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.
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."
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.
Discretization in Differential Equations and Enclosures
No detailed description available for "Discretization in Differential Equations and Enclosures".
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.
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 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.
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 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.
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.
Modeling and Simulation of Environmental Systems
This book presents an overview of modeling and simulation of environmental systems via diverse research problems and pertinent case studies, covering air pollution modeling, sustainable water resources modeling, IoT based applications in environmental systems, and future algorithms and conceptual frameworks in environmental systems.
Spline Approch for Solution of Fluid Flow Problems
The book on the numerical solution of Magnetohydrodynamic (MHD) fluid flow problems using the spline collocation method provides a comprehensive exploration of how spline functions can be applied to solve complex MHD equations. It covers the fundamentals of MHD, where fluid dynamics and electromagnetism intersect, and introduces spline collocation as an efficient numerical technique for approximating solutions. The book details the method's application in various MHD problems, emphasizing its accuracy and computational efficiency. Through examples and case studies, the text illustrates how the spline collocation method can effectively handle boundary layers, singularities, and other challenges typical in MHD fluid flow analysis.
Evolutionary Computation
Evolutionary computation offers powerful problem-solving methodologies inspired by models of natural genetics and evolutionary processes. Potential applications are wide-ranging and include problems related to combinatorial optimization, numerical optimization, multi-objective optimization, and others, as well as specific applications of these problems in diverse domains, such as engineering, design, medicine, robotics, science, etc. Techniques from evolutionary computation often lend themselves well to parallel and distributed implementations and are often more effective in dealing with challenging problem characteristics such as non-linearity and high dimensionality than alternative approaches. This Special Issue brings together recent advances in the theory and application of evolutionary computation.
Theory of Distributions
The Theory of Distributions, also known as the theory of generalized functions, is a mathematical analysis framework extending the classical notion of functions and derivatives. Introduced by Laurent Schwartz in the mid-20th century, this theory addresses limitations in traditional function analysis, particularly in handling functions that are not differentiable in the classical sense. Distributions generalize functions by defining them as continuous linear functional on a space of test functions, typically smooth and rapidly decreasing functions. This approach facilitates the rigorous treatment of objects like the Dirac delta function, which is pivotal in various applications across physics and engineering. Distributions are integral in solving differential equations, especially in contexts where classical solutions may not exist or be easily identifiable. They enable the extension of operations such as differentiation and convolution to a broader class of objects, thereby providing a robust toolkit for addressing problems in partial differential equations, signal processing, and quantum mechanics.
Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems
Due to rapid developments in computing, communication, and sensing technology, multi-agent systems have become increasingly ubiquitous. Their applications include mobile sensor networks, autonomous vehicles, intelligent transportation systems, and smart grids. The complex unknown environment and inaccurate dynamics prose additional challenges for the modeling, control, and optimization of such systems. Therefore, data science and machine learning are providing opportunities to develop artificial intelligence-based methods and enable new control and optimization paradigms for multi-agent systems. The aim of this Special Issue is to bring together significant developments in the interface between machine learning, neurodynamics, and swarm intelligence.
Utility of Quaternions in Physics
Utility of Quaternions in Physics, a classical book, has been considered important throughout the human history, and so that this work is never forgotten we at Alpha Editions have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies of their original work and hence the text is clear and readable.
Didactic games
This book arose from the desire and need to make maths lessons more attractive, interesting and enjoyable for both teachers and students. We are using didactic games as a way of intervening in maths lessons to try to reduce or solve the difficulties that students have in this subject. Our intention is to contribute to a reflection on the teacher's didactic-pedagogical action in order to improve the teaching-learning process in Maths, bringing about more meaningful learning, suggesting games as a teaching strategy that will reduce the existing blockages between the student and this subject, as well as reporting on some classroom experiences.
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications. Volume 15, issue 5, October 2024. Special Issue
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.
Problems and elegant solutions in mathematical analysis
This is a mathematical reference book for students, graduates and researchers who are interested in the challenging problems as the extreme of function, equation and series arising in the mathematical analysis. The book aims at encouraging those who were accustomed to standard calculation to be interested in solution of more challenging problems such as differential equation, integral equation and series. This research paper is the limit part of "challenging problems and elegant solution in mathematical analysis" to continuity of limit part, integral part and equation part. It can be widely used by students in mathematics and physics, and everyone who is interested in mathematical analysis. It is certain that this will be contributed to the students, the graduates and researchers who are going to mathematically analyze the physical situations arise in advanced science and technology.
