An Algebra for Secondary Schools
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Examples In Arithmetic Part II
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Data Structure Choice / Formal Differentiation. By Ssu-cheng Liu and Robert Paige
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Bank Administration
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Bulletin of the Iowa Engineering Experiment Station, Issues 14-24
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Magnetohydrodynamic Nozzle Flow With Three Transitions
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Mathematical Modeling and Simulation in Mechanics and Dynamic Systems
The present book contains the 16 papers accepted and published in the Special Issue "Mathematical Modeling and Simulation in Mechanics and Dynamic Systems" of the MDPI "Mathematics" journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering.It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity.
Drag on a Body in Nearly-free Molecular Flow
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Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications, Volume 9, Issue 2, April 2022
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.
Research on Cosmic Rays and Their Impact on Human Activities
The galactic cosmic-ray spectrum extends over 14 orders of magnitudes in energy and about 12 orders of magnitude in intensity, and it can be studied using two different methods: via the "direct detection" of the primary cosmic rays in space or at high altitude and via the "indirect detection" of secondary particles, namely the extensive air showers produced by a primary cosmic-ray particle impinging the atmosphere. In this Special Issue, both direct and indirect measurements are presented via from various experiments. Emphasis is placed on low-energy electrons and protons that are detected in flight as well as during geomagnetic storms. As for indirect detection, the muon flux determination and modulation at ground level are described in great detail. Some of the most interesting results are hereby presented, and a couple of new techniques in cosmic-ray detection are reported.
Fractional Calculus and the Future of Science
Newton foresaw the limitations of geometry's description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton's laws. Mandelbrot's mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton's macroscopic world view. Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton's laws to describe the many guises of complexity, most of which lay beyond Newton's experience, and many had even eluded Mandelbrot's powerful intuition. The book's authors look behind the mathematics and examine what must be true about a phenomenon's behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding.
Stability Problems for Stochastic Models
Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21-25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: - Limit theorems and stability problems; - Asymptotic theory of stochastic processes; - Stable distributions and processes; - Asymptotic statistics; - Discrete probability models; - Characterization of probability distributions; - Insurance and financial mathematics; - Applied statistics; - Queueing theory;and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia.
Applications of Mathematical Models in Engineering
The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools
Lie Symmetry Analysis of Fractional Differential Equations
In this book, the authors try to answer vital Fractional differential equations questions by analyzing different aspects of fractional Lie symmetries and related conservation law.
An Introduction to Infinite-Dimensional Differential Geometry
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.
Fractional Calculus and Special Functions with Applications
The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications because of their properties of interpolation between integer-order operators. This field includes classical fractional operators such as Riemann-Liouville, Weyl, Caputo, and Grunwald-Letnikov; nevertheless, especially in the last two decades, many new operators have also appeared that often define using integrals with special functions in the kernel, such as Atangana-Baleanu, Prabhakar, Marichev-Saigo-Maeda, and the tempered fractional equation, as well as their extended or multivariable forms. These have been intensively studied because they can also be useful in modelling and analysing real-world processes, due to their different properties and behaviours from those of the classical cases. Special functions, such as Mittag-Leffler functions, hypergeometric functions, Fox's H-functions, Wright functions, and Bessel and hyper-Bessel functions, also have important connections with fractional calculus. Some of them, such as the Mittag-Leffler function and its generalisations, appear naturally as solutions of fractional differential equations. Furthermore, many interesting relationships between different special functions are found by using the operators of fractional calculus. Certain special functions have also been applied to analyse the qualitative properties of fractional differential equations, e.g., the concept of Mittag-Leffler stability. The aim of this book is to explore and highlight the diverse connections between fractional calculus and special functions, and their associated applications.
Elements of ∞-Category Theory
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
Fundamental Maths
Do you need to improve your confidence in maths? Does your maths need to be refreshed and refocused for engineering or science? Are there some elements of school maths you have forgotten or never quite mastered? With clear explanations, lots of examples and a friendly, encouraging style, Fundamental Maths is a short, easy-to-follow textbook that makes maths accessible and manageable for all. Written for students entering HE or FE courses in engineering or science, the author covers all the core topics and breaks them down into easily digestible chunks, keeping explanations clear and concise throughout. Put past anxieties about maths or gaps in your knowledge behind you!
