Introduction to Potential Theory
This monograph is devoted to harmonic analysis and potential theory. The authors study these essentials carefully and present recent researches based on the papers including by authors in an accessible manner for graduate students and researchers in pure and applied analysis.
Differential Geometry and Its Application, 2nd Edition
This Special Issue provides a platform to showcase the latest achievements in many branches of theoretical and practical mathematical studies. These relate to Riemannian theories, generalized Riemannian spaces and their mappings. The scope of this Special Issue also includes Finsler geometry, Kenmotsu manifolds, Kaehler manifolds, manifolds with non-symmetric linear connections, cosymplectic manifolds, contact manifolds, statistical manifolds, Minkowski spaces, geodesic mappings, almost-geodesic mappings, holomorphically projective mappings, warped products of manifolds, complex space forms, quaternionic space forms, golden manifolds, inequalities, invariants, immersions, etc. Potential authors are encouraged to submit papers that present new ideas in the field of differential geometry, in addition to the above topics. Given the broad scope and widespread interest in this topic, more works should be published in this area.
Introduction to Probability and Statistics for Data Science
Introduction to Probability and Statistics for Data Science provides a solid course in the fundamental concepts, methods and theory of statistics for students in statistics, data science, biostatistics, engineering, and physical science programs. It teaches students to understand, use, and build on modern statistical techniques for complex problems. The authors develop the methods from both an intuitive and mathematical angle, illustrating with simple examples how and why the methods work. More complicated examples, many of which incorporate data and code in R, show how the method is used in practice. Through this guidance, students get the big picture about how statistics works and can be applied. This text covers more modern topics such as regression trees, large scale hypothesis testing, bootstrapping, MCMC, time series, and fewer theoretical topics like the Cramer-Rao lower bound and the Rao-Blackwell theorem. It features more than 250 high-quality figures, 180 of which involve actual data. Data and R are code available on our website so that students can reproduce the examples and do hands-on exercises.
Some insights on surface calculus
This book is about calculus of surfaces. Firstly, we present and prove the main results on surface integration in a clear and readable fashion. The following chapters are dedicated to solving new problems on the theory of surface integration of scalar and vector fields over parameterized regular surfaces. The book ends with a chapter on proposed problems and their solutions which many of them were used in classroom and in assessment in the last 20 years.
Geometric and Analytic Aspects of Functional Variational Principles
Algorithmic Aspects of Discrete Choice in Convex Optimization
This book develops a framework to analyze algorithmic aspects of discrete choice models in convex optimization. The central aspect is to derive new prox-functions from discrete choice surplus functions, which are then incorporated into convex optimization schemes. The book provides further economic applications of discrete choice prox-functions within the context of convex optimization such as network manipulation based on alternating minimization and dynamic pricing for online marketplaces.
Artificial Intelligence of Neuromorphic Systems
This book argues for neuromorphic systems as a technology of the future, which are oriented towards the energy efficiency of natural brains. Energy efficiency is a dramatic claim in times of environmental and climate challenges which should consider the sustainability goals of the United Nations (UN). Mathematically, neuromorphic computing is connected to analogue ('real') computing, which theoretically overcomes the limits of digital Turing computability. Therefore, the book also considers material sciences and engineering sciences which start to realize neuromorphic computing in hardware. Other mathematical formalisms such as quantum mechanics also open up new solutions (e.g., quantum computing) beyond the limits of digital Turing computability. These research fields are no longer merely of theoretical interest, they promise increasing innovation power of market interest. Nevertheless, neuromorphic computing is connected with deep logical, mathematical, and epistemic questions. Does it open new avenues to Artificial General Intelligence (AGI)? All these tendencies of research and innovation demonstrate that we need more integrated research in the foundations of logic, mathematics, physics, engineering sciences, cognitive science, and philosophy. The book is a plea for this kind of research.
Multiple Stopping Problems
This book presents the theory of rational decisions involving the selection of stopping times in observed discrete-time stochastic processes, both by single and multiple decision-makers. Readers will become acquainted with the models, strategies, and applications of these models.
