Leningrad Mathematical Olympiads (1961-1991)
This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11-12 through 17-18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961-1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period -- on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.
Random Patterns and Structures in Spatial Data
The book presents a general mathematical framework able to detect and to characterize, from a morphological and statistical perspective, patterns hidden in spatial data. The mathematical tool employed is a Gibbs point process with interaction, which permits us to reduce the complexity of the pattern. It presents the framework, step by step, in three major parts: modeling, simulation, and inference. Each of these parts contains a theoretical development followed by applications and examples.Features: Presents mathematical foundations for tackling pattern detection and characterisation in spatial data using marked Gibbs point processes with interactions Proposes a general methodology for morphological and statistical characterisation of patterns based on three branches, probabilistic modeling, stochastic simulation, and statistical inference Includes application examples from cosmology, environmental sciences, geology, and social networks Presents theoretical and practical details for the presented algorithms in order to be correctly and efficiently used Provides access to C]+ and R code to encourage the reader to experiment and to develop new ideas Includes references and pointers to mathematical and applied literature to encourage further study The book is primarily aimed at researchers in mathematics, statistics, and the above-mentioned application domains. It is accessible for advanced undergraduate and graduate students, so could be used to teach a course. It will be of interest to any scientific researcher interested in formulating a mathematical answer to the always challenging question: what is the pattern hidden in the data?
Leningrad Mathematical Olympiads (1961-1991)
This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11-12 through 17-18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961-1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period -- on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.
Theory of Stochastic Integrals
Theory of Stochastic Integrals aims to provide an answer to the problem of phenomena that cannot be analyzed through the classical It繫 theory by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales.
Database Systems for Advanced Applications
The seven-volume set LNCS 14850-14856 constitutes the proceedings of the 29th International Conference on Database Systems for Advanced Applications, DASFAA 2024, held in Gifu, Japan, in July 2024. The total of 147 full papers, along with 85 short papers, presented together in this seven-volume set was carefully reviewed and selected from 722 submissions. Additionally, 14 industrial papers, 18 demo papers and 6 tutorials are included. The conference presents papers on subjects such as: Part I: Spatial and temporal data; database core technology; federated learning. Part II: Machine learning; text processing. Part III: Recommendation; multi-media. Part IV: Privacy and security; knowledge base and graphs. Part V: Natural language processing; large language model; time series and stream data. Part VI: Graph and network; hardware acceleration. Part VII: Emerging application; industry papers; demo papers.
Approximation and Online Algorithms
This book constitutes the refereed proceedings of the 22nd International Workshop on Approximation and Online Algorithms, WAOA 2024, held in Egham, UK, during September 5-6, 2024. The 15 full papers included in this book were carefully reviewed and selected from 47 submissions. They were organized in topical sections as follows: algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for designing and analyzing approximation and online algorithms, resource augmentation, and scheduling problems.
Very First Steps in Random Walks
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Seminal Ideas and Controversies in Statistics
Statistics has developed as a field through seminal ideas and fascinating controversies. This book concerns a wide-ranging set of 13 important statistical topics, grouped into three general areas.
Algebras of Unbounded Operators
Derivations on von Neumann algebras are well understood and are always inner, meaning that they act as commutators with a fixed element from the algebra itself. The purpose of this book is to provide a complete description of derivations on algebras of operators affiliated with a von Neumann algebra. The book is designed to serve as an introductory graduate level to various measurable operators affiliated with a von Neumann algebras and their properties. These classes of operators form their respective algebras and the problem of describing derivations on these algebras was raised by Ayupov, and later by Kadison and Liu. A principal aim of the book is to fully resolve the Ayupov-Kadison-Liu problem by proving a necessary and sufficient condition of the existence of non-inner derivation of algebras of measurable operators. It turns out that only for a finite type I von Neumann algebra M may there exist a non-inner derivation on the algebra of operators affiliated with M. In particular, it is established that the classical derivation d/dt of functions of real variables can be extended up to a derivation on the algebra of all measurable functions. This resolves a long-standing problem in classical analysis.
A Bridge Between Lie Theory and Frame Theory
Comprehensive textbook examining meaningful connections between the subjects of Lie theory, differential geometry, and signal analysis A Bridge Between Lie Theory and Frame Theory serves as a bridge between the areas of Lie theory, differential geometry, and frame theory, illustrating applications in the context of signal analysis with concrete examples and images. The first part of the book gives an in-depth, comprehensive, and self-contained exposition of differential geometry, Lie theory, representation theory, and frame theory. The second part of the book uses the theories established in the early part of the text to characterize a class of representations of Lie groups, which can be discretized to construct frames and other basis-like systems. For instance, Lie groups with frames of translates, sampling, and interpolation spaces on Lie groups are characterized. A Bridge Between Lie Theory and Frame Theory includes discussion on: Novel constructions of frames possessing additional desired features such as boundedness, compact support, continuity, fast decay, and smoothness, motivated by applications in signal analysis Necessary technical tools required to study the discretization problem of representations at a deep level Ongoing dynamic research problems in frame theory, wavelet theory, time frequency analysis, and other related branches of harmonic analysis A Bridge Between Lie Theory and Frame Theory is an essential learning resource for graduate students, applied mathematicians, and scientists who are looking for a rigorous and complete introduction to the covered subjects.