Differential Geometry, Differential Equations, and Special Functions
This volume, the third of a series, consists of applications of Mathematica(R) to a potpourri of more advanced topics. These include differential geometry of curves and surfaces, differential equations and special functions and complex analysis. Some of the newest features of Mathematica(R) are demonstrated and explained and some problems with the current implementation pointed out and possible future improvements suggested. Contains a large number of worked out examples. Explains some of the most recent mathematical features of Mathematica(R). Considers topics discussed rarely or not at all in the context of Mathematica(R). Can be used to supplement several different courses. Based on actual university courses.
Finite Element Analysis
Finite Element Method popularly known as FEM has undergone a major paradigm shift from a detailed mathematical background to write tailor made computer programs, to an understanding of the subject for better utilisation of available software such as ANSYS, NISA, ADINA, PAFEC, NASTRAN etc. The author with his rich experience, has made an effort in this direction and prepared a textbook on FEM ideally suited for engineering students and design engineers. Special Features - Comprehensive study material including all relevant topics - approximate methods, matrix operations and theory of elasticity - Example problems & case studies for better understanding of the concepts - Includes properties of ductile and brittle materials, for design checks - Solved problems & objective questions - for students - Examples with a commercial software (ANSYS), common data mistakes and validation of results for code compliance - for practicing design engineers - Brief coverage of fracture mechanics, contact and gap elements & CFD.
Advanced Differential Equations
Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.
All the Math You'll Ever Need
A comprehensive and hands-on guide to crucial math concepts and terminology In the newly revised third edition of All the Math You'll Ever Need: A Self-Teaching Guide, veteran math and computer technology teacher Carolyn Wheater and veteran mathematics author Steve Slavin deliver a practical and accessible guide to math you can use every day and apply to a wide variety of life tasks. From calculating monthly mortgage payments to the time you'll need to pay off a credit card, this book walks you through the steps to understanding basic math concepts. This latest edition is updated to reflect recent changes in interest rates, prices, and wages, and incorporates information on the intelligent and efficient use of calculators and mental math techniques. It also offers: A brand-new chapter on hands-on statistics to help readers understand common graphs An easy-to-use-format that provides an interactive method with frequent questions, problems, and self-tests Complete explanations of necessary mathematical concepts that explore not just how math works, but also why it worksPerfect for anyone seeking to make practical use of essential math concepts and strategies in their day-to-day life, All the Math You'll Ever Need is an invaluable addition to the libraries of students who want a bit of extra help applying math in the real world.
Quick Calculus
Discover an accessible and easy-to-use guide to calculus fundamentals In Quick Calculus: A Self-Teaching Guide, 3rd Edition, a team of expert MIT educators delivers a hands-on and practical handbook to essential calculus concepts and terms. The author explores calculus techniques and applications, showing readers how to immediately implement the concepts discussed within to help solve real-world problems. In the book, readers will find: An accessible introduction to the basics of differential and integral calculus An interactive self-teaching guide that offers frequent questions and practice problems with solutions. A format that enables them to monitor their progress and gauge their knowledge This latest edition provides new sections, rewritten introductions, and worked examples that demonstrate how to apply calculus concepts to problems in physics, health sciences, engineering, statistics, and other core sciences. Quick Calculus: A Self-Teaching Guide, 3rd Edition is an invaluable resource for students and lifelong learners hoping to strengthen their foundations in calculus.
The Mathematical Mechanic
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.
Flatland A Romance of Many Dimensions
This book has been considered important throughout the human history, and so that this work is never forgotten we 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 and hence the text is clear and readable.
Student Solutions Manual for College Algebra and Trigonometry
The Statistical Foundations of Entropy
In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann-Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann-Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences. The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems.
Qualitative Theory of Odes: An Introduction to Dynamical Systems Theory
The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of the equations, without solving them explicitly. Therefore, in the first place such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that, even with the numerical approach to differential equations, all calculations are subject to a certain inevitable error. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state.Each chapter contains a series of problems (with varying degrees of difficulty) and a self-respecting student should solve them. This book is based on Raul Murillo's translation of Henryk Żolądek's lecture notes, which were in Polish and edited in the portal Matematyka Stosowana (Applied Mathematics) in the University of Warsaw.