Biostatistics for Bioassay
In recent decades, there has been enormous growth in biologics research and development, with the accompanying development of biological assays for emerging products. In parallel, there have been substantial advances in statistical methodology, as well as technological advances in computer power, enabling new techniques to be implemented via statistical software. Biostatistics for Bioassay presents an overview of the statistical analysis techniques that are needed in order to report the results of biological assays. These assays are needed for testing all biological medicines, such as vaccines and cell therapies, to allow them to be released for use. Beginning with consideration of the performance characteristics required of a bioassay, including accuracy, precision, and combinations of these two attributes, the book builds a framework for statistical bioassay design.Features: Explains the statistical methods needed at each stage of the lifecycle of a bioassay Describes the demonstration of the bioassay's performance, known as validation Covers the statistical techniques for monitoring the bioassay's performance over time Details how to transfer the bioassay to another laboratory or replace critical reagents Provides examples at every stage, to allow the reader to work through the techniques and consolidate their understanding The book provides a resource for interested bioassay analysts, and statisticians working with bioassays. In bringing together best practices in statistics across the bioassay lifecycle into a single volume, it aims to provide a comprehensive and useful textbook for statistical analysis in bioassay.
Adv Math & Comp Tool Metrol XIII
This volume contains original, refereed contributions by researchers from national metrology institutes, universities and laboratories across the world involved in metrology and testing. The volume has been produced by the International Measurement Confederation (IMEKO) Technical Committee 21, Mathematical Tools for Measurements, in association with IMEKO Technical Committee 6, Digitalisation, and the European Network for Mathematics and Statistics for Metrology, following presentations made at the Advanced Mathematical and Computational Tools in Metrology online conference, hosted by the Institute of Metrology of Bosnia and Herzegovina, Sarajevo, in September 2023. The volume covers the application of novel mathematical and statistical modelling techniques and data analysis and machine learning approaches to metrology and measurement science, uncertainty quantification, and knowledge representation and reasoning to enable the digitalization of metrological services.This volume is of interest to all researchers, data scientists, engineers and practitioners who need to characterize the capabilities of measurement systems, evaluate measurement data, quantify uncertainties and make inferences and decisions based on models and data. It will also be of interest to those working in the quality infrastructure concerned with the reliability, transparency, trustworthiness and reproducibility of data, data analytics, machine learning and AI, in engineering, physical, environmental and the life sciences.
Basic Concepts of Global Optimization
This textbook is an introduction to global optimization, which treats mathematical facts stringently on the one hand, but also motivates them in great detail and illustrates them with 80 figures. The book is therefore not only aimed at mathematicians, but also at natural scientists, engineers and economists who want to understand and apply mathematically sound methods in their field. With almost two hundred pages, the book provides enough choices to use it as a basis for differently designed lectures on global optimization. The detailed treatment of the global solvability of optimization problems under application-relevant conditions sets a new accent that enriches the stock of previous textbooks on optimization. Using the theory and algorithms of smooth convex optimization, the book illustrates that the global solution of a class of optimization problems frequently encountered in practice is efficiently possible, while for the more difficult-to-handle non-convex problems itdevelops in detail the ideas of branch-and-bound methods. This book is the English translation of the 2nd edition of "Grundz羹ge der Globalen Optimierung" (Springer, 2021) written in German. The translation was done with the help of artificial intelligence. A subsequent revision was performed by the author to further refine the work and to ensure that the translation is appropriate concerning content and scientific correctness. It may, however, read stylistically different from a conventional translation.
Multiple Stopping Problems
This book presents the theory of rational decisions involving the selection of stopping times in observed discrete-time stochastic processes, both by single and multiple decision-makers. Readers will become acquainted with the models, strategies, and applications of these models.
The First 500 Primes Written Out in Alphabetical Order
This book came to Mario one night in a dream. The cover, format, and content (except for the essay and index) is presented here exactly as he dreamed it. Page through the first five hundred primes to attain a meditative state of number appreciation. Then read Mario's wide-ranging essay in which he offers a personal account of primes and the beauty of mathematics.
