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.
Completely Regular Semigroup Varieties
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Pol獺k's theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Pol獺k's theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
Introduction to Enumerative and Analytic Combinatorics
These award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author's goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field.
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.
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.
Advances in Fuzzy Logic and Artificial Neural Networks
In a world where uncertainty and complexity dominate decision-making processes, Advances in Neural Networks and Fuzzy Logic presents groundbreaking studies exploring the potential of these Artificial Intelligence approaches to solve real-world problems. The chapters cover applications across various fields, such as robust galaxy classification, simulations in weighted finite automata, stock price prediction, large-scale water purification selection, speech deficiency detection in children, and supply chain management. Advanced techniques such as deep neural networks, fuzzy clustering, SHAP, LIME, and Hesitant Fuzzy Linguistic Term Sets are explored. This reprint is helpful for researchers, engineers, and students who wish to understand the latest advancements in and practical applications of neural networks and fuzzy logic. Within these pages, you will discover how these technologies solve complex problems and foster more transparent and reliable decision-support systems, as well as the state of the art in Artificial Intelligence, where neural networks and fuzzy logic converge to tackle modern challenges with innovation and precision.
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.
The calculating engine
The calculating engine" is a classic book, that has held significant value throughout history, and to ensure its timeless wisdom is never lost, Alpha Editions has carefully preserved it by republishing it in a modern, accessible format for both present and future generations. Thoughtfully reformatted, retyped, and newly designed, this edition offers a clear and readable text-free from scanned copies of the original work. Alpha Editions is dedicated to breathing new life into antique and classic books, making these literary treasures available once again for readers who cherish history, culture, and timeless knowledge.
Journal of Applied Logics. IfCoLog Journal of Logics and their Applications. Volume 12, number 1, January 2025. Special Issue
Lectures on the H-Cobordism Theorem
Important lectures on differential topology by acclaimed mathematician John Milnor These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.
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.
Fractions for Dummies
An easy, straightforward, and fun guide for learning fractions and its counterparts Fractions For Dummies is the perfect strategy guide for both understanding and using one of math's most common (and most challenging) topic areas. You'll explore current solving strategies for fraction-related problems, and you'll also discover how to solve problems involving fractions' closely related cousins, decimals and percentages. Dive deep into the basics of these topics before moving on to more advanced uses, such as word problems, with the help of author and experienced math teacher Mark Zegarelli. This straightforward and intuitive book also includes: Techniques for working with mixed numbers (numbers that include whole amounts and fractions) and more Ways to add, subtract, multiply, and divide fractions with whole numbers and with each other Strategies for helping and supporting the young student in your life who's struggling with fractions, decimals, and/or percentages It's time you showed these math areas who's boss. Fractions For Dummies shows you just how easy fractions and the like can be!
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.
Spectral Theory of Nonautonomous Dynamical Systems and Applications
Sentiment Analysis of Covid-19 Tweets Using Machine Learning Algorithm
Geometric Gems (V2)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties.
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.
Geometric Gems (V2)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties.
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.
The Math Book
Math's infinite mysteries unfold in this updated edition of the award-winning The Math Book. Beginning millions of years ago with ancient "ant odometers," and moving through time to our modern-day quest for higher dimensions, prolific polymath Clifford Pickover covers major milestones in mathematical history. Among the numerous concepts readers will encounter as they dip into this inviting anthology: cicada-generated prime numbers, magic squares, and the butterfly effect. Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems. This reissue includes four new entries: 2013 (Bounded Gaps Between Primes), 2015 (Erdős Discrepancy Problem Solved), 2016 (Sphere Packing in Dimension 8), and 2023 (Einstein Tiles and Beyond). Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems.
