Boundary Elements and Other Mesh Reduction Methods XLVII
Theoretical advances and new foundations are reported which contribute to expanding the range of applications as well as the type of materials modelled in response to current industrial and professional requirements. The contents of the volume reflect the ability of the subject matter to evolve and the establishment of a continuously renewed community of stakeholders.As design, analysis and manufacture become more integrated, the chances are that the users of computational software will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily in the integrated process.The maturity of BEM since 1978 has resulted in a substantial number of industrial applications which demonstrate the accuracy, robustness and easy use of the technique. Their range is still being widened, taking advantage of the potentialities of the Mesh Reduction techniques in general. This volume constitutes an important reference base from which to discuss new ideas and critically compare results before developed solutions and tools are released to end professional users.
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.
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.
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.
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.
General Quantum Variational Calculus
Quantum calculus is the modern name for the investigation of calculus without limits. The quantum calculus or q-calculus began with FH Jackson in the early twentieth century, but this kind of calculus had already been worked out by Euler and Jacobi.
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.
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.
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).
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.
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!
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.
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.
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.
Mathematical Analysis for Economists
This book provides economics students with a comprehensive foundation in mathematical analysis, focusing on key concepts necessary for advanced economic models and quantitative methods. Divided into five chapters, it covers essential topics: numerical series, numeric functions of two variables, double integrals, improper integrals, and differential equations. Each chapter is designed with exercises and practical applications relevant to economics, enabling students to build both theoretical understanding and applied skills. Through this approach, students gain a mathematical toolkit vital for advanced studies and future careers in economics.
The effect of heat and mass transfer on MHD flow in channels and ducts
Transport phenomena involving the combined influence of thermal and concentration buoyancy are often encountered in many engineering systems and natural environments. Combined heat and mass transfer problems with chemical reactions are important in many processes and received a considerable amount of attention in recent years. Obviously, an understanding of this transport process is desirable in order to effectively control the overall transport characteristics. In this context, we make an attempt to investigate the effect of dissipation, the Soret effect, and radiation on the unsteady double diffusive flow of a viscous and electrically conducting fluid through a porous medium in a vertical channel. Also, investigated the Heat and Mass transfer of a viscous fluid with radiation effect in channels/ducts. We discuss the effect of radiation, thermo-diffusion, dissipation, and heat sources on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular duct.
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.
Application of Statistical Computing to Statistical Learning
The study here is about supervised learning, an aspect of statistical learning. We identified prediction as the mainstay of supervised learning, and further noted that when the outcome of prediction is a categorical variable, classification obtains, otherwise what we have is regression, meaning that the prediction outcome is a continuous variable.A distinguishing aspect of this work is our ability to show both mathematically with a proof, and practically with some real-world datasets, that regression tools can be used as veritable tools for classification.
Theory and Applications of Analytical Integration Methods
Dive into a captivating journey through the complex world of integral calculus with this first volume, "Theory and Applications of Analytical Integration Methods: From Mathematical Foundations to Practical Solutions", the first tome of a two-volume series. This first volume delves deeply into analytical integration methods, while the second volume focuses on numerical methods and their implementation in Python. Through nine carefully structured chapters, explore the fundamentals of integral calculus and dive into its numerous practical applications in geometry, statistics, electricity, thermochemistry, and mechanics. Designed for a broad audience, whether you're a novice or an expert, this book offers a comprehensive and accessible approach to mastering integral calculus with little to no external assistance. Each chapter is enriched with clear examples and practical exercises, accompanied by detailed solutions to enhance understanding. The great strength of this series lies in the rigorous validation of results obtained by analytical resolution against those obtained using numerical methods, which are further confirmed by computer-generated results.
Dynamic Modelling Related to Mathematical Applications
This book provides an introduction to the concepts and methods of dynamic modeling related to mathematical applications and its applications to population dynamics and phylogenetics. It offers an overview of topics such as history, data analysis tools, equations, and various techniques used to solve differential, integral, linear, and discrete time dynamic models. The chapters also include case studies and examples of data analysis and graphical methods to illustrate simulation methods and the application of dynamic model characteristics. The underlying mathematical concepts and principles are discussed in detail to explain application to real-world problems.This book is written with the intention of providing an overview of dynamic modeling and its related mathematical applications, which would benefit students and researchers in mathematics, biology, and engineering.