The Language of Mathematics
A marvelous compendium of mathematical symbols and their fascinating histories Galileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one. In dozens of lively and informative entries, Ra繳l Rojas shows how today's mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, Ren矇 Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time. An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning.
Exploring Complex Survey Data Analysis Using R
Surveys are powerful tools for gathering information, uncovering insights, and facilitating decision-making. However, to ensure the accurate interpretation of results, they require specific analysis methods. In this book, readers embark on an in-depth journey into conducting complex survey analysis with the {srvyr} package and tidyverse family of functions from the R programming language. Intended for intermediate R users familiar with the basics of the tidyverse, this book gives readers a deeper understanding of applying appropriate survey analysis techniques using {srvyr}, {survey}, and other related packages. With practical walkthroughs featuring real-world datasets, such as the American National Election Studies and Residential Energy Consumption Survey, readers will develop the skills necessary to perform impactful survey analysis on survey data collected through a randomized sample design. Additionally, this book teaches readers how to interpret and communicate results of survey data effectively.Key Features: Uses the {srvyr} package and tidyverse family of packages. Grants a conceptual understanding of the statistical methods that the functions apply to. Includes practical walkthroughs using publicly available survey data. Provides the reader with the tools for interpreting, visualizing, and presenting results.
Nonstandard Analysis
Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard analysis and discusses logical, model-theoretic, and set-theoretic investigations to reveal possible mathematical reasons that may lead to reservations about nonstandard analysis. Also various foundational positions as well as ontological, epistemological, and application-related issues are addressed. It turns out that the one-sided preference for standard analysis is justified neither from a didactic, mathematical nor philosophical point of view. Thus, the book is especially valuable for students and instructors of analysis who are also interested in the foundations of their subject.
Introduction to Mathematical Modeling and Computer Simulations
This book continues to serve as an engaging and accessible textbook for undergraduates studying mathematical modeling and computer simulations. The book is heavily focussed on applications, and so may have a particular appeal to applied mathematicians, engineers, and others working in applied quantitative disciplines.
Decision Superhero Book 1
Decision Superhero is a modern practical guide to making better decisions using probability. Understand essential psychological and mathematical models for effective decision-making, implement decision science models in Excel, and build an organization that tests assumptions, discerns variables, and predicts outcomes using decision models.Eric Torkia and Bill Klimack have masterfully distilled decades of experience into a guide that is both accessible and profoundly insightful. This book is not just a manu-al for analysts but a blueprint for anyone looking to navigate the complex landscape of modern decision-making.In a world where data is king, "Decision Superhero" empowers its readers to become the architects of their own destiny, leveraging the principles of decision science to drive impactful outcomes. Whether you're a seasoned professional or just starting your journey, this book will equip you with the tools and mindset needed to make better, faster, and more informed decisions.With its blend of theory, practical application, and real-world examples, "Decision Superhero" stands out as an essential read for anyone looking to elevate their deci-sion-making prowess. Eric and Bill have created a resource that is sure to become a staple on the bookshelf of every data-driven leader. This is the book that will turn good analysts into great decision-makers. Jordan Goldmeier, Author of Becoming a Data Head and Data SmartDecision Superhero is a compelling guide to mastering decision science, crafted with clarity and depth. This book invites readers to explore the art and science of making better choices, blending real-world exam-ples, historical anecdotes, and practical insights to create a rich learning experience. From operations research during WWII to contemporary decision analysis, the authors present a cohesive narrative that demonstrates the evolution of this criti-cal field. The early chapters offer fascinating stories of decision-making challenges, such as Abraham Wald's work on survivorship bias, grounding readers in the time-less relevance of decision science.Douglas W. Hubbard, Author of How to Measure Anything: Finding the Value of Intangibles in Business and The Failure of Risk Management: Why It's Broken and How to Fix ItUnafraid to blend insights from famous statisticians and Arnold Schwarzenegger in the same breath, Tork-ia and Klimack provide spirited advocacy for the notion that our mental models should often be replaced or augmented by more explicit, conscious modeling and careful analysis; that this can lead to surprising results and drive organizational val-ue; and that it can often be