen Formen der geografischen Datenvisualisierung. Für jedes Beispiel werden reale Daten verwendet sowie die Abbildung und deren Programmierung Schritt für Schritt erläutert. Ein abschließendes Kapitel zur Gestaltung von Tabellen zeigt die Umsetzung eines konkreten Beispiels in mehreren Varianten und mit verschiedenen Paketen. Durch die direkt einsetzbaren Skripte ist das Buch für verschiedene Kenntnislevel in R gleichermaßen geeignet. Es dient als Inspiration oder Nachschlagewerk für verschiedenste Anwendungsfälle - etwa in Wissenschaft(skommunikation), Datenjournalismus und Marketing. Für die vorliegende 3. Auflage wurden umfassende Überarbeitungen, Aktualisierungen und Erweiterungen vorgenommen: Unter anderem wurden die enthaltenen Codes und Skripte leserfreundlicher formuliert sowie bei Bedarf aktualisiert; einige Beispiele wurden ergänzt. Das Kapitel zu interaktiven Visualisierungen gibt nun einen Einblick in die Steuerung des Online-Tools Datawrapper per API aus R heraus; ein Kapitel zu Tabellen wurde ergänzt. Inhaltsverzeichnis Daten für alle.- Teil I Grundlagen und Technik. Aufbau und technische Voraussetzungen.- Umsetzung in R.- Über R hinaus.- Zu den Beispielen.- Teil II Beispiele. Kategoriale Daten.- Verteilungen.- Zeitreihen.- Streudiagramme.- Karten.- Illustratives.- Anhang A Daten.- Literatur.- Index. Autorenportrait Thomas Rahlf arbeitet als Direktor in der Gruppe Qualitäts- und Verfahrensmanagement bei der Deutschen Forschungsgemeinschaft. Er hat über Methodologien der Statistik und Ökonometrie promoviert und ist Herausgeber einer Historischen Statistik von Deutschland. Den Themen Open Source, Datendesign und -visualisierung gilt seit vielen Jahren sein Interesse.

This monograph develops a field-theoretic framework for the analysis of point processes, treating them as random measures and generalized fields rather than purely combinatorial objects. By treating point processes in terms of empirical fields, generating functionals, and effective actions, it offers a unified analytical approach to their structure, dynamics, and inference. Standard constructions, such as Poisson processes, stochastic dynamics, and inference procedures, are recast as components of a single analytic structure. This makes explicit structural correspondences that are often implicit: between generating functions and entropy, cumulant hierarchies and interaction, convex duality and large deviations, stochastic evolution and functional differential equations, and Fisher information and precision geometry.

Dieses Open-Access-Essential leistet anhand ausgewählter Fallbeispiele einen ersten Beitrag zur Frage, ob generative KI-Systeme mathematische Lernprozesse verstehensorientiert unterstützen können. Es gibt Einblicke in Möglichkeiten und Grenzen, bietet Orientierung für deren mathematikdidaktische Einordnung und liefert Impulse für die Schulpraxis. Untersucht werden zwei Unterrichtssituationen: das Erklären eines mathematischen Inhalts und die Unterstützung bei einer konkreten Aufgabe. Antworten generischer, bildungs- und mathematikspezifischer KI-Systeme werden anhand dreier theoriegeleitet entwickelter mathematikdidaktischer Kriterien (fachliche Angemessenheit, konzeptueller Fokus sowie Lernendenorientierung und Adaptivität) untersucht. Diese bilden zugleich einen Vorschlag für einen übertragbaren Qualitätsrahmen. Die Analysen zeigen exemplarisch, dass viele KI-Systeme zwar fachlich angemessene Antworten liefern, dabei jedoch häufig einen schwach ausgeprägten konzeptuellen Fokus aufweisen sowie Lernendenorientierung und Adaptivität kaum berücksichtigen - die fachdidaktischen Anforderungen an eine konstruktive Unterstützung werden in den betrachteten Szenarien nur eingeschränkt erfüllt.

This book presents the foundations and concepts of modern combinatorics in a clear and illustrative manner. Its accessible exposition is aimed at students of mathematics, the natural sciences, computer science, and economics, and allows for an easy, example-driven approach to the methods of combinatorics. Beginning with the basic problems of combinatorics, the reader is gradually introduced to more advanced topics such as generating functions, recurrence relations and Möbius inversion, as well as graph polynomials and finite automata. A large number of examples and exercises with solutions facilitate understanding and support consolidation and practical application of the material. This book is a translation of the original German 4th edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.

