The Extension of Fixed Point Theorems in Various b-Metric Spaces
This book entitled "The Extension of Fixed Point Theorems in Various b-Metric Spaces" is divided into following 8 chapters Chapter - I: The first chapter is an introductory part of our research work which includes the brief introduction of our topic.Chapter - II: Our second chapter titled as "Fixed Point Results for Various Contractions in b-Metric Spaces." Chapter - III: The chapter third having the title "Common Fixed Point Theorem in b-Metric Spaces for Compatible Mapping of Type (A)"Chapter - IV: The fourth chapter titled as, "Common Fixed Point Theorems for Two Self Compatible Mapping Satisfying an Implicit Relation of b-Metric Spaces." Chapter - V: The Chapter five titled as, "Existence of Fixed Point Theorem of Integral Type Contractions in b-Metric Spaces". Chapter - VI: Chapter six titled as "Coupled Coincidence Fixed Point Theorem in Two Weakly Compatible Mapping in b-Metric Spaces ".Chapter - VII: The seventh chapter titled as "Coincidence and Common Fixed Point Theorem using Compatible Mapping of Type (P) in Intuitionistic Fuzzy b-Metric Spaces" Chapter - VIII: Our last chapter titled as "Some Generalized Theorems of q-Contraction in Symmetric Nb-Fuzzy Metric Spaces".
Handbook on Affective Interest in Mathematics
In Nigeria, mathematics holds a pivotal role as a mandatory subject in both primary and secondary education. Mathematics, as an academic discipline, delves into the realms of numbers, shapes, patterns, and their intricate relationships. It equips learners with the vital ability to communicate using symbols and logical reasoning, fostering logical thinking, precision, and spatial awareness (Arhin & Yanney, 2020). Mathematics is regarded as one of the core prime instruments for understanding and exploring the scientific, technological, economic, and social and information world. Science, Technology, Engineering and Mathematics (STEM). Mathematics education is considered as a precious way to make the education system keep up with the developments and to meet the expectations of 21st century skills (Kazu & Cemre, 2021; Ghazali, & Yusof, 2022).
Series and functional series associated with harmonic numbers
The book has five chapters. Chapter 1 gives the basic knowledge needed to understand the contents of this book. Chapter 2 describes several interesting formulas related to harmonic numbers. In Chapter 3, the series problems involving several kinds of harmonics in the general terms are shown together with the solution to these problems can be found in mathematical references dealing with difficult problems. Chapter 4 presents the problem of multiple series involving several kinds of harmonics in general terms with solutions. Chapter 5 presents interesting challenges and open problems involving harmonic numbers in general terms.Since we have raised a number of interesting problems and various technical problems to solve them, this book will be a good reference not only for those specializing in mathematics, but also for those specializing in physics or other natural sciences.
Fractional Calculus in Medical and Health Science
This book covers applications of fractional calculus used for medical and health science.
Digital resources in mathematics teaching
This book shows the work of designing and then implementing a Virtual Teaching and Learning Space (EVEA) that allows students to learn mathematical knowledge through the appropriate use of different technological resources. This proposal is aimed at 4th year students of the Oriented Cycle and is intended to teach with technology, through an easily accessible platform such as Classroom, organizing knowledge by topics and providing interactive resources where students, through ICT and virtual classes, are expected to acquire autonomy and commitment in their work, giving account of the concepts learned through the different activities proposed. In this way, students are expected to play an active role in their learning process, the teacher being a mediator of knowledge and a moderator in the proposed classes. We seek to design pedagogical actions by means of technological resources that allow the acquisition of minimum knowledge in conjunction with the students' interests, promoting activities that allow the construction of significant knowledge.
Visualisation and Epistemological Access to Mathematics Education in Southern Africa
This book demonstrates that using visualisation processes in mathematics education can help to enhance teaching and learning and bridge the inequality gap that exists between well-resourced and under-resourced schools in Southern Africa. Drawing on classroom research conducted in the Southern African region, it examines how epistemological access in a context of gross inequality can be constructively addressed by providing research-based solutions and recommendations. The book outlines the visualisation process as an integral but often overlooked process of mathematics teaching and learning. It goes beyond the traditional understanding of visualisation processes such as picture forming and using tools and considers visualisation processes that are semiotic in nature and includes actions such as gestures in combination with language. It adds value to the visualisation in mathematics education research discourse and deliberation in Africa.With a unique focus on Southern Africa and open avenues for further research and collaboration in the region, it will be a highly relevant reading for researchers, academics and post-graduate students of mathematics education, comparative education and social justice education.
