Bøger af Olga Moreira

"Basic Theory of Fractional Differential Equations" is a contemporary collection of 16 articles that explores modern methods and applications of FDEs. It covers the extended Jacobi elliptic function expansion method, numerical approximation techniques like -step continuous BDFs for FIVPs, stability theories, and various fractional derivatives. The book finds applications in diverse fields, making it a valuable tool for solving real-world problems in physics, engineering, finance, and biology.

"The Application of Probability Theory" is a comprehensive book that explores the diverse applications of probability theory across various fields, ranging from statistics and data analysis to machine learning and artificial intelligence, medical and health sciences, natural language processing, information retrieval, and engineering. The book delves into the fundamental principles and concepts of probability theory, such as sample space, events, probability distribution, random variables, probability laws, and expected value, and highlights the distinctions between frequentist and Bayesian approaches. With a collection of contemporaneous articles, it presents cutting-edge research and practical examples that showcase the relevance and impact of probability theory in understanding uncertainty, making predictions, assessing risks, designing experiments, and conducting statistical inference. Whether it's developing statistical models for missing data, enhancing machine learning algorithms with probability information, optimizing clinical trial designs for Alzheimer's disease, predicting urinary tract infections, or detecting fake news and hate speech, this book serves as a valuable resource for researchers, practitioners, and students seeking a deeper understanding of the applications of probability theory in today's rapidly evolving world.

"An Introduction to Algebraic and Combinatorial Coding Theory" is a comprehensive book that offers a thorough exploration of the principles and techniques of coding theory. It serves as a valuable resource for readers interested in gaining a deeper understanding of error detection and correction in communication systems. With its well-structured chapters covering coding theory fundamentals, algebraic codes, cyclic codes, block codes, and advanced coding techniques, this book caters to the needs of students, researchers, and professionals in the field. It provides a solid foundation in coding theory and showcases its practical applications in various domains, including telecommunications, data storage, and cryptography.

"Functional Calculus" is a comprehensive book that offers readers a thorough exploration of the subject, covering fundamental concepts, techniques, and applications. By establishing a solid foundation in calculus and functional analysis, the book ensures a clear understanding of the underlying principles. With a focus on topics such as operator theory, spectral theory, and Banach spaces, readers are guided through a wide range of essential areas. Through rigorous explanations and numerous examples, the book enables readers to develop a deep comprehension of functional calculus and its practical significance in solving problems involving operators, transformations, and function spaces. This invaluable resource is tailored to students, researchers, and professionals seeking to master functional calculus and apply its principles across various disciplines in mathematics and beyond.

"The Notion Of Mathematical Proof: Key Rules And Considerations" is an edited book consisting of 16 contemporaneous open-access articles that aim to cover the different aspects of learning and teaching mathematical proof. The first part of this book aims at summing up factors that influence the cognitive development required to successfully understand and solve mathematical proofs. The second part of the book aims to overview implementations of learning methods for constructing and evaluating the validity of mathematical proof, as well as to provide strategies for overcoming possible difficulties in mathematical proof processing. It also includes other studies related to mathematical proof and a motion-based program for improving mathematical reasoning through action. This book is intended to reach out to an academic audience ranging from undergraduate students to junior researchers.

"The Use Of Mathematical Structures: Modelling Real Phenomena" is an edited book consisting of 16 contemporaneous open-access articles that are devoted to the mathematical modelling of natural phenomena. To summarize, this book is about the use of applied mathematics and mathematical analysis in the context of its applications to real-world problems. It includes a selection of real-world problems in fluid dynamics, mechanical engineering, biology, and biochemistry. The last chapters include the mathematical modelling of the COVID-19 virus. The intended audience of this book is undergraduate and graduate students, as well as junior researchers. The reader must have a good knowledge of ordinary differential equations, boundary value problems, fractional calculus, stability theory, and wavelets in order to fully understand the real-world problems and their mathematical modelling included in this book.

"The Use of Abstraction and Logic in Mathematics" is an edited book consisting of 16 contemporaneous open-access articles that are essentially devoted to mathematical logic research, from classical to non-classical logical systems, from algebraic logic to fuzzy logic. The book addresses the following mathematical logic topics: first-order and higher-order logic; as well as infinitary, description, modal; fixed-point, algebraic and fuzzy logic. This book also includes examples of practical applications of logical systems in link prediction and image processing tasks, as well as in the training of neural networks and artificial intelligence. The intended audience of this book is undergraduate and graduate students, as well as junior researchers. Familiarity with first-order and higher-order logics, as well as set theory, and algebra is essential to grasp the concepts and methods described in this book.

"Advanced Techniques for Collecting Statistical Data" is an edited book consisting of 17 contemporaneous open-access articles focused on data collection methods, from qualitative research techniques to automated data collection systems. The first chapters include a practical guide to designing, sampling, and collecting qualitative research data. The second part of the book is devoted to data mining of information collected from clinical and social studies surveys, as well as from social media. The final chapters reflect on current efforts to optimize and automate data collection procedures. This book also includes new methodologies based on automatic data collection and analysis systems based on smartphone technology and artificial intelligence, as well as their application in clinical research, sociology, stock market prediction and other fields. This book is intended to reach an academic audience ranging from undergraduate students to junior researchers.

"Applied Mathematics in Engineering" is an edited book comprising 15 contemporaneous open-access articles focused on mathematical modelling, mathematical optimization, and fractal mathematics and their applications in modern engineering and industry. The first part covers a wide range of mathematical models for solving real-world problems in mechanical engineering, biomedicine, fluid dynamics, and other applications. The second part of the book presents various mathematical optimization methods and algorithms (e.g. topology optimization, hybrid arithmetic optimization, and isogeometric topology optimization) for solving engineering problems. The third part of the book is dedicated to the mathematics of fractals and its applications in the engineering of antennas, image compression technology, fracture mechanics, ophthalmology and more. The intended audience of this book is undergraduate and graduate students, as well as junior researchers.