Calculus
What knowledge should a calculus textbook cover? Are we able to tell the goals of learning on top of the content from the outline of the textbook? After every abstruse definition and theory, if there's only one or two simple demonstrations, what then, is the root cause for students' inability to solve those difficult practices, a lack of practice or the unfamiliarity of different practice variations? If there's an exam starting minutes away, what content can be remembered from a closed textbook? There are five highlights in this textbook: First of all, readers can be aware of the learning goals of each chapter from the outline, allowing beginners to calculus to have clear understanding of the textbook's structure.Secondly, before sample practices in each chapter, classic question variations are outlined with steps in solutions. Hence, after practicing, readers will be able to fully grasp the concepts and variation through steps of the solutions.Thirdly, the book contains more than 2,000 samples and each sample is demonstrated with the most thorough solution steps. Hence, readers will not find themselves confused with skipped steps.Fourthly, in hopes of allowing readers to understand the book as a whole, including relationships between chapters and significance in specific chapters, I've written the textbook as plain and straight-forward as possible. For instance, knowing where and how L'H繫pital's rule will be used in later chapters.Finally, in contrast with the simple explanations, each sample question is answered with great rigor and accuracy. Across all sample practices in the book, I've only used "Let", "Then", "Since", "Thus", and "Such that" to keep explanations simple and consistent. With all the above mentioned, I hope to present the most detailed context of calculus to all the readers.
On primes, sum of numbers, Mandelbrot fractal and theory of relativity
The book deals with the linear position of prime numbers, with the simultaneous chaotic nature of their distribution. It also derives some recursive formulas of prime numbers of nested square roots and shows their connection with the Pi. It also presents a new approach to the problem of the negative sum of natural numbers. The conclusion presents considerations on the special theory of relativity without the use of time and velocity.
Pencils of matrices and their applications
The present book is an important contribution of matrix theory and its applications. It consists of an introduction and (04) chapters where we review certain basic definitions also we introduce the concept of invariant polynomials. This book is dedicated to the application of pencils to solve implicit differential systems.
Advances in High-Order Predictive Modeling
Continuing the author's previous work on modeling, this book presents the most recent advances in high-order predictive modeling.
The Theory of Countable Borel Equivalence Relations
The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of group actions in a descriptive, topological, or measure-theoretic context. A key part of this theory is concerned with the structure of countable Borel equivalence relations. These are exactly the equivalence relations generated by Borel actions of countable discrete groups and this introduces important connections with group theory, dynamical systems, and operator algebras. This text surveys the state of the art in the theory of countable Borel equivalence relations and delineates its future directions and challenges. It gives beginning graduate students and researchers a bird's-eye view of the subject, with detailed references to the extensive literature provided for further study.
The Essential George Boole
The Essential George Boole: Logic, Love, and Legacy is a captivating biography that explores the extraordinary life of George Boole, a self-taught English mathematician whose groundbreaking work laid the foundation for the digital age. Despite his humble beginnings and lack of formal education, Boole's passion for learning and his relentless pursuit of knowledge led him to master multiple languages, explore various scientific disciplines and ultimately revolutionise the field of mathematics.This book not only showcases Boole's intellectual brilliance but also sheds light on his personal life, including his marriage to the remarkable Mary Everest, who hailed from a distinguished family. Together, they raised five talented daughters who left their own mark on the world in fields ranging from chemistry and mathematics to literature and medicine, creating a lasting legacy that spans generations.Through a compelling narrative, the authors paint a vivid picture of Boole's life, from his early struggles to support his family to his rise as a respected professor and his untimely death at the height of his career. The Essential George Boole: Logic, Love, and Legacy is a testament to the power of perseverance, the beauty of the human mind, and the enduring impact one person can have on the world.
Mathematics teaching-learning process
The proposed system of activities helps the development of calculus skills in the basic addition exercises with surplus in third grade students. It is necessary to improve the quality of the teaching-learning process of mathematics in elementary school. The diagnosis carried out revealed that the greatest difficulties are: lack of good memorization, skills, speed and accuracy.
Differential Geometry
This Special Issue presents recent developments in the field of structures on manifolds and their submanifolds. This volume covers a vast range of topics, including twister product Hermitian manifold, Legendrian warped product submanifold, Bertrand curve pair, CR-slant warped product, RW spacetime, Li-Yao-type gradient, Ricci-Yamabe solutions, etc., thus stimulating further research in this area.