Homogeneous Projective Varieties and Invariant Theory
The general theme of this book is the interplay between the geometry of homogeneous complex projective varieties, the structure and representation theory of their symmetry groups, and more specifically, invariant theory related to subgroups of the symmetry groups. The framework is based on the Borel-Weil theorem and the Geometric Invariant Theory of Hilbert-Mumford. The setting is classical and the basic objects of interest are widely studied. A source of unanswered questions lies in the notorious nonconstructiveness of Hilbert's theorem asserting the existence of a finite generating set for the ring of invariants in the homogeneous coordinate ring of a complex projective variety endowed with a reductive group action. The goal of this work is to contribute to the effort for further development of the structure theory of reductive Lie groups, aiming to bound and explore the variation of certain parameters related to generating sets of invariants. Particular attention is given to the geometry of unstable loci - the zero-loci of the invariants of positive degree.
Logic as a Tool
This textbook, written in a concise yet user-friendly style, will guide the reader in understanding and mastering the use of classical logic as a tool for performing logically correct reasoning. It offers a systematic and precise exposition of classical logic on both propositional and first-order level with many examples and exercises and only the necessary minimum of theory. Most of the exercises are provided with answers or detailed solutions.The book explains the grammar, semantics, and use of classical logical languages and teaches the reader how to grasp the meaning and translate the formulae of classical logic to and from natural language. It illustrates with many detailed examples the use of the most popular deductive systems - axiomatic systems, semantic tableaux, natural deduction, and resolution - for formalizing and automating logical reasoning and provides the reader with the technical skills needed for practical derivations. Systematic guidelines are offered on how to carry out logically correct and well-structured reasoning using the proof strategies and techniques that these deductive systems employ.The book is accompanied with a set of detailed slides available online and can be used as a textbook for introductory or intermediate courses in classical logic for students in mathematics, computer science, philosophy, or related disciplines, as well as for self-study.
Ordinary Differential Equations. Exercises and Problems
This book presents a variety of methods of analytic solution of ordinary differential equations and features a wealth of examples, both solved in detail and proposed. The goal of this work is to give a broad training in techniques of solution of equations and problems involving differential equations, which are important both in mathematics and applications.The book is aimed primarily at undergraduate students of mathematics, natural sciences and engineering, who need a solid knowledge of differential equations in their professional activities. The text contains many examples of scientific problems solved by constructing models involving differential equations, which introduce students to a number of interesting aspects of applications.The proposed material can also be useful for professors and instructors of differential equations courses, since the text contains an exposition of all the principal analytic techniques usually studied in undergraduate programs, which are illustrated with numerous examples. In this way, teachers/instructors can use this book both to teach classes and to administer exams/tests on the studied subjects.
G繹del's Incompleteness Theorems
In 1931, the mysterious-sounding article "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" shook the mathematical world. In this article, Kurt G繹del proved two incompleteness theorems that have fundamentally changed our view of mathematics. G繹del's theorems manifest that the concept of truth and the concept of provability cannot coincide. Since their discovery, the incompleteness theorems have attracted much attention, and a flood of articles and books have been devoted to their striking consequences. For good reasons, however, hardly any work deals with G繹del's article in its original form: His complex lines of thought described with meticulous precision, the many definitions and theorems, and the now largely outdated notation turn G繹del's historical masterpiece into a difficult read. This book explores G繹del's original proof in detail. All individual steps are carefully explained and illustrated with numerous examples. However, this book is more than just an annotated version of the historical article, as the proper understanding of G繹del's work requires a solid grasp of history. Thus, numerous excursions take the reader back to the beginning of the twentieth century. It was the time when mathematics experienced one of its greatest crises, when type theory and axiomatic set theory were taking shape, and Hilbert's formalistic logic and Brouwer's intuitionistic mathematics were openly confronting each other. This book is the revised translation of the second edition of the author's German language book "Die G繹del'schen Unvollst瓣ndigkeitss瓣tze".
Heat Source and Radiation on MHD Fluid Flow Over a Porous plate
The study of magnetohydrodynamic (MHD) fluid flow has garnered significant attention due to its wide range of applications in engineering, astrophysics, and industrial processes. When considering high-temperature systems, it becomes crucial to understand the impact of thermal radiation and heat sources on the flow characteristics. These factors play a pivotal role in processes such as nuclear reactor cooling, geothermal energy extraction, and in various metallurgical applications.In MHD flows, the interaction between the magnetic field and the electrically conducting fluid introduces complex dynamics, which are further influenced by the presence of a heat source and thermal radiation. The heat source can represent internal heating mechanisms such as chemical reactions or external sources like solar radiation. Thermal radiation, on the other hand, is essential in understanding the energy transport in high-temperature flows.