Mathematical Modelling for Engineering and Physical Applications
This edited volume from mathematical modelling experts employs a structured approach to showcase the latest research and provide a comprehensive guide to the principles, techniques, and practical applications of mathematical modelling in the fields of engineering and the physical sciences.
Braids, Conformal Module, Entropy, and Gromov's Oka Principle
This book studies the relation between conformal invariants and dynamical invariants and their applications, taking the reader on an excursion through a wide range of topics. The conformal invariants, called here the conformal modules of conjugacy classes of elements of the fundamental group, were proposed by Gromov in the case of the twice punctured complex plane. They provide obstructions to Gromov's Oka Principle. The invariants of the space of monic polynomials of degree n appeared earlier in relation to Hilbert's 13th Problem, and are called the conformal modules of conjugacy classes of braids. Interestingly, the conformal module of a conjugacy class of braids is inversely proportional to a popular dynamical invariant, the entropy, which was studied in connection with Thurston's celebrated theory of surface homeomorphisms. This result, proved here for the first time, is another instance of the numerous manifestations of the unity of mathematics, and it has applications. After prerequisites on Riemann surfaces, braids, mapping classes and elements of Teichm羹ller theory, a detailed introduction to the entropy of braids and mapping classes is given, with thorough, sometimes new proofs. Estimates are provided of Gromov's conformal invariants of the twice punctured complex plane and it is shown that the upper and lower bounds differ by universal multiplicative constants. These imply estimates of the entropy of any pure three-braid, and yield quantitative statements on the limitations of Gromov's Oka Principle in the sense of finiteness theorems, using conformal invariants which are related to elements of the fundamental group (not merely to conjugacy classes). Further applications of the concept of conformal module are discussed. Aimed at graduate students and researchers, the book proposes several research problems.
Artificial Intelligence: Towards Sustainable Intelligence
This book constitutes the proceedings of the Second International Conference on Artificial Intelligence: Towards Sustainable Intelligence, AI4S 2024, held in Alcala de Henares, Spain, during October 3-4, 2024. The 16 full papers and 2 short papers included in this book were carefully reviewed and selected from 59 submissions. They deal with trustworthy AI and related topics, focusing on software and its engineering; software development process management and methods, etc.
Decision Sciences
This book constitutes the proceedings of the Second Decision Science Alliance International Summer Conference, DSA ISC 2024, held in Valencia, Spain, in June 2024. The 33 full papers and 38 short papers included in this book were carefully reviewed and selected from 101 submissions. At the core of DSA ISC'24 are in-depth discussions and analyses across a spectrum of technological domains. Notably, experts shared their knowledge on areas such as Artificial Intelligence & Machine Learning, Mathematical Optimization, Operational Research & Management Science, Statistics, Simulation, and Decision Processes Analysis. Each of these areas represents a key aspect of decision science, contributing to the interdisciplinary nature of the conference.
Optimization and Applications
This book constitutes the refereed proceedings of the 15th International Conference on Optimization and Applications, OPTIMA 2024, held in Petrovac, Montenegro, during September 16-20, 2024. The 24 full papers presented in this volume were carefully reviewed and selected from 60 submissions. They are grouped into the following topics: Mathematical Programming; Global Optimization; Optimal Control; Game Theory and Mathematical Economics; Optimization in Economics and Finance; and Applications.
Decision Sciences
This book constitutes the proceedings of the Second Decision Science Alliance International Summer Conference, DSA ISC 2024, held in Valencia, Spain, in June 2024. The 33 full papers and 38 short papers included in this book were carefully reviewed and selected from 101 submissions. At the core of DSA ISC'24 are in-depth discussions and analyses across a spectrum of technological domains. Notably, experts shared their knowledge on areas such as Artificial Intelligence & Machine Learning, Mathematical Optimization, Operational Research & Management Science, Statistics, Simulation, and Decision Processes Analysis. Each of these areas represents a key aspect of decision science, contributing to the interdisciplinary nature of the conference.
Theoretical Foundations of Asset Pricing
This text provides an advanced introduction to the modeling of competitive financial markets, encompassing arbitrage and equilibrium pricing of financial contracts, as well as optimal lifetime consumption and portfolio choice. Notable features include its coverage of recursive utility in discrete and continuous time and several results not previously available in book form. Each chapter concludes with a set of exercises, with solutions available to verified instructors. Ideal as a graduate-level course text, this book can also serve as a valuable reference for researchers and finance industry practitioners. Readers with a finance focus can use the text to build analytical foundations for a significant component of the economics of financial markets, while readers with a mathematics focus will find a well-motivated introduction to basic tools of stochastic analysis and convex analysis.