This book explains what mathematical modeling is about, what considerations lead to established models, and how you can develop your own mathematical models. It covers applications from mechanics, population dynamics, microeconomics, and other fields of knowledge. At the same time, we reflect on what we do and what we often without realizing it assume when we model observed phenomena mathematically. People with scientific curiosity have always considered phenomena to be truly understood only when mathematical models have been established that provide accurate predictions. This curiosity persists today, leading to new insights, the development of modern approaches such as machine learning, and thus to ever new models. This book is a translation of the original German edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.

This book constitutes the refereed proceedings of the 33rd International Symposium on String Processing and Information Retrieval, SPIRE 2026, held in Hamilton, ON, Canada, during October 2026. The 19 full papers and 4 short papers included in this book were carefully reviewed and selected from 47 submissions. SPIRE continues the long and well-established tradition of encouraging high-quality research at the broad nexus of string processing, information retrieval, and computational biology.

This book presents a curated selection of papers from the International Conference on Sustainable Management and Advanced Research Technologies (IC-SMART 2026), held at the Rajarambapu Institute of Technology. It explores the critical intersection of sustainability and technological innovation, addressing the urgent need for resilient economies and societies in the face of environmental challenges and digital transformation. The chapters delve into key topics such as sustainable business models, circular economy strategies, ESG frameworks, and green finance. Readers will gain insights into smart resource management, climate-resilient infrastructure, and the role of AI and data analytics in sustainability. The volume also covers renewable energy systems, sustainable urban development, and responsible innovation ecosystems, offering a comprehensive view of the latest research and practical applications.

The chapters in this volume examine the pervasive issues of tax evasion and corruption, which affect both developing and developed countries. The book explores the detrimental effects these phenomena have on economies, including reduced public service provision and hindered economic growth. The contributions present findings from a PRIN research project funded by the Italian Ministry of University and Research (MUR) in 2022, focusing on theoretical models and empirical studies, particularly within the Italian context. The volume also includes papers presented at the Workshop "Tax Evasion and Corruption: Theoretical Approaches, Modeling Strategies, and Empirical Evidence", held at the University of Catania in May 2025. The results were subsequently presented at the PRIN2022 Final Conference "Tax Evasion and Corruption: Theoretical Models and Empirical Studies", held at the University of Macerata, in January 2026, with the participation of numerous representatives of institutions and other stakeholders. The volume investigates enforcement and monitoring tools and non-pecuniary factors influencing tax compliance, the relationship between industrial structure and tax evasion, and the impact of corruption on territorial resilience. Additionally, it addresses social influence, peer corruption, reciprocity effects, and behavioral models of tax compliance. This book is intended for academics, policymakers, researchers, and professionals working in institutions and organizations involved in the prevention and fight against tax evasion and corruption. Inhaltsverzeichnis Preface.- 1. Tax evasion and Industrial structure: a review [Coppier, Scaccia].- 2. Theoretical Models of Tax Evasion: A Survey [Bischi, Frollichi, Tramontana].3. Tax Evasion and Compliance: Evolutionary Dynamics and Behavioral Insights [De Giovanni, Lamantia, Pezzino].- 4. Corruption in public procurement: theory and evidence [Mammana, Michetti].- 5. Regional resilience in Europe: the role of institutions and structural change [Cutrini, Ninivaggi]. 6. Integrity and gender: Some empirical evidence from Italian municipalities [Scaglioni, Rizzo, Galli].- 7. Fighting Corruption and Enhancing Tax Revenue Collection in Italy: Strategies for Effective Governance [Lopez Gomez, Policardo, Sanchez Carrera].- 8. Understanding Tax Compliance: an experimental framework to analyze group influence on tax behaviors [Bianco, Gallicchio, Merlone].- 9. Nudge and Tax compliance: A Survey of the experimental literature [Canova, Tramontana]. Autorenportrait Fabio Lamantia is Full Professor of Mathematical Economics at the University of Catania and Coordinator of the PhD Programme in Economics, Management and Decision Making (EMADE). His research interests include game theory, dynamic systems, and socio-economic modeling. Elisabetta Michetti is Full Professor of Mathematical Economics at the University of Macerata and member of the Scientific Committee of AMASES (Italian Association for Mathematics Applied to Economic and Social Sciences). Her research interests include dynamic models on topics such as environmental economics, active aging, and the underground economy. Fabio Tramontana is Associate Professor of Mathematical Economics at the University of Urbino Carlo Bo. His research interests include nonlinear dynamics, heterogeneous-agent models, and behavioral economics.