Euclid Transmogrified
This book tells the extraordinary story of how in the mid twentieth century, in a well-developed European country, a mathematically solid system of geometry was altered to such an extent that more than one million students were taught foundationally flawed geometry over more than a quarter of a century. The almost unbelievable situation came about in Ireland in the wake of early postcolonial developments that gave rise to an impressionable and unqualified civil service in a position of power over a nation's educational development. This is a multifaceted tale of a perfect storm within mathematics development in Ireland whose result was so destructive that its ramifications continue to be felt into the twenty-first century, forty years after a report of a Royal Irish Academy commission of professors of mathematics described the matter as a national scandal. Euclid Transmogrified: A National Scandal may be of interest to mathematics teachers, lecturers in mathematics, mathematical historians, lecturers in education, students of mathematical education, administrators of mathematical education, science administrators, science journalists and those educated in mathematics in Ireland, especially those born between 1954 and 2000. https: //sites.google.com/view/euclidtransmogrified1
Applications of partial differential equations in plasma physics I
Authors introduced advanced applications of partial differential equations in plasma physics using analytical methods based on Boltzmann-Maxwell equations. The book creates theoretical tools for predicting and controlling plasma behavior in many outstanding applications. In the study was introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and flux variables as two new scientific achievements. Secondly, with reasonable accuracy, was determined the thermodynamic equilibrium time of electrons under an external force. Authors clarify the difference between an equilibrium velocity distribution function and a perturbed one. The book introduces the extended Gibbs equation, which predicts ratios between various contributions to the internal energy change for diamagnetic and paramagnetic plasmas. A standard laboratory argon plasma model is used to apply the results. It advances our understanding of plasma physics and holds immense potential for practical applications in aerospace engineering, plasma technology, and materials science. This book lays the groundwork for future innovations and technological advancements in plasma.
Mathematical Logic
The book "Mathematical Logic" has been meticulously prepared to serve the students of the B.A./ B.Sc./ B.Com. third semester (As per NEP-2020 new syllabus) Mathematics skill enhancement course under Dibrugarh University. Mathematical logic is a fundamental course in undergraduate mathematics, providing essential tools and concepts that are foundational for further studies in the field. This book covers all the topics outlined in the syllabus.
Methods of Graph Decompositions
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Lexy and Kaylee's Advanced Nurikabe for Adults and Teens Volume Two
From the creators of Lexy and Kaylee's Canine Coloring Book for Children series now have put together an activity book for Adults and Teens. Inside there are 52 advanced 24x24 Nurikabe Puzzles in an easy to carry 6 x 9 format. Great for taking with you on plane and train rides or to sit at the beach or by the pool.Nurikabe is a logic puzzle that originated in Japan. The puzzle is named after a mythical creature from Japanese folklore, believed to create invisible walls to block travelers. Here's an overview of its history and how it has evolved: Origins and Development: The name "Nurikabe" is derived from a Japanese folklore creature that is said to appear as an invisible wall obstructing travelers' paths. This connection to the mythical creature adds a cultural layer to the puzzle's identity. The exact origins of the Nurikabe puzzle is not well-documented, but it is known to have been popularized by the Japanese puzzle company Nikoli. Nikoli has been instrumental in developing and spreading various types of logic puzzles, including Sudok. Nurikabe was first introduced in Nikoli's Puzzle magazine in the late 20th century. The puzzle quickly gained a following among puzzle enthusiasts in Japan and later internationally.Spread and Popularity: Like many other logic puzzles, Nurikabe became popular in Japan through Nikoli's publications. Japanese puzzle solvers appreciated its unique challenge and engaging nature. Nurikabe began to spread outside Japan in the early 21st century as puzzle enthusiasts and publishers in other countries discovered it. The rise of the internet and puzzle apps contributed significantly to its global popularity. Nurikabe is now available on various online puzzle platforms and mobile apps, allowing a global audience to enjoy the puzzle.Mechanics and Rules: Nurikabe is played on a rectangular grid, with some cells containing numbers. The goal is to shade specific cells to form a continuous "wall" while leaving the remaining cells as "islands."Cultural and Educational Impact: Nurikabe has a dedicated following among puzzle enthusiasts. It is often featured in puzzle magazines, websites, and competitions. The puzzle is also used in academic settings to teach logical reasoning and problem-solving skills. Its unique rules and requirements make it an excellent exercise in spatial awareness and deductive logic.Variations and Adaptations: Over time, different variations of Nurikabe have emerged, introducing new challenges and twists to the original rules. Some puzzles may have different grid shapes or additional constraints to increase difficulty. Nurikabe has also inspired hybrid puzzles that combine their elements with other logic puzzles, creating new and innovative challenges for solvers.Nurikabe is a logic puzzle deeply rooted in Japanese culture and folklore. It has grown in popularity both in Japan and internationally, thanks to its challenging nature and the efforts of puzzle publishers like Nikoli. Today, it continues to be a beloved puzzle enjoyed by many worldwide.