Dynamic Modeling and Simulation for Control Systems, 2nd Edition
This special issue contains all the articles published in the Special Issue "Dynamic Modeling and Simulation for Control Systems, Second Edition" from the MDPI Mathematics journal. This Special Issue is a follow-up to our first successful edition. It offers researchers and practitioners a platform to explore topics related to the dynamic modeling, simulation, and optimization of control systems in various engineering fields. The aim is to cover vital aspects of optimizing the dynamic behavior of physical systems using algorithms and artificial intelligence. The applications span diverse areas such as astronautics, aerospace, avionics, robotics, manufacturing systems, mechanical engineering, power energy, materials technology, and neurorehabilitation. We hope this Special Issue will make a significant contribution to the research on modeling, simulation, and optimization techniques for dynamic control systems.
Principles and Applications of Numerical Integration Methods
Dive into a captivating journey through the complex world of integral calculus with this second volume, "Analytical Integration Methods - Courses and Exercises", part of a two-volume series. This tome focuses on numerical integration methods and their implementation in Python. It follows the first volume which explores analytical methods in integral calculus. Together, these two volumes offer a comprehensive approach to mastering integral calculus. Designed for a broad audience, whether you're a novice or an expert, this book provides a thorough and accessible approach to mastering numerical methods with little to no external assistance. It delves deeply into methods such as rectangles, midpoint, trapezoids, Simpson's, Weddle's, and Gauss's, while emphasizing precision and error management. Each chapter is enriched with clear examples and practical exercises, accompanied by detailed solutions to enhance understanding. The great strength of this series lies in the rigorous validation of results obtained by analytical resolution against those obtained using numerical methods, which are further confirmed by computer-generated results.
Advanced Mathematics for Science and Technology
This book presents the fundamental concepts essential to the second-year mathematics program in science and technology. The first chapter thoroughly explores integral calculus, including the Riemann integral, double and triple integrals, and their applications in calculating areas and volumes. The second chapter addresses improper integrals and their properties. The third chapter is dedicated to ordinary differential equations, focusing on linear differential equations of the first and second order, as well as partial differential equations. The fourth chapter delves into numerical series, sequences and series of functions, power series, and Fourier series. In the fifth chapter, we introduce the Fourier transform and its properties. The sixth chapter covers the Laplace transform, its properties, and its application in solving differential equations. Each chapter is accompanied by a series of exercises designed to reinforce the understanding of the presented concepts.
Introduction to Financial Mathematics
The second edition of this successful and widely recognized textbook again focuses on discrete topics. The author recognizes two distinct paths of study and careers of actuarial science and financial engineering. This text can be very useful as a common core for both. Therefore, there is substantial material in Introduction to Financial Mathematics, Second Edition on the theory of interest (the first half of the book), as well as the probabilistic background necessary for the study of portfolio optimization and derivative valuation (the second half). A course in multivariable calculus is not required.The material in the first two chapters should go a long way toward helping students prepare for the Financial Mathematics (FM) actuarial exam. Also, the discrete material will reveal how beneficial it is for the students to know more about loans in their personal financial lives.The notable changes and updates to this edition are itemized in the Preface, but overall, the presentation has been made more efficient. One example is the chapter on discrete probability, which is rather unique in its emphasis on giving the deterministic problems studied earlier a probabilistic context. The section on Markov chains, which is not essential to the development, has been scaled down. Sample spaces and probability measures, random variables and distributions, expectation, conditional probability, independence, and estimation all follow.Optimal portfolio selection coverage is reorganized and the section on the practicalities of stock transactions has been revised. Market portfolio and Capital Market Theory coverage is expanded. New sections on Swaps and Value-at-Risk have been added. This book, like the first edition, was written so that the print edition could stand alone. At times we simplify complicated algebraic expressions, or solve systems of linear equations, or numerically solve non-linear equations. Also, some attention is given to the use of computer simulation to approximate solutions to problems.
Risk Factors & Prevention of Coronary Heart Disease
"Coronary heart disease (CHD) is a leading cause of morbidity and mortality worldwide. This study aims to investigate the demographic and clinical characteristics of patients with CHD at ESI Hospital, Maniktala, Kolkata, and assess the prevalence of risk factors for CHD. Additionally, it explores the perspectives of healthcare professionals and policymakers on CHD prevention, identifies challenges and barriers in CHD management, and proposes evidence-based recommendations for effective prevention strategies."
Solution Curve For Control Systems on Lie Groups
In the context of Lie groups, Control Theory is primarily concerned with the study of invariant, linear, bilinear and affine control systems. For invariant systems - considering that the control functions are piecewise constant - the solutions of the system has a well known and good description. This brings us to the first objective of this work: to give an explicit description of the solution curve for the other systems under the assumption that the linear vector fields commute. These solutions are obtained as the integral curve of a convenient invariant vector field on a semidirect product of a Lie group with an Euclidean space. In particular, we consider the case where the derivations associated to the linear vector fields are inner (which occurs, for example, in every semi simple Lie algebra), in which case the solutions are described in a considerably simpler and more elegant way. Thenceforth, our achievements are applied to obtain new propositions. The results range from expressions that relate the controllability of linear/affine control systems with associated invariant ones to the study of system semiconjugation by Lie group homomorphisms and properties of stability sets.
