D'Oh! Fourier: Theory, Applications, and Derivatives
D'oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively.The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D'oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book.
Modern Problems of Mathematical Physics and Their Applications
There are many applications of mathematical physics in several fields of basic science and engineering. Thus, we have tried to provide the Special Issue "Modern Problems of Mathematical Physics and Their Applications" to cover the new advances of mathematical physics and its applications. In this Special Issue, we have focused on some important and challenging topics, such as integral equations, ill-posed problems, ordinary differential equations, partial differential equations, system of equations, fractional problems, linear and nonlinear problems, fuzzy problems, numerical methods, analytical methods, semi-analytical methods, convergence analysis, error analysis and mathematical models. In response to our invitation, we received 31 papers from more than 17 countries (Russia, Uzbekistan, China, USA, Kuwait, Bosnia and Herzegovina, Thailand, Pakistan, Turkey, Nigeria, Jordan, Romania, India, Iran, Argentina, Israel, Canada, etc.), of which 19 were published and 12 rejected.
Metric Spaces
- 1. Metric Spaces. - 2. Basic Theory of Metric Spaces. - 3. Completeness of the Classical Spaces. - 4. Compact Spaces. - 5. Separable Spaces. - 6. Properties of Complete Spaces. - 7. Connected Spaces. - Afterword.
In Memoriam, Solomon Marcus
This book commemorates Solomon Marcus's fifth death anniversary with a selection of articles in mathematics, theoretical computer science, and physics written by authors who work in Marcus's research fields, some of whom have been influenced by his results and/or have collaborated with him.
Perfect Codes and Related Structures
In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics - Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tilings, combinatorial designs, and more. The goal is to give the aspects of all these codes, to derive bounds on their sizes, and present various constructions for these codes.The intention is to offer a different perspective for the area of perfect codes. For example, in many chapters there is a section devoted to diameter perfect codes. In these codes, anticodes are used instead of balls and these anticodes are related to intersecting families, an area that is part of extremal combinatorics. This is one example that shows how we direct our exposition in this book to both researchers in coding theory and mathematicians interested in combinatorics and extremal combinatorics. New perspectives for MDS codes, different from the classic ones, which lead to new directions of research on these codes are another example of how this book may appeal to both researchers in coding theory and mathematicians.
Classical and Modern Optimization
The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.
Classical and Modern Optimization
The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.
Diffusion Processes, Jump Processes, and Stochastic Differential Equations
This book provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, SDEs and the fractional infinitesimal operators. The draft of this book has been extensively classroom tested by the author at CWRU in a course that enrolled seniors and graduate students.
Set Function T
Preliminaries.- The Set Function T.- Decomposition Theorems.- T-Closed Sets.- Continuity of T.- Images of T.- Applications.- Questions.- References.- Index.
Frameworks, Tensegrities, and Symmetry
This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.
The Mordell Conjecture
The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell-Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole.
Math Girls 6
This sixth entry in the highly acclaimed Math Girls series focuses on the Poincar矇 Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of K繹nigsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the M繹bius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincar矇 Conjecture. Math Girls 6: The Poincar矇 Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators.
Math Girls 6
This sixth entry in the highly acclaimed Math Girls series focuses on the Poincar矇 Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of K繹nigsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the M繹bius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincar矇 Conjecture. Math Girls 6: The Poincar矇 Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators.
Discrete Fractional Calculus and Fractional Difference Equations
This brief aims to merge the theories of fractional calculus and discrete calculus in a concise but comprehensive manner. It is designed for graduate students, but will be useful for any researcher interested in the theory of discrete fractional calculus and fractional difference equations.
Fractals in Engineering: Theoretical Aspects and Numerical Approximations
C. Alberini and S. Finzi Vita, A numerical approach to a nonlinear diffusion model for self-organised criticality phenomena.- M. Cefalo et al., Approximation of 3D Stokes flows in fractal domains.- S. Fragapane, ∞-Laplacian obstacle problems in fractal domains.- M. Gabbard, Discretization of the Koch Snowflake Domain with Boundary and Interior Energies.- M.V. Marchi, On the dimension of the Sierpinski gasket in l2.- U. Mosco and M.A. Vivaldi, On the external approximation of Sobolev spaces by M-convergence.- A. Rozanova-Pierrat, Generalization of Rellich-Kondrachov theorem and trace compacteness for fractal boundaries.