accomplished with fewer prerequisites than we might be inclined to assume.Peter Cotton, Author of Microprediction: Buildiung an Open AI Network and, Co-Founder and Chief Scientific Officer at Crunch LabsDecision Superhero by Eric Torkia and Bill Klimack is a standout guide in the field of decision science, penned by a pioneer whose expertise illuminates every chapter. They masterfully bridge the gap between complex theoretical concepts and practical business applications, making decision science accessible to data professionals of varying technical skill levels. Through historical anecdotes and real-world exam-ples, they illustrate the impactful role of decision science across various industries and its pairing with data science to optimize business strategies.George Mount, Author of Advancing into Analytics and Modern Data Analytics in Excel
Decision Superhero Book 1
Decision Superhero is a modern practical guide to making better decisions using probability. Understand essential psychological and mathematical models for effective decision-making, implement decision science models in Excel, and build an organization that tests assumptions, discerns variables, and predicts outcomes using decision models.Eric Torkia and Bill Klimack have masterfully distilled decades of experience into a guide that is both accessible and profoundly insightful. This book is not just a manu-al for analysts but a blueprint for anyone looking to navigate the complex landscape of modern decision-making.In a world where data is king, "Decision Superhero" empowers its readers to become the architects of their own destiny, leveraging the principles of decision science to drive impactful outcomes. Whether you're a seasoned professional or just starting your journey, this book will equip you with the tools and mindset needed to make better, faster, and more informed decisions.With its blend of theory, practical application, and real-world examples, "Decision Superhero" stands out as an essential read for anyone looking to elevate their deci-sion-making prowess. Eric and Bill have created a resource that is sure to become a staple on the bookshelf of every data-driven leader. This is the book that will turn good analysts into great decision-makers.Jordan Goldmeier, Author of Becoming a Data Head and Data SmartDecision Superhero is a compelling guide to mastering decision science, crafted with clarity and depth. This book invites readers to explore the art and science of making better choices, blending real-world exam-ples, historical anecdotes, and practical insights to create a rich learning experience. From operations research during WWII to contemporary decision analysis, the authors present a cohesive narrative that demonstrates the evolution of this criti-cal field. The early chapters offer fascinating stories of decision-making challenges, such as Abraham Wald's work on survivorship bias, grounding readers in the time-less relevance of decision science.Douglas W. Hubbard, Author of How to Measure Anything: Finding the Value of Intangibles in Business and The Failure of Risk Management: Why It's Broken and How to Fix ItUnafraid to blend insights from famous statisticians and Arnold Schwarzenegger in the same breath, Tork-ia and Klimack provide spirited advocacy for the notion that our mental models should often be replaced or augmented by more explicit, conscious modeling and careful analysis; that this can lead to surprising results and drive organizational val-ue; and that it can often be accomplished with fewer prerequisites than we might be inclined to assume.Peter Cotton, Author of Microprediction: Buildiung an Open AI Network and, Co-Founder and Chief Scientific Officer at Crunch LabsDecision Superhero by Eric Torkia and Bill Klimack is a standout guide in the field of decision science, penned by a pioneer whose expertise illuminates every chapter. They masterfully bridge the gap between complex theoretical concepts and practical business applications, making decision science accessible to data professionals of varying technical skill levels. Through historical anecdotes and real-world exam-ples, they illustrate the impactful role of decision science across various industries and its pairing with data science to optimize business strategies.George Mount, Author of Advancing into Analytics and Modern Data Analytics in Excel
Model & Computat Approach Multi-Scale Phenom Cancer Research
Cancer development and progression is the result of biological phenomena that occur across multiple temporal and spatial scales. Recent years have seen a flurry of multi-scale mathematical models developed to generate and test new biological hypotheses related to cancer development, progression, and various treatment approaches. This has led to the development of new computational and analytical approaches aimed at investigating these multi-scale models.This review volume summarises the state of the art related to the modelling, experimental investigation, and data assimilation of multi-scale phenomena during cancer development, evolution, and treatment, as well as the computational and analytical investigation of the multi-scale models developed to reproduce the biological phenomena. The book also identifies the experimental and theoretical open problems that will have to be addressed in the near future in order to advance this field. Modelling and Computational Approaches for Multi-Scale Phenomena in Cancer Research is an excellent resource for both early career and advanced researchers.