Geocomputation with Python
Geocomputation with Python is a comprehensive resource for working with geographic data with the most popular programming language in the world. The book gives an overview of Python's capabilities for spatial data analysis, as well as dozens of worked-through examples covering the entire range of standard GIS operations. A unique selling point of the book is its cohesive and joined-up coverage of both vector and raster geographic data models and consistent learning curve. This book is an excellent starting point for those new to working with geographic data with Python, making it ideal for students and practitioners beginning their journey with Python.Key features: Showcases the integration of vector and raster datasets operations. Provides explanation of each line of code in the book to minimize surprises. Includes example datasets and meaningful operations to illustrate the applied nature of geographic research. Another unique feature is that this book is part of a wider community. Geocomputation with Python is a sister project of Geocomputation with R (Lovelace, Nowosad, and Muenchow 2019), a book on geographic data analysis, visualization, and modeling using the R programming language that has numerous contributors and an active community.The book teaches how to import, process, examine, transform, compute, and export spatial vector and raster datasets with Python, the most widely used language for data science and many other domains. Reading the book and running the reproducible code chunks within will make you a proficient user of key packages in the ecosystem, including shapely, geopandas, and rasterio. The book also demonstrates how to make use of dozens of additional packages for a wide range of tasks, from interactive map making to terrain modeling. Geocomputation with Python provides a firm foundation for more advanced topics, including spatial statistics, machine learning involving spatial data, and spatial network analysis, and a gateway into the vibrant and supportive community developing geographic tools in Python and beyond.
Spectral Theory of Nonautonomous Dynamical Systems and Applications
Innovation and Emerging Trends in Computing and Information Technologies
This book constitutes the proceedings of the First International Conference on Innovation and Emerging Trends in Computing and Information Technologies, IETCIT 2024, held in Mohali, India, in March 1-2, 2024. The 44 full papers presented in these two volumes were carefully reviewed and selected from 417 submissions. The papers are organized in the following topical sections: Part I: machine learning and deep learning; pattern and speech recognition; internet of things (IoT). Part II: data science and data analytics; communication, network and security.
Innovation and Emerging Trends in Computing and Information Technologies
This book constitutes the proceedings of the First International Conference on Innovation and Emerging Trends in Computing and Information Technologies, IETCIT 2024, held in Mohali, India, in March 1-2, 2024. The 44 full papers presented in these two volumes were carefully reviewed and selected from 417 submissions. The papers are organized in the following topical sections: Part I: machine learning and deep learning; pattern and speech recognition; internet of things (IoT). Part II: data science and data analytics; communication, network and security.
Sentiment Analysis of Covid-19 Tweets Using Machine Learning Algorithm
A Comprehensive Summary of the Benford's Law Phenomenon
Our digital language system writes numbers by the convenient utilisation of the ten digits 0 to 9 in much the same way as the English language system writes sentences and books by the convenient utilisation of the 26 letters A to Z. Against all common sense or intuition, the spread of these ten digits within numbers of random data is not uniform, but rather highly uneven. Benford's Law predicts that the first digit on the left-most side of numbers is proportioned between all possible digits 1 to 9 approximately according to LOG(1 + 1/digit), such that occurrences of low digits such as 1, 2, and 3 in the first position are much more frequent than occurrences of high digits such as 7, 8, and 9. Remarkably, Benford's Law is found to be valid in almost all real-life statistics, from data relating to physics, chemistry, and biology to data relating to economics, engineering, and governmental censuses. Benford's Law stands as the only common thread running through and uniting all scientific disciplines.This book represents an intense and concentrated effort by the author to narrate this digital, numerical, and quantitative story of the Benford's Law phenomenon as briefly and as concisely as possible, while still ensuring a comprehensive coverage of all its aspects, results, causes, explanations, and perspectives. The most recent research results and discoveries in this field are included within this book in such a way as to be comprehensible and engaging to readers of all proficiencies.
Handbook of Generalized Pairwise Comparisons
This book covers the statistical foundations of generalized pairwise comparisons (GPC), applications in various disease areas, and considerations for patient-centricity in clinical research. It stands as an essential resource for a more holistic and patient-centric assessment of treatment effects.
Measure Theory and Fine Properties of Functions
This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.
Applied Statistics with Python
Applied Statistics with Python concentrates on applied and computational aspects of statistics, focussing on conceptual understanding and Python-based calculations. It compiles multiple aspects of applied statistics, teaching useful skills in statistics and computational science.
Distributed Generation and Reliability of Local Distribution System
Modelling returns in South Africa using Jump Diffusion Processes
Set Theo & Found Math (V1-2nd Ed)
This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.
Mathematical Methods for Curves and Surfaces II
Contains more than fifty carefully refereed and edited full-length papers on the theory and applications of mathematical methods arising out of the Fourth International Conference on Mathematical Methods in Computer Aided Geometric Design, held in Lillehammer, Norway, in July 1997.
Mathematical Models in Medical and Health Science
A unique assemblage of cutting-edge research on mathematical models in biology and medicine. This book is composed of refereed and carefully edited research articles derived from the Conference on Mathematical Models in Medical and Health Sciences, held at Vanderbilt University in conjunction with the thirteenth annual Shanks Lectures Series (May 1997).
Advanced Topics on Semilinear Evolution Equations
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fr矇chet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