Partial Truths
A fast-food chain once tried to compete with McDonald's quarter-pounder by introducing a third-pound hamburger--only for it to flop when consumers thought a third pound was less than a quarter pound because three is less than four. Separately, a rash of suicides by teenagers who played Dungeons and Dragons caused a panic in parents and the media. They thought D&D was causing teenage suicides--when in fact teenage D&D players died by suicide at a much lower rate than the national average. Errors of this type can be found from antiquity to the present, from the Peloponnesian War to the COVID-19 pandemic. How and why do we keep falling into these traps? James C. Zimring argues that many of the mistakes that the human mind consistently makes boil down to misperceiving fractions. We see slews of statistics that are essentially fractions, such as percentages, probabilities, frequencies, and rates, and we tend to misinterpret them. Sometimes bad actors manipulate us by cherry-picking data or distorting how information is presented; other times, sloppy communicators inadvertently mislead us. In many cases, we fool ourselves and have only our own minds to blame. Zimring also explores the counterintuitive reason that these flaws might benefit us, demonstrating that individual error can be highly advantageous to problem solving by groups. Blending key scientific research in cognitive psychology with accessible real-life examples, Partial Truths helps readers spot the fallacies lurking in everyday information, from politics to the criminal justice system, from religion to science, from business strategies to New Age culture.
Machine Learning for Decision Sciences with Case Studies in Python
This book provides a detailed description of machine learning algorithms in Data Analytics, Data Science Lifecycle, Python for Machine Learning, Linear Regression, Logistic Regression and so forth. The focus is on Python programming for machine learning and patterns involved in decision science for handling data including real-world examples.
Advanced Engineering Mathematics
The topics include essential, advanced mathematics to access as a refresher or to add to the mathematical education and address the needs of engineers and scientists who need to expand their working knowledge. These topics are driven by applications and exercises with solutions are offered to confirm understanding.
Science Sketches
This book is the second collection of over 50 articles and essays authored by Sidney Perkowitz. Appearing in diverse outlets such as Discover, Washington Post, Aeon, Los Angeles Review of Books, Nautilus, Museum of the Moving Image, and Physics World, they represent the best of his writing about science and technology, and their links to culture and society, the arts and the media, and the humanities. Written for general readers, the pieces explore the outer and inner universes from cosmic space to the human mind, from the artistic use of science to the impact of technology and AI in the justice system, in medicine, and in dealing with COVID-19.
Carbon-Based Materials
New carbon materials with improved mechanical, electrical, chemical, and optical properties are predicted and considered to be very promising for practical application. Carbon-based materials in the form of films, fabrics, aerogels, or microstructural materials are known for their large surface areas and pore volumes, light weight, and a great variety of structural morphology. Such unique structures can then be employed for a variety of purposes, for example, the production of new electronic devices, energy storage, and the fabrication of new materials. Nowadays, clear understanding of carbon materials via several examples of synthesis/processing methodologies and properties characterization is required. This Special Issue, "Carbon-Based Materials", addresses the current state regarding the production and investigation of carbon-based materials. It consists of 13 peer-reviewed papers that cover both theoretical and experimental works in a wide a range of subjects on carbon structures.
Mathematical Modeling the Life Sciences
The purpose of this unique textbook is to bridge the gap between the need for numerical solutions to modelling techniques through computer simulations to develop skill in employing sensitivity analysis to biological and life sciences applications.