Mesure et int矇gration. Cours et exercices corrig矇s.
Ce livre est un ouvrage, principalement destin矇 aux 矇tudiants de troisi癡me ann矇e LMD math矇matiques. Le contenu de ce livre, correspond au programme de la mati癡re Mesure et Int矇gration enseign矇 en troisi癡me ann矇e. Le livre s'articule autour de quatre chapitres. A la fin de chaque chapitre on pourra trouver une s矇rie d'exercices. A la fin de ce manuscrit, nous avons donn矇 quelques bibliographies de base classiques. Nous esp矇rons que ce livre r矇ponde aux attentes des 矇tudiants et qu'il les aidera ? r矇ussir.Le programme du cours est le suivant.1. Tribus et mesures.2. Fonctions mesurables, variables al矇atoires.3. Fonctions int矇grables.4. Produit d'espaces mesur矇s.
Domination Numbers and Radius in Trapezoidal Graphs
Trapezoidal graphs, a significant class of intersection graphs, have garnered interest due to their applicability in various real-world scenarios. Defined as intersection graphs of trapezoids between two parallel lines, these graphs are useful in scheduling problems, bioinformatics, and network design.Understanding the relationships between different domination numbers and the radius of a graph can provide deeper insights into its structure and properties. In this context, we explore three specific domination numbers: the Roman domination number, the total domination number, and the distance-2 domination number. These parameters offer different ways of measuring how subsets of vertices can influence or dominate the entire graph.
Intro to Calcul Varia (4th Ed)
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist -- mathematicians, physicists, engineers, students or researchers -- in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Solitons, Instantons, and Twistors
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well-behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations. The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.
Intro to Calcul Varia (4th Ed)
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist -- mathematicians, physicists, engineers, students or researchers -- in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Fuzzy Sets Applications, Methodological Approaches, and Results
No detailed description available for "Fuzzy Sets Applications, Methodological Approaches, and Results".
Journal of Applied Logics. IfCoLog Journal of Logics and their Applications. Volume 11, number 4, August 2024
The Journal of Applied Logics- IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.
School assessment from the point of view of maths teachers and students
This work brings together the conceptions of school assessment held by public school maths teachers working in the final grades of primary school, as well as students' views on school assessment in the final grades of primary school in the public school system in the state of Paran獺. The educational institutions where the questionnaires were administered were spread across various regions of Paran獺.
Singularly Perturbed Differential Equations
No detailed description available for "Singularly Perturbed Differential Equations".
Mathematical Modeling
The co-infection of tuberculosis (TB) and malaria poses significant challenges for public health, particularly in regions where both diseases are endemic. This study presents a mathematical model to elucidate the dynamics of TB and malaria co-infection, considering the influence of interference treatments and vaccination resistance. The model incorporates compartmental dynamics for susceptible, latent TB-infected, active TB-infected, malaria-exposed, symptomatic malaria-infected, co-infected, and recovered individuals. Additionally, it integrates mechanisms of interference between treatments for TB and malaria, as well as compartments representing vaccinated individuals and those resistant to vaccination.
Study on Posbist Reliability Theory and Its Applications
"Imprecision" here is meant in the sense of vagueness rather than the lack of knowledge about the value of a parameter as in tolerance analysis. Fuzzy set theory provides a strict mathematical framework (there is nothing fuzzy about fuzzy set theory!) in which vague conceptual phenomena can be precisely and rigorously studied. It can also be considered as a modeling language well suited for situations in which fuzzy relations, criteria, and phenomena exist. Fuzziness has so far not been defined uniquely semantically, and probably never will. It will mean different things, depending on the application area and the way it is measured. This book entitled "Study on Posbist Reliability Theory and its Applications" present some important aspects Fuzzy Set theory and some recent results in its development. This embodies four chapters . The first chapter consists of an introduction on fuzzy set theory and different ideas with definitions that lead to the growth and extension of Fuzzy Set Theory. In second chapter we describe fuzzy variables. The third chapter consists of study on Posbist systems. At last chapter, we have presented a brief description on application of Fuzzy Set Theory.