Language, Logic, and Computation
This book constitutes the refereed proceedings of the 13th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2019, held in Batumi, Georgia, in September 2019. The volume contains 17 full revised papers presented at the conference from 17 submissions. The scientific program consisted of tutorials, invited lectures, contributed talks, and two workshops. The symposium offered two tutorials in language and logic and aimed at students as well as researchers working in the other areas: - Language: Sign language linguistics. State of the art, by Fabian Bross (University of Stuttgart, Germany) - Logic: Axiomatic Semantics, by Graham E. Leigh (University of Gothenburg, Sweden)
Bernoulli's Fallacy
There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations. Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics. Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach--that is, to incorporate prior knowledge when reasoning with incomplete information--in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli's Fallacy explains why something has gone wrong with how we use data--and how to fix it.
Plato's Ghost
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincar矇, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of na簿ve set theory and the revived axiomatic method-debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Optimization for Data Analysis
Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; foundations of the analysis of nonsmooth functions and optimization duality; and the back-propagation approach, relevant to neural networks.
Topological Data Analysis with Applications
The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.
Hilbert's Proof Theory and its modern Development
Seminar paper from the year 2021 in the subject Mathematics - Miscellaneous, grade: 1,0, University of Hagen, course: Philosophy of Mathematics, language: English, abstract: Imagine a world where the very bedrock of mathematical truth crumbles beneath your feet-this was the reality facing mathematicians in the early 20th century, a period of intense scrutiny and doubt known as the foundational crisis. This book delves into the fascinating story of how David Hilbert, a towering figure in mathematics, sought to rebuild this foundation through his ambitious program of proof theory. Explore the contrasting philosophies of classical versus intuitionistic mathematics, the revolutionary impact of Cantor's set theory, and the ensuing objections that threatened to unravel the entire mathematical edifice. Witness the rise of mathematical formalism, as signs are elevated to objects of study, and the birth of metamathematics, a new discipline dedicated to proving the consistency of mathematical systems. Unravel the intricacies of Hilbert's program, his attempt to secure mathematical certainty through finite means, and the devastating blow dealt by G繹del's incompleteness theorems, which revealed the inherent limitations of formal systems. Discover how Gentzen's groundbreaking work on natural deduction and transfinite induction offered a new path forward, transforming proofs into objects of mathematical inquiry in their own right. Finally, journey into the realm of modern proof theory, where category theory and lambda calculus provide powerful new frameworks for understanding the essence of mathematical truth and developing novel identity criteria for proofs. This book offers a comprehensive exploration of Hilbert's program, its challenges, and its enduring legacy, making it an essential read for anyone interested in the foundations of mathematics, mathematical logic, and the quest for absolute certainty. Keywords: Hilbert's program, proof theory, foundational crisis, classical m
The Asymptotic and Oscillatory Behaviour of Difference and Differential Equations
Doctoral Thesis / Dissertation from the year 2009 in the subject Mathematics - Applied Mathematics, London Metropolitan University, language: English, abstract: This thesis deals with the asymptotic and oscillatory behaviour of the solutions of certain differential and difference equations. It mainly consists of three parts. The first part is to study the asymptotic behaviour of certain differential equations. The second part is to look for oscillatory criteria for certain nonlinear neutral differential equations. And the third part is to establish new criteria for a class of nonlinear neutral difference equations of any order with continuous variable and another type of higher even order nonlinear neutral difference equations to be oscillatory. A functional differential equation is a differential equation involving the values of the unknown functions at present, as well as at past or future time. The word "time" here stands for the independent variable. In the thesis, the concept of a functional differential equation is confined to ordinary differential equations, although it suits partial ones as well. Functional differential equations can be classified into four types according to their deviations: retarded, advanced, neutral and mixed. A neutral equation is one in which derivative of functionals of the past history and the present state are involved, but no future states occur in the equation. The order of a differential equation is the order of the highest derivative of the unknown function. A difference equation is a specific type of recurrence relation, which is an equation that defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. On the other hand, difference equations can be thought of as the discrete analogue of the corresponding differential equations. By analogy with differential equations, difference equations also can be classified into four types: delay, advanced, neutral, and mixed. The or
Graph Algorithms and Applications
The mixture of data in real-life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. This book contains some papers reporting recent achievements regarding graph models, algorithms, and applications to problems in the real world, with some focus on optimization and computational complexity.
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.
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.
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.
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.
Set Function T
Preliminaries.- The Set Function T.- Decomposition Theorems.- T-Closed Sets.- Continuity of T.- Images of T.- Applications.- Questions.- References.- Index.
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.
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.
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.
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.