Theory of Groups of Finite Order
CHAPTER I. ON SUBSTITUTIONS.CHAPTER II. THE DEFINITION OF A GROUP.CHAPTER III. ON THE SIMPLER PROPERTIES OF A GROUP WHICH ARE INDEPENDENT OF ITS MODE OF REPRESENTATION.CHAPTER IV. ON ABELIAN GROUPS.CHAPTER V. ON GROUPS WHOSE ORDERS ARE POWERS OF PRIMESCHAPTER VI. ON SYLOW'S THEOREM.CHAPTER VII. ON THE COMPOSITION-SERIES OF A GROUP.CHAPTER VIII. ON SUBSTITUTION GROUPS: TRANSITIVE AND INTRANSITIVE GROUPS.CHAPTER IX. ON SUBSTITUTION GROUPS: PRIMITIVE AND IMPRIMITIVE GROUPS.CHAPTER X. ON SUBSTITUTION GROUPS: TRANSITIVITY AND PRIMITIVITY: (CONCLUDING PROPERTIES).CHAPTER XI. ON THE ISOMORPHISM OF A GROUP WITH ITSELF.CHAPTER XII. ON THE GRAPHICAL REPRESENTATION OF A GROUPCHAPTER XIII. ON THE GRAPHICAL REPRESENTATION OF GROUPS: GROUPS OF GENUS ZERO AND UNITY: CAYLEY'S COLOUR GROUPS CHAPTER XIV. ON THE LINEAR GROUP.CHAPTER XV. ON SOLUBLE AND COMPOSITE GROUPS
On The Study and Difficulties of Mathematics
I. Introductory Remarks on the Nature and Objects of MathematicsII. On Arithmetical NotationIII. Elementary Rules of ArithmeticIV. Arithmetical FractionsV. Decimal FractionsVI. Algebraical Notation and PrinciplesVII. Elementary Rules of AlgebraVIII. Equations of the First DegreeIX. On the Negative Sign, etcX. Equations of the Second DegreeXI. On Roots in General, and LogarithmsXII. On the Study of AlgebraXIII. On the Definitions of GeometryXIV. On Geometrical ReasoningXV. On AxiomsXVI. On ProportionXVII. Application of Algebra to the Measurement of Lines, Angles, Proportion of Figures, and Surfaces
Mathematical Logic
This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene's theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht- Fra簿ss矇 game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson's theory, Peano's axiom system, and G繹del's incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic. Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style and topics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including G繹del's famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
Polynomial Methods and Incidence Theory
The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.
Large-Scale Convex Optimization
Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods - including parallel-distributed algorithms - through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.
100+1 Problems in Advanced Calculus
This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination.In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l'Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found atthe end of each chapter.Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.
Applications of Wavelet Multiresolution Analysis
Fabio, M. et al., Approximate Solutions to Fractional Boundary Value Problems by Wavelet Decomposition Methods.- Calder籀n, L., Wavelet B-splines bases on the interval for solving boundary value problems.- La Mura, G. et al, Kalman-Wavelet combined Filtering.- Arouxet, M. et al., Using the Wavelet Transform for Time Series Analysis.- Muszkats, J. et al., Application of Wavelet Transform to Damage Detection in Brittle Materials via Energy and Entropy Evaluation of Acoustic Emission Signals.
Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification
This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference "Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification", held on the occasion of Chari's 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari's significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorificationQuantum affine algebras and cluster algebrasSteinberg groups for Jordan pairsDynamical quantum determinants and PfaffiansInteractions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
Mathematical Analysis in Interdisciplinary Research
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
Minimal Surfaces from a Complex Analytic Viewpoint
1 Fundamentals.- 2 Basics on Minimal Surfaces.- 3 Approximation and Interpolations Theorems for Minimal Surfaces.- 4 Complete Minimal Surfaces of Finite Total Curvature.- 5 The Gauss Map of a Minimal Surface.- 6 The Riemann-Hilbert Problem for Minimal Surfaces.- 7 The Calabi-Yau Problem for Minimal Surfaces.- 8 Minimal Surfaces in Minimally Convex Domains.- 9 Minimal Hulls, Null Hulls, and Currents.- References.- Index.
Linear Algebra
Linear algebra is a vital course for students. Few subjects can claim to have such widespread applications in other areas of mathematics-multi variable calculus, differential equations, probability, and in physics, biology, chemistry, economics, finance, psychology, sociology. and all fields of engineering. It also presents the students with an excellent opportunity to learn how to deal with abstract concepts. This module introduces the basic ideas and computational techniques of linear algebra. It also includes a wide variety of carefully selected applications. It also introduces the students to working with abstract concepts. Finally, in covering the basic ideas of linear algebra, the abstract ideas are carefully balanced by a considerable emphasis on the geometrical and computational aspects of the subject. Throughout this module, a great variety of examples and exercises of the important concepts are included. The study of such examples is of fundamental importance. It tends to minimize the number of students who can repeat definition, theorem, and proof logically without grasping the meaning of the abstract concepts. Assessments are also included in every section of this module to measure the students' learning as to how far they have learned the concepts. Finally, answers on exercises are provided for the students to answer the assessments. As with the rest of the book, the exercises and assessments aim to buildability and help students experience the pleasure of doing mathematics. Students should see how the ideas arise and should be able to picture themselves doing the same type of work.
Advances in Transmission Electron Microscopy for the Study of Soft and Hard Matter
This book provides readers with some examples of advanced applications of electron microscopy on organic and inorganic specimens, highlighting out how new original approaches could provide a deeper understanding of the properties of matter and how a transmission electron microscope is not only a microscope but also a flexible tool for tailoring experiments, properly suited, to the issue of interest.