Linear Algebra for Teaching Activities
In this second volume of Linear Algebra you will find topics related to Matrices and Determinants, making reference to great authors of books focused on linear algebra, such as Baldor (Baldor, 2019) with authorships on Algebra, and other expert authors on the subject (David C. Lay, Ron Larson, Grossman, Estrada, Guzm獺n, among others) that is why, the topics related to Matrices and Determinants; are essential for the application in real life, with the demonstration of exercises related to the methods and an annex of proposed exercises for practice.
Laplace Substitution Method
There are several methods to solve linear and nonlinear partial differential equations. However, these methods are not effective for solving nonlinear partial differential and integral equations involving mixed partial derivatives. Therefore, we focused on developing a new method to obtain exact solutions for these equations with fewer computations and in a shorter time. This method is called the Laplace Substitution Method. We derived the idea for this method from the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM). In this book, we address initial value problems of nonlinear partial differential and integral equations involving mixed partial derivatives of any order using our developed method, the Laplace Substitution Method. This study includes both linear and nonlinear partial differential and integral equations with mixed partial derivatives.
The Perfect Handbook for Science
Embark on a captivating journey through the vast realms of science with our comprehensive handbook, meticulously crafted to be your perfect companion. Whether you're a curious novice or a seasoned enthusiast, this book is designed to unlock the mysteries of the universe and deepen your understanding of the natural world. Discover the wonders of physics, unravel the complexities of chemistry, explore the intricacies of biology, and delve into the mysteries of astronomy and earth sciences. Each chapter is expertly curated to provide clear explanations, captivating illustrations, and practical insights into key scientific concepts. Navigate effortlessly through our alphabetical index, ensuring quick access to a wealth of topics-from Acids and Bases to Quantum Mechanics, from Genetics to Plate Tectonics. Thematic groupings further enhance accessibility, guiding you through interconnected fields such as ecology, space exploration, and mathematical foundations. So lets take a leap of faith towards this profound and legible book.
Maths and Technologies in Teaching Practice
This book shows through existing literature how information and communication technologies (ICT) are used as a form of production in the school environment and how those involved in the process make use of these tools in teaching practice. As it is a new tool, it is necessary to encourage older teachers to use these new means in order to achieve excellence, as the Internet can help with guided school research, as well as the use of numerous software programmes to support teachers and students. The book demonstrates the use of ICT and seminars in maths and other subjects.
Lattice Path Combinatorics and Special Counting Sequences
This book endeavors to deepen our understanding of lattice path combinatorics, to explore key types of special sequences, to elucidate their interrelations, and at the same time to advocate the author's interpretation of the "combinatorial spirit".
Applied Mathematics
This book aims to provide a basic and self-contained introduction to Applied Mathematics within a computational environment. The book is aimed at practitioners and researchers interested in modelling real world applications and verifying the results.
The World through the Lens of Mathematics
This amazing book aims to shatter the barrier between students and mathematics. By encouraging students to look at mathematics from a different perspective, build a bridge between their surroundings and mathematics and, at the same time, enrich them with the culture, history, customs, and geography of different parts of the world.
How to Write & Do Proofs
This Study Guide has been teaching students how to write & do proofs for over 30 years. This text provides an excellent approach for teaching students how to read, understand, and do proofs. The various examples and techniques explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique based on the form of the problem. The goal is to enable students to learn advanced mathematics on their own. This book is suitable as: (1) a text for a transition-to-advanced-math course, (2) a supplement to any mathematics course, and (3) self-guided teaching.
Math for English Majors
In this trailblazing work from the internet's most empathetic math teacher, Ben Orlin unravels the secrets behind the world's most confounding language. Math, it is said, is the "universal language." But if a language brings people together, why does math make so many of us feel so alone? In Math for English Majors, bestselling author Ben Orlin (Math with Bad Drawings) offers fresh insights for the mathematically perplexed and mathematical masters alike. As Orlin reveals, the "universal language" is precisely that: a language. It has nouns (numbers), verbs (calculations), and grammar (algebra). It has funny idioms ("exponential"), quirky etymologies ("squaring"), and peculiar ambiguities ("PEMDAS"). It even has its own form of literature, with equations ranging from the simple wisdom of A2 + B2 = C2 to the startling profundity of eπi + 1 = 0. Along the way, he shares relatable stories of his own mathematical misunderstandings and epiphanies, as well as the trials and triumphs of his students. And, as always, he sheds further light and levity on the subject with his inept--yet strangely effective--drawings.