Discretization in Differential Equations and Enclosures
No detailed description available for "Discretization in Differential Equations and Enclosures".
Reverse Dynamic Inequalities on Time Scales
Inequalities lie at the heart of the mathematical analysis which is a major and important branch of mathematics. Throughout the history, many researchers discovered agreat number of inequalities that are very useful in many fields of mathematics. Thestudy of inequalities became very popular in the twentieth century specially afterthe publishing of the pioneering book. In 1988, Stephan Hilger introduced in his PhD thesis a new theory, the theoryof time scales, which builds bridges between continuous and discrete mathematics.The main idea is to prove a result for a dynamic inequality where the domain of theunknown function is a so-called time scale T, which is defined as an arbitrary closedsubset of the real numbers R, to avoid proving results twice, once in the continuouscase which leads to an integral inequality and once again on a discrete case whichleads to a discrete inequality.Recently, the study of dynamic inequalities on time scales has attracted the attention of many mathematicians. One of the applications of this kind of inequalitiesis to study the behavior of solutions of dynamic equations on time scales.
Fuzzy Soft Ternary Γ-Semirings
Fuzzy soft ternary gamma semirings are an advanced mathematical structure that combines elements from fuzzy logic, soft set theory, ternary operations, and gamma semirings. This book provides information on Fuzzy Soft Quasi TΓ-Ideals in Fuzzy Soft TΓ-Semirings, On Fuzzy Soft Interior TΓ-Ideals, Fuzzy Soft Radicals in Fuzzy Soft TΓ-Semirings, Fuzzy Soft TΓ-Homomorphism in TΓ-Semirings. Each topic has been started with introductory part and developed gradually up to the standard form.
The Philosophy of Penelope Maddy
This volume features more than 20 essays that explore the work of one of the most important contemporary philosophers of mathematics. It will help readers to better appreciate this significant and prolific philosopher. Within philosophy of mathematics, Penelope Maddy initially advocated realism. She then went on to advance naturalism. Both of her positions became very influential in the field, along with her other work in the philosophy of logic. The contributors comment on and otherwise engage with Maddy's work. They also weigh in on the state of set theory and its philosophy, the philosophy and history of logic, naturalism, skepticism, and the myriad other areas to which Maddy left her mark. Overall, coverage traces her influence on these various ideas over the years. It will also help readers to better understand how philosophers working at the forefront of these areas see these concepts today. These essays will be essential reading for the wide group of philosophers working in these different areas as well as graduate students studying philosophy of mathematics and logic and the other related issues to which Maddy has contributed. The volume will also appeal to logicians and set theorists in general, as well as to philosophers working in analytic philosophy more widely, as well as to those working in the history of philosophy.
The Relay Race to Infinity
Why were most historically important mathematicians wealthy? Why were they often lawyers and many had pastors for fathers? Why were original results sometimes discovered by two mathematicians independently within a short time of each other? Why did the Italian Fibonacci, speak Arabic?It all began a couple of years ago, when one of the authors started to write short biographies of important historical mathematicians for the teaching journal Australian Primary Mathematics Classroom. It was felt that teachers generally knew very little about the way the subject developed or the people who developed it. And it was felt that historical knowledge would help them see how the subject progressed and enable them to fit in with the historical episodes that would be of interest to students.Clearly, the book that developed contains mathematics up to the 17th century, but we are keen to set the subject in those times, to try to give short biographies of the people involved, as well as provide a perspective of the events that led up to the times and led up to the mathematics. Importantly, it is shown that the maths enterprise was not undertaken by a small few, but worked like a relay race. One or a few might take up an idea and develop it, but it often gets only so far. Later, others would take up the idea, the baton, and the relay race to find results continues.