Standard and Non-Standard Methods for Solving Elementary Algebra Problems
Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, and problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters.The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort and solutions are provided in all cases. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiad level.The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.
Standard and Non-Standard Methods for Solving Elementary Algebra Problems
Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, and problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters.The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort and solutions are provided in all cases. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiad level.The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.
Plausibility and the Solution to the Behrens-Fisher Problem
'Plausibility and the Solution to the Behrens-Fisher Problem' is a detective story that reveals the solution to a mathematical conundrum that has kept statisticians perplexed for over a century.The problem concerns what we can say about the difference between the true mean values of two normal distributions from the information available in small samples.Despite years of attempts by academia to find the answer, usually involving either Fisher's notion of 'fiducial probability' or Bayes' Rule and a 'prior' distribution, until now, a precise solution has not been found.The book shows that the Behrens-Fisher problem concerns what is plausible and that, while they are connected, what is plausible is not the same as what is probable. Moreover, plausibility cannot be defined; it must be discovered.In the first part of the book, we follow a familiar trail that leads to Behrens' and Fishers' solution, but then by correctly interpreting an observation by Bartlett (who questioned Fisher's approach), we are shown that this solution cannot be true because it does not utilise all the available information.The second part shows how to find the plausibility of the features of any probability distribution and proceeds to obtain the plausibility densities of all the parameters controlling the Normal distribution. But all this is cast into doubt when a well-known result obtained by Neyman (who was a fierce critic of Fisher) is shown to be false.This surprising twist leads to the conclusion that some entrenched assumptions must be abandoned and shows why all previous attempts to find a solution have failed.We are also forced to acknowledge that none of the results obtained so far reveal how to combine one plausibility with another, a Combinatorial Rule which is essential for the solution to the problem.In part three, we find the answer to all these issues and, with the resolution of another troubling problem in statistics, the only possible correct solution to the Behrens-fisher problem is revealed.This book brings a fresh perspective to one of the most daunting challenges in the field and is a must-read not only for statisticians, but anyone fascinated by the power of logical reasoning and the thrill of cracking what was once considered an unsolvable problem.While pitched at the mathematically sophisticated reader, it provides useful insights for anyone interested in assessments and deductions from statistical data.
Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence
Artificial intelligence (AI) and digital engineering have become prevalent in business, industry, government, and academia. However, the workforce still has a lot to learn on how to leverage them. This handbook presents the preparatory and operational foundations for the efficacy, applicability, risk, and how to take advantage of these tools and techniques. Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence: A Systems Methodology provides a guide for using digital engineering platforms for advancing AI applications. The book discusses an interface of education and research in the pursuit of AI developments and highlights the facilitation of advanced education through AI and digital engineering systems. It presents an integration of soft and hard skills in developing and using AI and offers a rigorous systems approach to understanding and using AI. This handbook will be the go-to resource for practitioners and students on applying systems methodology to the body of knowledge of understanding, embracing, and using digital engineering tools and techniques.The recent developments and emergence of Chatbots (AI tools) all have mathematical foundations for their efficacy. Such AI tools include ChatGPT, GPT-4, Bard, Tidio Support Bot, Kuki AI Companion, Meena, BlenderBot, Rose AI Chatbot, Replika: AI Friend, Eviebot, and Tay. This handbook highlights the importance of mathematical and digital foundations for AI developments. The handbook will enhance the understanding and appreciation of readers about the prevailing wave of artificial intelligence products, and, thereby, fitting the current market needs.