Think Like a Molecule
Despite their complex structures, molecules most likely do not take time to ponder the ways they fit into the big scheme of things. They just are. But when zillions of molecules bond into organized, functional systems, we get everything, including you and me - and some seven billion others. Chuck Champlin, a writer, journalist, and a former Walt Disney Co. communications executive, seeks inspiration via deep imaginative journeys into the infinitely vast and invisibly tiny realms of the cosmos in this small book with a big message. In observing molecular assemblies, we can see that physically matter came together, possibly all on its own, to create life and thinking minds. It is profound that our minds, perhaps born from accidental creativity, can intentionally assemble marvelous new things. To think like a molecule is to be aware of the physical foundations in matter that have given rise to our thoughts - and from there, it's onward into the realm of pure imaginations and the twinkling stars of our infinite potential.
Advanced Guidance and Control of Flight Vehicle
The application of advanced guidance and control to missiles, hypersonic vehicles, and unmanned aerial vehicles has long represented a research hotspot in academia, and the development of more advanced and intelligent guidance and control technology for flight vehicles has become a focus of research in recent years. In this reprint, studies on the mathematical theory and application of flight vehicle guidance and control are presented. This includes trajectory optimization, online planning, advanced intermediate guidance theoretical methods, terminal guidance theoretical methods, intercept guidance and pursuit and escape guidance, and other topics.
AI Empowered Sentiment Analysis
With the popularity of the social media, a large amount of user-generated content, such as comments, is emerging, which is crucial for all industries. Recently, the development of deep learning and computing power have made it possible to handle complex data. However, there are still some including (but are not limited to): (1) How can we construct a multi-modal sentiment analysis framework? (2) How can we accurately extract aspect-sentiment quadruples? (3) How can we generate fine-grained sentiment text? To tackle these challenges, this Special Issue focuses on multi-modal sentiment analysis, aspect-sentiment extraction, interpretability, and so on. In the following, we briefly summarize the selected two papers that we believe will make significant contributions. (1) "Generative Aspect Sentiment Quad Prediction with Self-Inference Template" by Li et al., considered that current research predominantly confines templates to single sentences, limiting the model's reasoning opportunities. Therefore, the authors introduce a self-inference template (SIT) to guide the model in thoughtful reasoning. (2) "Interpretability in Sentiment Analysis: A Self-Supervised Approach to Sentiment Cue Extraction" by Sun et al., proposes a new sentiment cue extraction (SCE) self-supervised framework, aimed at improving the interpretability of models. In conclusion, we extend our heartfelt appreciation to all the authors and reviewers who selflessly put their energy to ensure the successful completion of this Special Issue.
Mathematical Modelling and Numerical Analysis in Electrical Engineering
This special issue focuses on the mathematical modelling and numerical analysis methods employed in electrical engineering applications. The 11 manuscripts included utilize various analytical and computational techniques such as parameter modelling methods and numerical analyses to solve engineering problems in domains such as electric motors, power systems. One of these papers investigates line-start permanent magnet synchronous motors and explores the starting performance when parameters such as the supply voltage and cable length are varied; in addition, simulation and experimental methods are employed to characterize the motor behavior. Another study employs the finite element modelling technique to study the electric field distributions for lightning rod design. Additionally, optimization techniques such as the Nelder-Mead algorithm are applied to optimize a synchronous homopolar motor. Mathematical and numerical analyses of the induction and flux-switching motors are also presented. Transient simulations of the starting and synchronization processes, which incorporate the lumped parameter motor models of a line-start permanent magnet synchronous motor, are also undertaken. Other studies employ accurate models that have been developed for adjustable permanent magnet couplers, external magnetic fields and switched reluctance motors. Validation using finite element analyses and experiments demonstrates the feasibility and superiority of the proposed modelling approaches. The broad range of topics addressed reflects the extensive application of analytical techniques in electrical engineering research.
Advanced Mathematical Modeling with Technology
Mathematical modeling is both a skill and an art and must be practiced in order to maintain and enhance the ability to use those skills. This book will be of interest to instructors and students offering courses focused on discrete modeling or modeling for decision making.
The Secret Formula
The legendary Renaissance math duel that ushered in the modern age of algebra The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccol簷 Tartaglia was a talented and ambitious teacher who possessed a secret formula--the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret. Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel. A lively account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.
Separation of Variables and Exact Solutions to Nonlinear PDEs
The book is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear PDEs. It also presents the direct method of symmetry reductions and its more general version.