This monograph develops a unified approach to some central questions of control theory in infinite-dimensional settings: whether a system can be steered to a desired state, how rapidly this can be achieved, and how much control effort is required. Working within the general framework of Banach spaces, it brings together controllability theory, minimum-time control, and minimum-norm control, emphasizing the relationships between these problems and the value functions that characterize them. Particular attention is given to quantitative estimates, maximum principles, and dynamic programming methods, which are developed in a common analytical framework and used to derive regularity and optimality results. The treatment also extends from linear systems to semilinear evolutions and differential inclusions, demonstrating that the underlying ideas remain effective in the presence of nonlinearities, uncertainties, and multivalued dynamics. Combining classical results with original research by the authors, this monograph provides both a coherent reference for researchers and an advanced introduction for graduate students working in infinite-dimensional control theory and optimization. Inhaltsverzeichnis Some Preliminaries in Functional Analysis.- Controllability of Linear Systems.- The Minimum Time and the Minimum Norm for Linear Control Systems.- Maximum Principles.- Semilinear Control Systems.- The Minimum-Time Function for Mulitvalued Semilinear Evolutions. Autorenportrait Ovidiu Cârja is a professor at the Alexandru Ioan Cuza University of Ia i and a researcher at the Romanian Academy, Ia i Branch. His research interests include controllability and time-optimal control for linear and nonlinear systems in Banach spaces, feedback controls, Lyapunov pairs, and viability and invariance theory. He is a coauthor of a monograph on viability, invariance, and applications published by Elsevier in 2007. Alina Ilinca Lazu is an associate professor at the Gheorghe Asachi Technical University of Ia i. Her research focuses on time-optimal controllability, with particular attention paid to feedback controls and Lyapunov pairs. She has also contributed to the study of near viability for nonlinear differential inclusions.

Aus den Rezensionen: "Was das Buch vor allem auszeichnet, ist die unkonventionelle Darstellungsweise. Hier wird Mathematik nicht im trockenen Definition-Satz-Beweis-Stil geboten, sondern sie wird dem Leser pointiert und mit viel Humor schmackhaft gemacht. In ungewöhnlich fesselnder Sprache geschrieben, ist die Lektüre dieses Buches auch ein belletristisches Vergnügen. Fast 200 sehr instruktive und schöne Zeichnungen unterstützen das Verständnis, motivieren die behandelten Aussagen, modellieren die tragenden Beweisideen heraus. Ungewöhnlich ist auch das Register, das unter jedem Stichwort eine Kurzdefinition enthält und somit umständliches Nachschlagen erspart". Wiss. Zeitschrift der TU Dresden Jetzt in der achten Auflage des bewährten Lehrbuches! Inhaltsverzeichnis Die Grundbegriffe.- Topologische Vektorräume.- Die Quotiententopologie.- Vervollständigung metrischer Räume.- Homotopie.- Die beiden Abzählbarkeitsaxiome.- CW-Komplexe.- Konstruktion von stetigen Funktionen auf topologischen Räumen.- Überlagerungen.- Der Satz von Tychonoff.- Letztes Kapitel. Mengenlehre. Rezension "... Es handelt sich um ein sehr überschaubares Werk, dessen Qualität wohl gerade darin liegt, daß es trotz Beschränkung im Umfang (gut 200 kleinformatige Seiten) einen schönen Einblick in die wichtigsten Grundideen der Topologie vermittelt. ... Sehr reizvoll in Jänichs Buch sind auch die zahlreichen suggestiven Abbildungen. Vor allem jene zu Beginn der Kapitel werden jeden Topologieliebhaber durch ihre manchmal geradezu poetische Originalität erfreuen." Internationale Mathematische Nachrichten Österreich Autorenportrait Prof. Dr. Klaus Jänich, Regensburg.

The third edition of this book offers original and advanced problems proposed from 1995 to 2026 at the Mathematics Olympiads, extending the previous edition by approximately 100 new pages of material. Versatile and comprehensive in content, this book of problems will appeal to students in nearly all areas of mathematics. Essential for undergraduate students, PhD students, and instructors, the problems in this book vary in difficulty and cover most of the core courses given at the undergraduate level, including calculus, algebra, geometry, discrete mathematics, measure theory, complex analysis, differential equations, and probability theory. Detailed solutions to all of the problems from Part I are supplied in Part II, giving students the ability to check their solutions and discover new and unexpected ideas. Most of the problems in this book are not technical and allow for short and elegant solutions. The problems given are unique and non-standard; solving them requires a creative approach as well as a deep understanding of the material. This book will prove to be useful to university instructors for composing assignments and preparing course material. Nearly all of the problems are authored by lecturers, PhD students, students, and alumni of the Faculty of Mechanics and Mathematics of Taras Shevchenko National University of Kyiv as well as by many others from Belgium, Canada, Great Britain, Hungary, and the United States.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This four-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section, and Part III includes a section commemorating Walter's prematurely deceased twin brother, Werner. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science.