Algebraic Topology
The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory. A simple approach based on point-set Topology is used throughout to introduce many standard constructions of fundamental and homological groups of surfaces and topological spaces. The approach does not rely on Homological Algebra. The constructions of some spaces using the quotient spaces such as the join, the suspension, and the adjunction spaces are developed in the setting of Topology only. The computations of the fundamental and homological groups of many surfaces and topological spaces occupy large parts of the book (sphere, torus, projective space, Mobius band, Klein bottle, manifolds, adjunctions spaces). Borsuk's theory of retracts which is intimately related to the problem of the extendability of continuous functions is developed in details. This theory together with the homotopy theory, the lifting and covering maps may serve as additional course material for students involved in General Topology. The book comprises 280 detailed worked examples, 320 exercises (with hints or references), 80 illustrative figures, and more than 80 commutative diagrams to make it more oriented towards applications (maps between spheres, Borsuk-Ulam Theory, Fixed Point Theorems, ...) As applications, the book offers some existence results on the solvability of some nonlinear differential equations subject to initial or boundary conditions. The book is suitable for students primarily enrolled in Algebraic Topology, General Topology, Homological Algebra, Differential Topology, Differential Geometry, and Topological Geometry. It is also useful for advanced undergraduate students who aspire to grasp easily some new concepts in Algebraic Topology and Applications. The textbook is practical both as a teaching and research document for Bachelor, Master students, and first-year PhD students since it is accessible to any reader with a modest understanding of topological spaces. The book aspires to fill a gap in the existing literature by providing a research and teaching document which investigates both the theory and the applications of Algebraic Topology in an accessible way without missing the main results of the topics covered.
The Relay Race to Infinity
Why were most historically important mathematicians wealthy? Why were they often lawyers and many had pastors for fathers? Why were original results sometimes discovered by two mathematicians independently within a short time of each other? Why did the Italian Fibonacci, speak Arabic?It all began a couple of years ago, when one of the authors started to write short biographies of important historical mathematicians for the teaching journal Australian Primary Mathematics Classroom. It was felt that teachers generally knew very little about the way the subject developed or the people who developed it. And it was felt that historical knowledge would help them see how the subject progressed and enable them to fit in with the historical episodes that would be of interest to students.Clearly, the book that developed contains mathematics up to the 17th century, but we are keen to set the subject in those times, to try to give short biographies of the people involved, as well as provide a perspective of the events that led up to the times and led up to the mathematics. Importantly, it is shown that the maths enterprise was not undertaken by a small few, but worked like a relay race. One or a few might take up an idea and develop it, but it often gets only so far. Later, others would take up the idea, the baton, and the relay race to find results continues.
The Four Corners of Mathematics
This book describes the historical development of the 'big ideas' in mathematics in an accessible and intuitive manner. In delivering this bird's-eye view of the history of mathematics, the author uses engaging diagrams and images to communicate complex concepts while also exploring the details of the main results.
Computational mathematics in R Programming
Computational mathematics in R programming harnesses the power of R's extensive libraries and tools to tackle complex numerical analysis, statistical computations, and data visualization tasks. This versatile programming language is widely adopted in a range of scientific and engineering disciplines for executing matrix operations, optimization techniques, and solving differential equations. Whether applied in data science, physics, economics, or engineering, R provides a robust platform for performing sophisticated mathematical computations, enabling researchers and professionals to analyze data efficiently, model real-world systems, and gain deeper insights from their work. Its user-friendly interface, combined with powerful computational capabilities, makes it an invaluable resource for anyone engaged in computational mathematics.
Singularities and Low Dimensional Topology
The special semester 'Singularities and low dimensional topology' in the Spring of 2023 at the Erdős Center (Budapest) brought together algebraic geometers and topologists to discuss and explore the strong connection between surface singularities and topological properties of three- and four-dimensional manifolds. The semester featured a Winter School (with four lecture series) and several focused weeks. This volume contains the notes of the lecture series of the Winter School and some of the lecture notes from the focused weeks. Topics covered in this collection range from algebraic geometry of complex curves, lattice homology of curve and surface singularities to novel results in smooth four-dimensional topology and grid homology, and to Seiberg-Witten homotopy theory and 'spacification' of knot invariants. Some of these topics are already well-documented in the literature, and the lectures aim to provide a new perspective and fresh connections. Other topics are rather new and have been covered only in research papers. We hope that this volume will be useful not only for advanced graduate students and early-stage researchers, but also for the more experienced geometers and topologists who want to be informed about the latest developments in the field.
Geometric mathematics in the slab cistern
This work came about through research in the rural community of S穩tio Barra do Japi in the municipality of Japi-RN. It shows the step-by-step mathematics involved in building a cement slab cistern. However, the aim was to bring together the mathematical concepts involved in carrying out this work. The aim is for the community's math teacher to be able to integrate his lessons with the daily reality of these people, bringing the school closer to the daily lives of the community's residents.