Plausibility and the Solution to the Behrens-Fisher Problem
'Plausibility and the Solution to the Behrens-Fisher Problem' is a detective story that reveals the solution to a mathematical conundrum that has kept statisticians perplexed for over a century.The problem concerns what we can say about the difference between the true mean values of two normal distributions from the information available in small samples.Despite years of attempts by academia to find the answer, usually involving either Fisher's notion of 'fiducial probability' or Bayes' Rule and a 'prior' distribution, until now, a precise solution has not been found.The book shows that the Behrens-Fisher problem concerns what is plausible and that, while they are connected, what is plausible is not the same as what is probable. Moreover, plausibility cannot be defined; it must be discovered.In the first part of the book, we follow a familiar trail that leads to Behrens' and Fishers' solution, but then by correctly interpreting an observation by Bartlett (who questioned Fisher's approach), we are shown that this solution cannot be true because it does not utilise all the available information.The second part shows how to find the plausibility of the features of any probability distribution and proceeds to obtain the plausibility densities of all the parameters controlling the Normal distribution. But all this is cast into doubt when a well-known result obtained by Neyman (who was a fierce critic of Fisher) is shown to be false.This surprising twist leads to the conclusion that some entrenched assumptions must be abandoned and shows why all previous attempts to find a solution have failed.We are also forced to acknowledge that none of the results obtained so far reveal how to combine one plausibility with another, a Combinatorial Rule which is essential for the solution to the problem.In part three, we find the answer to all these issues and, with the resolution of another troubling problem in statistics, the only possible correct solution to the Behrens-fisher problem is revealed.This book brings a fresh perspective to one of the most daunting challenges in the field and is a must-read not only for statisticians, but anyone fascinated by the power of logical reasoning and the thrill of cracking what was once considered an unsolvable problem.While pitched at the mathematically sophisticated reader, it provides useful insights for anyone interested in assessments and deductions from statistical data.
Data Science and Artificial Intelligence
This book constitutes the proceedings of the Second refereed proceedings of the Second International Conference on Data Science and Artificial Intelligence, DSAI 2024, held in Medan, Indonesia, during November 13-15, 2024. The 18 full papers, 2 short papers and 3 invited talks were included in this book were carefully reviewed and selected from 69 submissions. They are organized in the following topical sections: Keynote Presentations; Natural and Sign Language Processing; Applications of Data Science and Artificial Intelligence; Affective Computing and AI Games; Embedded AI and Applications; Data Science; AI and Healthcare.
Stochastic Lagrangian Adaptation
This book introduces a cutting-edge continuous time stochastic linear quadratic (LQ) adaptive control algorithm for fully observed linear stochastic systems with unknown parameters. The adaptive estimation algorithm is engineered to drive the maximum likelihood estimate into the set of parameters representing the true closed-loop dynamics. By incorporating a performance monitoring feature, this approach ensures that the estimate converges to the true system parameters. Concurrently, it delivers optimal long-term LQ closed-loop performance. This groundbreaking work offers a significant advancement in the field of stochastic control systems.
Innovative practices of the "good math teacher"
To be excellent educators, it's not enough just to "be a teacher", we must have something more, something that transforms us and changes students' lives. We worked together with innovative practices and differentiated methodologies, which were part of the theme of our research. It deals with the innovative practices of the good math teacher, from which we searched through the words of authors who have worked with the theme of the good teacher, the meaning, the basis of the good teacher, and thus we founded our theoretical practical research. We set ourselves the objectives of getting to know their teaching practices, methods that increase the quality of teaching and what pedagogical innovations we are finding in math teachers. We tried to find out what the attributions of a good teacher are from the suggestions made by the students. By analyzing these three problems, we found the characteristics of a good teacher. Our research was initially based on a theoretical foundation, elaborated in order to understand what the main attributes of a good math teacher are, and we sought to formulate some questions to find answers within our journey.
Ethnomathematics and Law 10.639/03 in the Quilombola Community of Curia繳
This book is the result of research carried out in the school of the Quilombola Community of Curia繳, in the city of Macap獺, in the state of Amap獺, Brazil. The main focus was to investigate the teaching and learning of mathematics in this school. We reflect on the perceptions of some researchers in Ethnomathematics, regarding the production and dissemination of knowledge, with regard to the history of black education, more specifically education in Quilombola Communities. To answer some of these questions, we reported on the work carried out by teachers at the community school. We interviewed teachers, school staff and rural workers in their work environment and analyzed the mathematical knowledge that exists in their work activities, checking how it happens and whether it is related to Law 10.639/03. The records made during the field activities served to confirm that different mathematical knowledges can be worked on by math teachers in the classroom, and that these knowledges produced by the workers in the community answer important existential questions for the cultural group in question.