Advances in Modal Logic 15
Since ancient times, philosophers have recognised that truth comes in many 'modes', so that a proposition can be not only true or false, but also, for example, 'necessary' or 'possible'. These ideas led to the modern field of modal logic, a lively area of research at the interface of philosophy, mathematics and computer science. Nowadays, the term 'modal logic' is understood in a broad sense, allowing it to encompass logics for reasoning about seemingly unrelated phenomena such as knowledge, obligations, time, space, and proofs, among many others. Contemporary research in modal logic draws on techniques from many disciplines, including complexity theory, combinatorics, universal algebra, category theory, topology, and proof theory. These proceedings record the papers presented at Advances in Modal Logic 2024, the 15th in a series of biennial conferences that aim to report on important new developments in pure and applied modal logic. Topics in this issue include epistemic modal logic, constructive and many-valued modal logic, unification, algebraic and neighbourhood semantics, proof theory and complexity of modal logics, conditional and quantified modal logic.
Asymptotic formulas in the Esterman problem
This monograph is a study in analytical number theory, related to the field of the theory of short trigonometric sums, and its applications to classical additive problems with more stringent conditions, namely, when the terms are almost equal. Short trigonometric sums that arise when solving additive problems with almost equal terms were first studied by I. M. Vinogradov. The relevance and appropriateness of this monograph are determined by the fact that it- studied the behavior of G. Weyl's short trigonometric sums of the formT(α, x, y)=∑_(x-yin large arcs;- the results obtained made it possible to find an asymptotic formula for the number of representations of a sufficiently large natural number as a sum of three almost equal terms, two of which are prime numbers, and the third is the fourth power of a natural number.
Mathematical Innovation
The transition to a competency-based approach in mathematics education is based on the need for students to acquire competencies that go beyond mere theoretical knowledge. This approach focuses on the practical application of knowledge, developing in students the ability to solve problems, think critically and work in teams. Traditional assessment, based on written tests, has proven to be insufficient to measure these competencies effectively. In contrast, competency-based assessment methods, such as performance tests and projects, allow for a more holistic and contextualized assessment of student learning. Gamification, on the other hand, defined as the use of game elements in non-game contexts, has gained popularity as a pedagogical strategy in teaching and learning. This strategy is based on the premise that gaming can make learning more attractive and motivating for students, gamification allows teachers to adapt their strategies to the needs and preferences of students, awakening their love and interest for the subject.
Application of Artificial Intelligence Methods in Processing of Emotions, Decisions and Opinions
During recent years, social infrastructure has become irreversibly linked to the Internet through its everyday manifestations, such as social networking services (Twitter, Facebook, etc.). Every second, this new tangible information-based reality provides large amounts of data filled with 1) emotional expressions; 2) people's opinions on various topics; and 3) their reasoning, revealing their decision-making processes. As these three categories are also closely interrelated with each other, they should be studied together to obtain a more robust view on all of the topics involved. This, as never before, provides an opportunity for the development and application of natural language processing methods, in particular those regarding such topics as emotion processing, decision-making, and opinion mining.
Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators
This reprint contains a collection of research papers on spectral theory for differential and functional differential operators. Spectral theory plays a fundamental role in mathematics and has applications in various fields of science and engineering, e.g., in quantum and classical mechanics, geophysics, acoustics, and electronics. The collection includes recent studies on a variety of topics such as analytical and numerical methods for solving direct and inverse spectral problems, new developments in the theory of partial differential equations, pseudo-differential equations with fractional derivatives, asymptotical analysis for solutions of differential equations, spectral theory for abstract operators in Hilbert spaces, and inverse nodal problems.
Machine Learning for Pattern Recognition
In recently arisen digital age, machine learning technology has made huge significant progress, revolutionizing applications in fields such as image recognition, speech processing, and natural language processing. These technologies have not only changed our daily lives, but have also had a profound impact on medicine, finance, transportation and other fields. However, pattern recognition, as an important branch of machine learning, still faces many challenges and problems. This reprint brings together contributions from leading experts in their fields. Each paper provides valuable insights into the latest trends, methods, and challenges in state-of-the-art applications of machine learning for pattern recognition. In addition, the research in each paper not only showcases the latest advancements in machine learning algorithms but also discusses their successful applications and the challenges encountered in real-world scenarios. As editors, we are honored to present this reprint, and we hope that readers, whether they be researchers, engineers, and students, will find inspiration and guidance in these papers as they explore the growing field of machine learning for pattern recognition. We express our gratitude to the authors for their outstanding contributions, to the reviewers for their critical evaluation, and to the assistant editor Mr. Musea Wu for his enthusiastic help. We are also sincerely grateful to our readers, whose curiosity and enthusiasm continue to drive innovation in this exciting field.