Modeling of biomechanical heat transfer in human physiology
This book explores the intricate connections between various disciplines such as anatomy, physiology, neurology, and the biomechanical aspects of heat transfer within the human body. It highlights the significant overlap between kinesiology, the systematic study of human movement, and biomechanics, particularly in analyzing movement patterns, enhancing physical performance, and addressing mechanical factors underlying injuries and diseases. The primary objectives include optimizing physical performance and understanding injury processes for prevention strategies. Biomechanics, as delineated in the book, comprises two principal sections: kinematics and kinetics. Kinematics involves the detailed description of motion, encompassing movement patterns and the sequencing of body segments that influence coordination and performance outcomes. In contrast, kinetics investigates the causes of motion, particularly the forces acting on the body. This distinction underscores kinetics' focus on force analysis, setting it apart from kinematics which primarily concerns itself with describing motion patterns.
Contributions to the Theory of Special Functions and Number Theory
The author has given a brief introduction of an all-time great Mathematician Srinivasa Ramanujan, the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including Mathematical analysis, Infinite series, Continued fractions, Number theory and Game theory.He has established new general theorems for the explicit evaluations of Ramanujan's remarkable product of theta function and their new explicit assessment.He has also established several new P - Q eta-function identities which were obtained, leading to several new modular relations for the Ramanujan-G繹llnitz-Gordon continued fraction.He has obtained a continued fraction of order 12 and evaluated several new identities analogous to the Rogers-Ramanujan continued fraction and Ramanujan's cubic continued fraction.He has derived some new modular equations of degree 5 for the ratios of Ramanujan's theta function and new modular relations for Ramanujan's parameters related to Rogers-Ramanujan's continued fraction were also established along with their explicit evaluations.
Mathematical Methods for Operations Research Problems
This reprint of the Special Issue in the journal Mathematics presents research in the area of Operations Research. The subjects addressed in the 15 research papers cover a broad spectrum of subjects, such as machine learning, scheduling, timetabling, or graph theory.
Some Studies on Theta Functions and Their Related Identities
The author has given a brief introduction of an all-time great Mathematician Srinivasa Ramanujan, the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including Mathematical analysis, Infinite series, Continued fractions, Number theory and Game theory.He has established several interesting and new explicit evaluations for newly defined parameters by using Ramanujan Weber class invariants, modular equations and mixed-modular equations.He has established several new explicit evaluations of Ramanujan's remarkable product of theta-function.He has established some new general theorems for explicit evaluations of the product of theta-function.He has derived several general formulas for explicit evaluations of Ramanujan's cubic continued fractions, reciprocity theorems, two formulas connecting V(q) and V(q3) and also established some explicit evaluations using the values of the remarkable product of theta-function.He has obtained a modular transformation formula for the theta-function.
Fuzzy Optimization Techniques in the Areas of Science and Management
This book helps to enhance the application of fuzzy logic optimization in the areas of science and engineering. It includes implementation and modeling paradigms such as path planning and routing design for different wireless networks, organization behavior strategies modeling, and so forth.
High Dimensional Space to Formulate Marriage and Birth Functions
The reaction-diffusion system describes the fertility decline process, elaborating where and when fertility declines and analyzes how to slow down the fertility decline using Brittany as a testing ground. The model used suggests that our behaviors are not governed by our conscious wills but by surrounding environment.
Quantitative Literacy Through Games and Gambling
This book was developed to address a need. Quantitative Literacy courses have been established in the mathematics curriculum for decades now. The students in these courses typically dislike and fear mathematics, and the result is often a class populated by many students that are unmotivated and uninterested in the material.