Fractals and Chaotic Phenomena in Chemical Reactor Models
The heart of most chemical plants is a chemical reactor. Basically there are two types of reactors: tubular and tank. Depending on the type, they are described by system of partial differential equations or by system of ordinary differential equations. Each of these models can generate complex solutions, including chaos. Analysis of this type of equations requires using sophisticated mathematical methods and complex numerical algorithms. In this study these phenomena and methods of analysis were presented. Particular attention is paid to the bifurcation problem and chaotic oscillations. Different mathematical - numerical methods were presented which were used to solve above mention problems. The following concepts as: bifurcation, Lyapunov's exponent, Lyapunov's time and power spectrum were used for this purpose. The way of chaos crisis prediction was presented and optimization of reactor's process by relaxation method. At the end, it was presented two-parameter continuation method for Hopf bifurcation. This book is an extension of my previously published book "Chaotic Dynamics and Fractals in Chemical Reactor Systems" from 2019 (LAP).
Buckling of Beams, Plates and Shells
This book contains an introduction to the fundamental principles of the theory of stability of elastic bodies and structures. Beginning with very basic explanations of stability problems, this book starts with the treatment of systems of rigid beams, before beams under normal force and bending as well as the classical field of beam buckling are treated. For the case of beam buckling, an energetic consideration then follows, which forms the basis for a series of approximation methods. In addition to beam buckling, the stability cases of lateral-torsional buckling and lateral buckling are also of fundamental importance, to each of which a separate chapter is dedicated. This is followed by a discussion of plate buckling, and the book concludes with an introduction to shell buckling. This book is aimed at students at technical colleges and universities, as well as engineers in practice and researchers in the engineering sciences.
An Introduction to Classical and Modal Logics
Classical logic - which studies the structural features of purported claims of fact - and modal logic - which studies relations of necessity and possibility - are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Mindmatics
Mindmatics invites readers into a captivating exploration where the boundaries between mind and mathematics dissolve. Professor Neuman delves into the profound connections between cognitive processes and mathematical expression in this groundbreaking work. From how children grasp abstract concepts to symmetry's role in art and mathematics, this book uncovers the hidden structures that shape our understanding of the world. With insightful discussions on the relationship between poetry and mathematics and the essential role of the unconscious in fostering mathematical imagination, Mindmatics offers a unique perspective on the interplay of thought, creativity, and logic. This book is a must-read for anyone curious about the deeper links between the human mind and the mathematical universe.
Multidimensional Differential and Integral Calculus
This textbook proposes an informal access to the most important issues of multidimensional differential and integral calculus. The traditional style-characterized by listing definitions, theorems, and proofs-is replaced by a conversational approach, primarily oriented to applications. The topics covered, developing along the usual path of a textbook for undergraduate courses, are always introduced by thoroughly carried out examples. This drives the reader in building the capacity of properly use the theoretical tools to model and solve practical problems. To situate the contents within a historical perspective, the book is accompanied by a number of links to the biographies of all scientists mentioned as leading actors in the development of the theory.