Mathematical Music
Mathematical Music offers a concise and easily accessible history of how mathematics was in fact used broadly to create music.
Application of Multi-Sensor Fusion Technology in Target Detection and Recognition
Application of multi-sensor fusion technology has drawn a lot of industrial and academic interest in recent years. The multi-sensor fusion methods are widely used in many applications, such as autonomous systems, remote sensing, video surveillance, and the military. These methods can obtain the complementary properties of targets by considering multiple sensors. On the other hand, they can achieve a detailed environment description and accurate detection of interest targets based on the information from different sensors.This book collects novel developments in the field of multi-sensor, multi-source, and multi-process information fusion. Articles are expected to emphasize one or more of the three facets: architectures, algorithms, and applications. Published papers dealing with fundamental theoretical analyses, as well as those demonstrating their application to real-world problems.
Dynamics of Disasters
Based on the "Fourth International Conference on Dynamics of Disasters" (Kalamata, Greece, July 2019), this volume includes contributions from experts who share their latest discoveries on natural and unnatural disasters. Authors provide overviews of the tactical points involved in disaster relief, outlines of hurdles from mitigation and preparedness to response and recovery, and uses for mathematical models to describe natural and man-made disasters. Topics covered include economics, optimization, machine learning, government, management, business, humanities, engineering, medicine, mathematics, computer science, behavioral studies, emergency services, and environmental studies will engage readers from a wide variety of fields and backgrounds.
Evolutionary Algorithms in Engineering Design Optimization
Evolutionary algorithms (EAs) are population-based global optimizers, which, due to their characteristics, have allowed us to solve, in a straightforward way, many real world optimization problems in the last three decades, particularly in engineering fields. Their main advantages are the following: they do not require any requisite to the objective/fitness evaluation function (continuity, derivability, convexity, etc.); they are not limited by the appearance of discrete and/or mixed variables or by the requirement of uncertainty quantification in the search. Moreover, they can deal with more than one objective function simultaneously through the use of evolutionary multi-objective optimization algorithms. This set of advantages, and the continuously increased computing capability of modern computers, has enhanced their application in research and industry. From the application point of view, in this Special Issue, all engineering fields are welcomed, such as aerospace and aeronautical, biomedical, civil, chemical and materials science, electronic and telecommunications, energy and electrical, manufacturing, logistics and transportation, mechanical, naval architecture, reliability, robotics, structural, etc. Within the EA field, the integration of innovative and improvement aspects in the algorithms for solving real world engineering design problems, in the abovementioned application fields, are welcomed and encouraged, such as the following: parallel EAs, surrogate modelling, hybridization with other optimization techniques, multi-objective and many-objective optimization, etc.
Big Data Analytics and Information Science for Business and Biomedical Applications
The analysis of Big Data in biomedical as well as business and financial research has drawn much attention from researchers worldwide. This book provides a platform for the deep discussion of state-of-the-art statistical methods developed for the analysis of Big Data in these areas. Both applied and theoretical contributions are showcased.
The Making of Mathematics
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of G繹del's incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem provingby the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Introduction to Statistical Modelling and Inference
The book is based on the model-based theory, used widely by scientists in many fields. It covers simple experimental and survey designs, and　probability models up to and including generalised linear (regression) models and some extensions of these, including finite mixtures.
Formal and Analytic Solutions of Differential Equations
The book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.
Plane Geometry
The contents of the book are1 GEOMETRY.2 PLANE GEOMETRY.BOOK I. RECTILINEAR FIGURESBOOK II. THE CIRCLE.BOOK III. PROPORTION. SIMILAR POLYGONSBOOK IV. AREAS OF POLYGONS.BOOK V. REGULAR POLYGONS AND CIRCLES
A Primer Of Quaternions
The contents of the book are as follows1. Steps Definitions and Theorems Centre of Gravity Curve Tracing, Tangents Parallel Projection Step Proportion Examples2. Rotations. Turns. Arc StepsDefinitions and Theorems of Rotation Definitions of Turn and Arc Steps Examples3. QuaternionsDefinitions and Theorem Examples Multiplication The Rotator q()q-1 Powers and Roots Representation of Vectors Examples Addition Formulas Geometric Theorems Examples 4. Equations of First Degree Scalar Equations, Plane and Straight LineExamplesNonions Vector Equations, the Operator φ Linear Homogeneous Strain Finite and Null Strains Solution of φρ = δ Derived Moduli. Latent Roots Latent Lines and Planes The Characteristic Equation Conjugate Nonions Self-conjugate Nonions Examples