An Introduction to Classical and Modal Logics
Classical logic - which studies the structural features of purported claims of fact - and modal logic - which studies relations of necessity and possibility - are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Mathematics
REVISED AND UPDATED EDITION Here is the latest edition of this essential guide to mathematics, an authoritative reference book and timeline that explores the work of history's greatest mathematicians. These include the teasing genius of Pierre de Fermat, who said he knew the answers but rarely gave them up, the helpful guidance of Fibonacci, whose 13th-century compendium for bookkeepers proved to be a valuable tool for the most high-minded mathematicians, and the fractal pattern discovered by Waclaw Sierpinski now used to plan the route a mailman takes. With a glimpse of the abstract landscapes of infinite numbers and multi-dimensional shapes that these incredible minds explore, we can begin to get beyond school-day sums and understand the true power of mathematics. 100 milestone facts reveal the greatest mathematical breakthroughs through the eyes of the people who made them. Authoritative text, historical imagery, and helpful diagrams are combined with stories and everyday examples to make the complex mathematics accessible to everyone. Includes a 12-page foldout Timeline poster which stretches out to 8.5 feet (2.6 meters) long. Mathematics is part of the bestselling 100 Ponderables series which tackles STEM subjects by partnering lively text about significant milestones with stunning illustrations. Every book includes a timeline/chart poster which puts these milestones in historical context. Perfect for smart kids and curious adults!
Foundation of Probability Theory
This textbook presents measure theory in a concise yet clear manner, providing readers with a solid foundation in the mathematical axiomatic system of probability theory. Unlike elementary probability theory, which deals with random events through specific examples of random trials, Foundations of Probability Theory offers a comprehensive mathematical framework for rigorous descriptions of these events.As a result, this course embodies all the characteristics of mathematical theories: abstract content, extensive applications, complete structures, and clear conclusions. Due to the abstract nature of the material, learners may encounter various challenges. To overcome these difficulties, it is essential to keep concrete examples in mind when trying to understand abstract concepts and to compare the abstract theory with related courses previously studied, particularly the Lebesgue measure theory.To enhance the readability of the book, each section begins with a brief introduction outlining the main objectives based on the preceding content, highlighting the primary structure, and explaining the key ideas of the study. This approach ensures that readers can follow the material more easily and grasp the essential concepts effectively.
Brownian Motion and Potential Theory, Modern and Classical
In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
Probability Analysis of Selected Population Models
This book explores the dynamics of some population models under stochastic perturbations and regime switching across different environmental patches. By integrating Markovian switching processes, we investigate the stability and ergodicity characteristics of the model, providing insights into how random fluctuations and discrete regime shifts impact population persistence and extinction probabilities. The research initially focuses on the stability and ergodicity of some stochastic models under regime switching, highlighting how environmental variability across patches influences the long-term behavior of the population. Mathematical analysis and numerical simulations demonstrate that the model exhibits varying degrees of stability depending on the stochastic parameters and the switching mechanisms involved. Further, the analysis extends to the impact of Markovian switching on the population model, elucidating how changes in environmental states governed by a Markov process affect population dynamics. This study examines the conditions under which the population persists or faces extinction, considering both slow and fast switching regimes.
Nonexictence results on the Heisenberg group
This book is devoted to prove a nonexictence theorems for solutions of some nonlinear evolution equations and systems of the same type on the Heisenberg group. The proofs are based on the test function method developed by Mitidieri and Pohozaev, Pohozaev and Tesei, Kirane and L. Ragoub. The method relies on a suitable choice of the test function in the weak formulation of the sought solutions.
Brownian Motion and Potential Theory, Modern and Classical
In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
Fundamentals of Heat & Mass Transfer Analysis due to Stretching Sheet
Many mechanisms can be responsible for the movement of fluid. These mechanisms includes the pressure gradient, movement of surface the fluid is resting upon or the surfaces the fluid is contained in and buoyancy force resulting due to density gradients. Of these, two important mechanisms are studied in this book i.e., the stretching of the surfaces and/or thermal buoyancy or both. These two basic mechanisms, surface motion due to stretching i.e. contracting/expanding walls and buoyancy force, determine the momentum and thermal transport processes for the problems. Considerable interest has been also arisen in these years regarding the flows caused by the buoyant forces such flows have promising applications in engineering such as drawing of wires, laments spinning, extrusion of metal, growth of crystals, continuous casting, fiberglass production, pulsating diaphragms modeling, and separation of isotopes, irrigation, sweet cooling or heating filtration and manufacturing of paper. Due to fluid complexity, it is impossible to provide unique governing linear partial differential equation describing the characteristics of all types of dusty fluids. So, these are discussed in this book.
